Birth weight (BW) predicts many health outcomes, but the relative contributions of genes and environmental factors to BW remain uncertain. Some studies report stronger mother-offspring than father-offspring BW correlations, with attenuated father-offspring BW correlations when the mother is stunted. These findings have been interpreted as evidence that maternal genetic or environmental factors play an important role in determining birth size, with small maternal size constraining paternal genetic contributions to offspring BW. Here we evaluate mother-offspring and father-offspring birth weight (BW) associations and evaluate whether maternal stunting constrains genetic contributions to offspring birth size.Data include BW of offspring  born to female members (n = 382) and spouses of male members (n = 275) of a birth cohort (born 1983–84) in Metropolitan Cebu, Philippines. Regression was used to relate parental and offspring BW adjusting for confounders. Resampling testing was used to evaluate whether false paternity could explain any evidence for excess matrilineal inheritance. In a pooled model adjusting for maternal height and confounders, parental BW was a borderline-significantly stronger predictor of offspring BW in mothers compared to fathers (sex of parent interaction p = 0.068). In separate multivariate models, each kg in mother’s and father’s BW predicted a 271±53 g (p<0.00001) and 132±55 g (p = 0.017) increase in offspring BW, respectively. Resampling statistics suggested that false paternity rates of >25% and likely 50% would be needed to explain these differences. There was no interaction between maternal stature and maternal BW (interaction p = 0.520) or paternal BW (p = 0.545).Each kg change in mother’s BW predicted twice the change in offspring BW as predicted by a change in father’s BW, consistent with an intergenerational maternal effect on offspring BW. Evidence for excess matrilineal BW heritability at all levels of maternal stature points to indirect genetic, mitochondrial, or epigenetic maternal contributions to offspring fetal growth. Individuals with lower birth weights (BW) have heightened risk of mortality in infancy and early childhood in utero. In this model, paternal factors were more important as influences on postnatal growth and final size.Because fetal growth serves as a marker of prenatal conditions that influence an array of later biological functions and health outcomes, there is a need to understand the causes of variation in fetal nutrition, growth and birth outcomes. Estimates of heritability for BW typically range between 0.2 and 0.4 In humans, evidence for a disproportionate maternal contribution to birth outcomes comes from several sources. Studies have compared the strength of father-offspring and mother-offspring BW correlations e.g.  and mostin utero, could override genetic influences on the prenatal nutritional environment experienced by the next generation and be reflected in fetal growth rate and birth size. This idea has gained limited support in some In addition to evidence for stronger intergenerational BW correlations through the matriline, a related hypothesis posits that genetic contributions to BW are constrained in women who experienced early life histories of nutritional stress in utero, and whether the intergenerational BW correlations are reduced among women who were shorter as adults.Here we contribute to the literature on genetic and environmental contributions to BW by reporting the strength of mother-offspring and father-offspring BW associations in a well-characterized birth cohort in Cebu City, the Philippines. As part of this analysis, we run a resampling analysis in an effort to determine the false-paternity rate that would be needed to account for any differences in matrilineal and patrilineal intergenerational correlations in this sample. Finally, we test for maternal constraint on fetal growth rate by evaluating whether the strength of parental-offspring BW correlations is stronger among heavier babies that were less likely growth-restricted Data come from the Cebu Longitudinal Health and Nutrition Survey (CLHNS), a population-based study that originally enrolled 3327 pregnant mothers and has since followed their offspring into adulthood, many of whom are now parents with offspring of their own Offspring BW information was obtained through recall among female birth cohort members and among the current spouses of male cohort members. Each mother was asked to recall, among other factors, the status of each pregnancy , birth date, whether the baby’s weight was weighed and if so the BW, gestational age at parturition, and sex of each of her offspring. Because BW is reduced in twin pregnancies, and twin pregnancies were rare, analyses were limited to singleton liveborn pregnancies. In addition to birth outcome characteristics, we obtained information on characteristics of each pregnancy, including whether the woman worked while pregnant and whether she obtained prenatal care. Current height and weight were obtained using standard anthropometric techniques Of the 1235 singleton liveborns for which all maternal and birth control variables were available, the baby was not weighed at 134 of these births (10.9%) and these pregnancies were therefore excluded from analysis. We compared women whose babies were weighed at birth to those whose baby was not. Women who did not have their baby weighed at birth came from lower income households , they were slightly less likely to receive prenatal care , and they were also less likely to report having worked during pregnancy . However, women whose baby was not weighed had a similar adult stature to women whose baby was weighed at birth .All analyses were performed with Stata version 10 , except the paternal uncertainty analyses which were conducted in R . In a model predicting birth outcomes in female cohort members and spouses combined, there was a borderline sex of parent by parental BW interaction (p = 0.068), showing that maternal and paternal BW relate to offspring BW with (borderline) different slopes. All subsequent models were stratified on gender of the parent for whom BW was measured.While we can say with high certainty that the mothers in this study are the biological mothers of the children, paternity is less certain. False paternity would tend to cause an attenuation of father-offspring BW associations that could imitate a maternal effect in utero, the hypothesis of maternal constraint leads to the expectation that genetic contributions to BW will be stronger in larger newborns. Because prior work on maternal constraint in humans and other non-human primates reported evidence for an effect specific to the matriline We next tested for evidence of maternal constraint in the sample using several strategies. First, following Veena et al Finally, we tested whether maternal and paternal BW were stronger predictors of offspring BW when the mother was taller ; Model 5In this sample of Filipino young adults, we find evidence for stronger intergenerational BW correlations through the matriline than through the patriline, consistent with disproportionate maternal contributions to offspring BW. However, contrary to the concept of maternal constraint, there was no evidence that either patrilineal or matrilineal intergenerational BW correlations were stronger among taller women. Thus, there was no evidence that a woman’s history of nutritional stress, as reflected in her adult stature, constrain hereditary contributions to birth weight in this sample.The finding of stronger maternal-offspring than paternal-offspring BW correlations has been described in most prior human studies. In a study of more than 67,000 Norwegian births, the correlation between mothers’ and offspring BW (r = 0.226) was stronger than that of the paternal BW-offspring BW correlation (r = 0.126) Although the pattern that we find is generally consistent with most past studies, little is currently known about the causes of the difference in strength of mother-offspring versus father-offspring BW correlations. Higher false paternity rates will tend to decrease the correlation between putative father and offspring for all traits with a genetic component in utero also tends to influence her child in utero. While these explanations are difficult to disentangle, here we consider some of the prime candidates in hopes of guiding future studies aimed at clarifying underlying mechanisms.Other possible explanations for this pattern include sex-linked genetic effects, indirect genetic effects, epigenetic effects, and shared environmental or cultural effects. Although varying widely in mechanism, these explanations all share an intergenerational character. They all require that some environmental, physiological, or genetic factor which influences the mother Fathers do not pass on their X chromosomes to sons but only to daughters, which results in a distinctive inheritance pattern for X chromosome-linked traits which in theory could in result discrepancies in patrilineal and matrilineal inheritance. However, consistent with previous large studies Macaca nemestrina) suggested that mitochondrial inheritance could account for 9% of the variance in BW Another well-established sex-linked genetic effect which might explain excess matrilineal inheritance, mitochondrial inheritance, cannot be ruled out so readily. Mitochondria are present in the cytoplasm of cells, and contain their own 16,569 base-pair circular genome Indirect genetic effects are another plausible contributor to excess matrilineal BW heritability. In contrast to mitochondrial effects or non-genetic maternal effects, indirect genetic effects occur because the presence of alleles in the offspring predicts the alleles of the mother and some of these alleles alter maternal physiology or metabolism, thereby influencing offspring phenotypes such as BW. As one concrete example, maternal alleles associated with type 2 diabetes influence the BW of offspring in part by influencing maternal fasting glucose and insulin levels during pregnancy Environmental or cultural factors might also help explain the excess matrilineal BW heritability. Mothers and grandmothers often provide advice to their daughters and granddaughters about ideal behaviors during pregnancy , which could contribute to similarities in the gestational environments and birth weights of successive generations (shared family effects). Similarly, wealth is transmitted across generation, which could lead to similarities across generations in environmental factors like nutrition and access to health care Finally, there is also increasing evidence that the fetal growth conditions experienced by the mother, as reflected in her own gestational nutrient or hormonal milieu, can lead to durable epigenetic or developmental changes that influence offspring through several possible pathways. This can occur when the mother’s early life experiences influence her own fetal growth and also have durable effects on her adult physiology and metabolism that modify fetal growth rate of her offspring Regardless of the specific causes of the differences in matrilineal and patrilineal BW inheritance observed here, our findings, and those of previous investigators, clearly show that maternal contributions are more important than paternal contributions in determining offspring BW. Because prenatal nutrition and growth rate predict an expanding array of long-term functional and health outcomes Some limitations of this study warrant consideration. Most notably, offspring BW information was recalled by women during interviews, rather than being prospectively collected after each pregnancy. In Cebu, most women have birth records, and analyses were limited to births that were weighed. Although this will minimize recall error, female cohort members were asked about their reproductive histories during several survey rounds, while the spouses of male participants were asked only once in 2009. Thus, it is possible that female participants were better able to recall, or have records of, their offspring’s BW, which could reduce measurement error among the offspring of female participants. However, we found that maternal socioeconomic and pregnancy characteristics were as strong or often stronger as predictors of offspring BW among spouses of male participants, suggesting that the apparently weaker relationship between paternal BW and offspring BW was not simply an artifact of poor measurement reliability of BW among offspring of male participants.In conclusion, mother’s BW is a stronger predictor of offspring BW than is the father’s BW in this population, independent of the mother’s adult size. This suggests that some combination of maternal indirect genetic, environmental or epigenetic factors influence the intrauterine environment or fetal growth above and beyond any direct genetic effects. Although this contributes to an excess of BW heritability through the matriline, we found no evidence that the slope of intergenerational BW relationships were steeper or stronger in heavier offspring or among newborns born to taller women, as would be predicted if maternal nutritional stress or stunting constrained genetic contributions to birth size. These findings suggest that maternal effects on fetal growth are present across the full range of maternal stature in this population. By extension, they suggest that maternal environmental, epigenetic or indirect genetic factors influence the diverse array of offspring phenotypes that are downstream of fetal nutrition and growth.File S1Non-paternity analysis.(DOC)Click here for additional data file.


Materials with strong spin-orbit coupling, which competes with other particle-particle interactions and external perturbations, offer a promising route to explore novel phases of quantum matter. Using LDA + DMFT we reveal the complex interplay between local, multi-orbital Coulomb and spin-orbit interaction in elemental bismuth. Our theory quantifies the role played by collective dynamical fluctuations in the spin-orbit Kondo state. The correlated electronic structure we derive is promising in the sense that it leads to results that might explain why moderate magnetic fields can generate Dirac valleys and directional-selective magnetoresistance responses within spin-orbit Kondo metals. EF. Beyond the inherent importance of exploring complex phases of quantum matter5T)Elemental bismuth, a material with a strong spin-orbit (SO) interaction, plays a key role in solid-state physics235678911P-band semimetals like bulk bismuth and graphite undergo a metal-insulator-like transition upon exposure to modest magnetic fieldsT2 dependence works quite well down to 4 KT study showed significant deviation from canonical FL systems, where the T2 behaviour changes smoothly into a T5-like form at very low temperaturesT behavior. Complex low-energy physics in bismuth is also unveiled by optical measurements, showing large changes in plasma frequency and anomalous midinfrared features23During the 20th century, transport properties of bismuth were extensively studied12p-band topological insulators, we have recently shown that Kondo- and Mott-like features are well accounted for by the diagrammatic multi-orbital (MO) iterated-perturbation-theory27Ueff  ≡ U/WLDA ≈ 1, U and WLDA are, respectively, the on-site Coulomb repulsion and the LDA band width) good semiquantitative accord with experimental data can be obtained. MO-Hubbard plus SO interaction qualitatively account for dynamical signatures of bulk correlation effects in photoemission (PES)611Deviations from FL-like behaviour61118p31323334sp, s-carriers) is appreciable compared to the electron-electron interactions, as distinct from d-band systems, where the d electrons reside in much narrower bands (hence the effective U/WLDA is sizable). However, we recall here that in canonical s metals like elemental lithium evidences for correlated electron physics have been reported by Stutz et al.97Li3p or s bands is undoubtedly an issue of great contemporary interest. In light of the discussion above, we study how an orbital-selective interplay between appreciable p-band itinerance and on-site Coulomb repulsion, U, plays a central role in this unique spin-orbit Kondo state of elemental bismuth.The possibility of correlated electron physics in purely A7, α-arsenic type structure (1EF), see 41EF. Elemental bismuth has a formal +3 oxidation state, which implies an equal number of electrons and holes in the p sector. As pointed out, all electronic 6p states acquire some itinerance, providing valence and conduction band states in all active 6p- orbitals. The situation encountered here with three half-filled bands provides the underlying microscopic one-band seeds of a quantum correlated scenario in elemental bismuth.Bismuth crystallises in the tructure . In the a = x, y, z labels the diagonalised 6p-bands. In light of the sizable correlation effects within the Bi-channel of bulk Bi2Se3 and Bi2Te2Se topological insulators27U′ ≡ U − 2JH and U(U′) is the intra- (inter-) orbital Coulomb repulsion. JH and V are, respectively, the Hund’s rule and the local SO coupling. Within our formulation, the SO interaction acts as a transverse magnetic-fieldpa spin states of bismuth. The DMFT self-energy, Σa(ω), requires a solution of the MO quantum impurity problem self-consistently embedded in an effective mediumWithin LDA, the one-electron part of the many-body Hamiltonian for bismuth is U promotes a gradual reduction of the bulk band gap size and coherent Kondo clouds are created near EF in Bi-chalcogenide topological insulators27U the energy gap is suppressed by dynamic transfer of spectral weight characteristic of correlated electron systems502Y2X , X = Se) topological materials. In JH = 0.5 eV27nt = 3.0, showing that a quantum correlated scenarioU, U′ and JH leads to spectral weight redistribution over large energy scales and the formation of an electronic structure similar to topological Kondo systems27spin-orbit Kondo state is characterised by the presence of sharp in-gap states near the Fermi energy, EF(= ω = 0). As a first testing ground to our proposal, in Electron-electron interactions may induce topologically nontrivial electronic phases that can change the nature of single-particle excitation of topological insulators48A7 element, we show in the main panel of T dependence of dc resistivity computed using the orbital resolved, LDA + DMFT spectral functions, x, y, z) 6p-bands, f(ω) is the Fermi function. As in ref. k-dependence of electron’s velocity, vk,a. In this situation, following Saso et al.54vk,a by a single average carrier velocity (v) for all orbitals. In fact, Saso et al. and Baldassare et al.σac(ω) for Kondo insulators (FeSi and YbB12) as well as for V2O3, supporting our approximation in σdc(T) above. The observed features in resistivity ρdc(T) ≡ 1/σdc(T) originate from SO and Zeeman-field induced spectral changes: Showing how this provides a compelling description of extant experimental data is our focus here.To elucidate the crucial role played by local quantum correlations on electric transport in this V = 1.05 eV we obtain a quasilinear T-dependence above 30 K which is close to that observed in bulk crystalsT. Interestingly, this drop in resistivity at low-T is enhanced with increasing the SO interaction V, see bottom-right panel of V ≤ 1.25 eV. In our theory this robust phenomenon is the fingerprint of SO-induced local quantum fluctuationsp-band semimetals like bismuth and graphiteU = 10 eV supports our proposal of non negligible electron-electron interactions in bismuth. In 0.9Sb0.10.9Sb0.1 system might exhibit some sort of lattice disorder effects induced by antimony. While PES experiment resolves a low-energy bump which was interpreted as gapless surface states coexisting with an insulating bulkpz DOS unveil a quasiparticle peak structure near EF, which is consistent with observation of out-of-plane surface states in (AR)PES6pz orbital symmetry in surface-like states would place our theory in a solid ground.The dc resistivity in μB is the Bohr magneton, g is the Landé factor, and Ba is the external (Zeeman) magnetic field applied along the a directionha, keeping the total band filling (nt = 3) fixed to simulate the electronic changes upon Zeeman field splitting. As seen in ha drives appreciable SWT, producing drastic orbital-selective renormalisations of the one-particle spectral functions: The out-of-plane pz band is most severely affected. As expected, ha shifts the relative positions of the spin polarised bands at which the magnetism changes. The resulting magnetisation can be directly calculated from ma = 〈na↑〉 − 〈na↓〉, with the particle’s number 〈naσ〉 being computed using orbital and spin resolved spectral functions. According to our results a trial field applied along the hexagonal plane, i.e hx,y = h  gives negligibly small magnetisation values, mx,y ≈ 0.01. This is an indication of reduced magnetic moments in the frustrated hexagonal plane. Interestingly, in this regime the in-plane Zeeman field drives the system towards to a Kondo insulating state with emergence of a narrow semiconducting band gap in the spin resolved spectral functions. Our results are thus consistent with a Dirac valley scenario in bulk bismuth12V = 1.25 eV compared to V = 1.05 eV can be regarded as the manifestation of SO induced weak antilocalisation effectspz spectral functions. Here, we obtain mz = 0.14 which arises from the formation of local moments in the majority (spin-↑) channel. As seen in the right panels of pz-band is pushed towards to a Mott insulating state with appearance of a lower Hubbard band , the minority (↓) channel undergoes to a Kondo-like metallic state characterised by a broad quasiparticle peak at EF. This unexpected field-induced phase transition is apparently consistent with recent DMFT studyWe now turn to the interplay between local transverse-field fluctuations induced by SO coupling and intra-orbital Zeeman level splittings upon application of an external magnetic field in bismuth. To proceed, we consider the orbital-dependent on-site energy term, p-band semimetals is mandatory for designing novel MR materials. An affirmative theoretical answer to the MR effect in elemental bismuth is shown in ρdc(T)] computed using LDA + DMFT spectral functions within the Kubo formalismha: Showing how this provides a compelling explanation for the MR effect for in-plane  and out-of-plane (hz) magnetic fields is our focus here. Various interesting features immediately stand out in T → 0 the resistivity curve for a trial field μBT-dependence, in accordance with the insulating behaviour at small fields seen in experimentha the dc resistivity in ρdc(T) increases as T → 0 at finite in-plane field, hx,y, which is consistent with a semiconducting like behaviour due to field-induced Dirac valley spectrumT metallicity accompanying an insulator-to-metal crossover. The interplay between local spin fluctuations27T. This is our mechanism for the experimentally observed reduction of ρdc(T) at low T in bismuth, where a crossover from a metal to an insulating-like behaviour above T = 10 K is obtained, in good semiquantitative agreement with extant data11p-band semimetal.An understanding of the correlated nature of p electrons differs because of various competing local quantum fluctuations. For fields applied parallel to the hexagonal plane the emergent Dirac valley reflects the competition between Zeeman field splitting and screening of local moments. On the other hand, for fields perpendicular to the basal plane spin-selective metallic and insulating states similar to that of correlated half-metalsp-band semimetals1864In conclusion, using LDA + DMFT for a multi-band model, we resolve the nature of the metallic regime in bismuth. Good semiquantitative accord with key spectral6The local-density-approximation plus dynamical-mean-field-theory (LDA + DMFT) by construction takes into consideration the most relevant multi-orbital correlation effects and all-electron degrees of freedom. It is an ideal starting point towards the description of Coulomb-driven metal-to-insulator transitions, Fermi and non-Fermi liquid metallic states and in general grounds the role played by dynamical correlations in idealised many-particle models as well as in real multi-orbital systemsp-band electronic states in elemental bismuth, we employ our state-of-the-art implementation of LDA + DMFTk-points. The radii of the atomic spheres were chosen as r = 3.35 a.u. in order to minimise their overlap. To incorporate the effects of electronic correlations in this p-band semimetal, we use the multi-orbital iterated-perturbation-theory (MO-IPT) as an impurity solver of the many-particle problem in DMFT, as described in detail in refs. In order to prove the orbital-selective nature of the U = 10 eV was necessary for a good semi-quantitative agreement with experiments within LDA + DMFT, see U larger than typical values for transition metals are the consequence of orbital hybridisation and covalent bonds, which localise electrons between atoms35U ≤ 12), orbital occupancy yields nx,y = nz = 1.0. Biasing nx,y, LDA + U calculations (U ≈ 10 eV) converge towards the ground state with nx,y = 1.05, nz = 0.9 in good agreement with LDA + DMFT.A Hubbard How to cite this article: Craco, L. and Leoni, S. Magnetoresistance in the Spin-Orbit Kondo State of Elemental Bismuth. Sci. Rep.5, 13772; doi: 10.1038/srep13772 (2015).


Here, we use the density functional dynamical mean-field theory (DFDMFT) scheme to comprehensively explain why tetragonal FeS shows both semiconducting and metallic responses in contrast to tetragonal FeSe which is a pseudogaped metal above the superconducting transition temperature. Within local-density-approximation plus dynamical mean-field theory (LDA+DMFT) we characterize its paramagnetic insulating and metallic phases, showing the proximity of mackinawite to selective Mott localization. We report the coexistence of pseudogaped and anisotropic Dirac-like electronic dispersion at the border of the Mott transition. These findings announce a new understanding of many-particle physics in quantum materials with coexisting Dirac-fermions and pseudogaped electronic states at low energies. Based on our results we propose that in electron-doped FeS substantial changes would be seen when the metallic regime was tuned towards an electronic state that hosts unconventional superconductivity.Transport properties of tetragonal iron monosulfide, mackinawite, show a range of complex features. Semiconductive behavior and proximity to metallic states with nodal superconductivity mark this  On the other hand, iron-based superconductors are materials in which the electronic states near EF are derived from Fe-3d orbitals. Given the fact that the spin-orbit interaction on iron is rather weak compared to Bi-based p-band TIs might look as if these two systems belonged to a different material class. However, a perusal of extant experimental567891012139Over the past few years iron-based superconductors122As2 was the first material to reveal an anisotropic Dirac point near EF2A2 until SDW ordered phase vanishes73 substrate where nontrivial (Z2) topology can be tuned through band inversion at M point of the Brillouin zoneIn the recent history of Dirac-fermion physics in iron-based superconductors0.88Tc ≈ 5 K) in tetrahedral FeS single crystals were recently reported by different groups272831282731μSR dataμSR measurements indicate coexistence of low-moment magnetism and bulk superconductivityTetragonal FeS is found naturally as the mineral mackinawite, which was identified as the initial product from corrosion of metallic iron on sulphur202425272425d bandwidth in PES spectra is 25-to-30% narrower than that predicted by first-principles band-structure calculations. The one-particle density-of-states (DOS) was shown to be accompanied by an intense tail at high binding energies, consistent with the correlated fingerprints found in iron-superconductorsd band narrowing at low energies and the satellite features at high-binding energies can be explainedThe localized nature of hexagonal FeS (troilite) and its correlated electronic structure has been investigated by photoemission (PES) and inverse-photoemission spectroscopy experimentsab initio density functional calculations for FeX  demonstrate that the chalcogen p states lie well below EF and are weakly hybridized with Fe 3d states2+ (with d6 electronic configuration) layers with almost direct Fe-Fe hopping. In previous work we undertook systematic local density approximation plus dynamical-mean-field-theory (LDA+DMFT)40Currently, the theoretical understanding of tetragonal FeS is restricted to one-electron band structure calculations41A proper microscopic description of localization-delocalization transition26P4/nmm) structure  is seen in the orbital-resolved DOS of FeS. While the x2 − y2 and xz, yz orbitals show less pronounced effects due to smaller ionic radii of sulphur compared to selenium, the 3z2 − r2 and the xy channels display appreciable one-particle band narrowing and small changes in the bonding/antibonding splitting of the electronic states close to EF, characteristic of the tetragonal unit cell. As seen in the inset (right-lower panel) of xy orbital shows tendency towards the formation of a V-shaped electronic spectrum, which is the one-particle seed towards a reconstructed Dirac-like linear band dispersion in tetragonal FeS, as shown below. As comprehesivelly described in this work, due to one-particle band narrowing correlations effects can increase dramatically in FeS compared to FeSe, leading to an orbital blocking mechanism and appearance of marginal Dirac fermions in the d-band electronic states of FeS.Within the tetragonal  denotes the diagonalized 3d orbitals of FeS and εa(k) is the one-electron band dispersion, which encodes details of the actual one-electron (LDA) band structure. We evaluated the many-particle Green’s functions of the Hamiltonian above within LDA+DMFTwhere U = 4.0 eV (and JH = 0.7 eV)40r2 − z2 orbital shows strong correlation effects with pronounced charge gap and Hubbard bands, while the x2 − y2 orbital has less tendency towards local moment formation (LHB). In this figure we also display our previous LDA+DMFT results for FeSe superconductorU = 3.6 eV and that of stoichiometric d6 FeSe. Clearly, the two spectral functions show similar behavior at low energies, indicating that FeS is able to host an unconventional superconducting state at low T if its electronic structure is properly tuned via suitable sample preparation conditions2728U in metallic FeS is at least 0.4 eV smaller than that of tetragonal FeSe as in U/W), driving the electronic states of stoichiometric FeS close to that of tetragonal FeSe superconductor.We now discuss our LDA+DMFT results. In z2 − r2, xz, yz) and quasi-linear  spectral functions near EF can be tuned in the bulk. Also, the Dirac cones in tetragonal FeS appears to be anisotropic, consistent with observations for BaFe2As2EF. This result can be taken as an evidence that the interplay between band narrowing and Coulomb perturbationsz2 − r2, xz, yz) states coexisting with Dirac-like fermions at the x2 − y2, xy orbitals. Thus, within the hidden Dirac-liquid phase the reconstructed Fermi surface is expected to be composed of two distinct components, and future angle-resolved photoemission (ARPES) experiments could verify this aspect.To characterize the hidden Dirac-liquid regimeV-shaped liner dispersions with Dirac-cone like carriers4EF and the contribution of the psedogaped bands must be suppressed to extract the unique carrier transport intrinsic to Dirac cones6y1+Tex1−Sex single crystalsUc < 4.0 eV. Electron-electron interactions renormalizes the LDA+DMFT results in two steps. First, the MO self-energy [Σa(ω)] renormalizes the relative band positions depending upon their orbital occupations. The frequency-dependent self-energy . Below the Mott transition only the degenerated xz, yz orbitals show characteristic FL like features, while the more correlated orbitals display deviations from the −ω2 FL form at small ω, being consistent instead with (sub-) linear ω-dependence of marginal Fermi liquidsmarginal Dirac-liquid.Our main result in ergy see  causes SV-shaped ω-dependence in ω = 0. This implies that, close to the Mott insulator-metal transition, we have a renormalized (by DMFT) picture where effectively Dirac-like fermions co-exist with incoherent electronic states from the remaining  bands. In our LDA+DMFT, the FL quasiparticle coherence would be destroyed near the Mott transition in the disorder-free case of FeS, as evidenced by the fact that EF while ω dependence could result in experiments: recall that our DMFT self-energies are not inconsistent with a weak power-law (in ω) dependence at low energy. In this case, V-shaped spectral functions were also obtained within LDA+DMFT for tetragonal FeSe superconductorAs shown in U, U′ increases a subset of d-orbitals gets selectively Mott localized. The metallic phase is then the orbital-selective metal found in various contexts59EF) is pinned to the renormalized orbital energy of the localized orbital(s). This behavior is understood from the mapping of the corresponding impurity model to that of the “X-ray edge”, where the orthogonality catastrophe destroys FL coherence. The spectral functions then exhibit asymmetric continuum at low energy, instead of symmetric Abrikosov-Suhl Kondo resonance features at low energies, and the metallic phase is non-Fermi liquid. As shown here, the frequency-dependence of the self-energy imaginary parts is important in stabilizing the marginal Dirac liquid state, and consideration of the instability of such an orbital-selective state to a superconducting (SC) state should lead to a strongly frequency-dependent superconducting gap function.  As expected, in a correlated electron picture, the physical response functions in the normal state are controlled by both, intrinsic orbital degrees of freedom as well as the ω dependent damping originating in the incoherent normal state. Future observation of features such as the presence or absence of an incoherent low-energy peak in X-ray emission spectroscopy (XES)What is the microscopic origin of the orbital-selective features found in the LDA+DMFT solution of tetragonal FeS system near the Mott transition? On general grounds, as d bands are usually shifted relative to each other because of the action of structural induced changes in the crystal-field splittings: the six d electrons found in iron-based superconducting materials are distributed among all d orbitals and, in the case of a system with sizable MO interactions, this might induce orbital polarization and SWT. In this situation, MO correlations cause various intimately linked changes: the static MO Hartree shifts, which depends upon the occupations of each orbital as well as on the inter-orbital correlations [U′ and JH] renormalizes the on-site energies of each orbital in different ways. In particular, it causes inter-orbital charge transfer between the different d-orbitals, self-consistently, modifying their energies and occupationsxy, xz, yz orbitals in LDA will be lowered in energy while the 3z2 − r2, x2 − y2 will be pushed further up by the MO-Hartree shifts. The amount of this electronic modification is normally determined by the orbital occupation(s) and by the values of U, U′, JH relative to their respective LDA band width(s), and to the bare crystal-field splittings. As common to correlated electron systems, the dynamical correlations associated with U, U′, JH results in a large-scale dynamical SWT. Here, small changes in the bare (LDA) band structure induced by MO electronic correlations  are sensitive functions of orbital orientation in the real crystal structure. Moreover, the 3U = 3.6 eV and that of FeSe (see T) dependence of the dc resistivity computed using the orbital resolved LDA+DMFT spectral functions, Aa. Within the Kubo formalismdc-conductivity can be expressed asFinally, to elucidate close similarities between the metallic state found for FeS at FeSe see  as well d-bands, V is the unit cell volume, and f(ω) is the Fermi function.where U = 3.6 eV and JH = 0.7 eV) derived using the LDA+DMFT spectral functions. In the same figure we also display our theory-experiment comparison of the normalized resistivity n > 6.0) shows the S-like shape characteristic of a pseudogaped metal similar to FeSe superconductorT, the FL-like T2 behavior is not seen in n = 6.0, ρdc(T) becomes more metallic-like at low temperatures, smoothly suppressing the S-like form below n = 6.1. At low T, T2 form is also not observed upon partially electron doping the parent compound. The underlying reason for this behavior is that at small U, JH, the moderately correlated FL behavior cannot be destabilized by a small JH. For large U and sizable JH, however, the correlated-Landau Fermi-liquid scale, already driven to small values by sizable U, can be readily destroyed by U′. As seen, with increasing total electron concentration n > 6.0 of the iron d shell, ρdc(T) becomes more bad-metallicX  systems, showing similar metallic behavior in both cases . In order to highlight the possibility of a correlation induced proximity to an unconventional superconducting state in undoped FeS, in this figure we also display the experimental resistivity data of tetragonal FeSe superconductorn = 5.6 and U = 4.0 eV, with decreasing the on-site Coulomb interaction ρdc(T) of metallic FeS becomes more incoherent-like below T-dependence resembles that of the FeSe system.We now describe our electric transport results for metallic FeS. In n > 6.0) metallic FeS parent compound. An intriguing observation is that a strong orbital reconstruction occurs at small electron doping. Hence, based on our previous LDA+DMFT results for iron-chalcogenide systemsEF are visible for n = 6.0 and n = 6.1. Also interesting is low-energy electronic reconstruction near the Fermi energy with further increasing the averaged occupation number of the iron d shell, where a more quasicoherent normal state behavior sets in for electron-doping above n = 6.2. We propose that future photoemission and X-ray absorption spectroscopy results, which probe one-electron subtraction and addition spectra, can be directly compared with these: In particular, a broad incoherent peak below −0.4 eV should be seen in both pure and doped cases. Additionally, drastic modification of the LDA+DMFT spectra at high binding energies with n is visible, notwithstanding large-scale dynamical spectral weight transfer common in all cases. These are stringent tests for our proposal, and experimental verification should place it on solid ground.In To summarize, we have used LDA+DMFT for a five-band Hubbard model to derive a correlation-induced orbital reconstruction in layered iron-chalcogenides. In particular, considering FeS as a suitable template, we have analyzed its paramagnetic insulating and metallic behavior, unraveling it as an effect of multi-orbital dynamical correlations. Also interesting is the orbital-selective electronic behavior obtained at the border of the Mott metal-insulator transition, where pseudogaped and Dirac fermions coexist at low energies. This coexistence arrises from charge-carrier scatterings due to interplay between multiband itinerance and electron-electron interactions, and this could be tested by a combination of spectral and transport measurements on metallic samples. Such studies are called for, and should confirm or refute our proposal of a marginal Dirac liquid for tetragonal FeS, which we ascribe to a lattice orthogonality catastrophed transition-metal chalcogenide, we use the multi-orbital iterated-perturbation-theory (MO-IPT) as an impurity solver of the many-particle problem in DMFT, as described in detail in refs To reveil insulating and metalic phases probed in electric transport experiments as well as the coexistence of pseudogaped and anisotropic Dirac-like electronic dispersion at the border of the Mott transition in tetragonal FeS, we employ the local-density-approximation plus dynamical-mean-field-theory (LDA+DMFT) which by construction takes into consideration the most relevant multi-orbital correlation effects and all-electron degrees of freedom. The state-of-the-art LDA+DMFTHow to cite this article: Craco, L. and Leoni, S. Selective orbital reconstruction in tetragonal FeS: A density functional dynamical mean-field theory study. Sci. Rep.7, 46439; doi: 10.1038/srep46439 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Finding of superconductivity in solid O2 on the border of an insulator-metal transition at high pressures close to 96 GPa is thus truly remarkable. Neither the insulator-metal transition nor superconductivity are understood satisfactorily. Here, we undertake a first step in this direction by focussing on the pressure-driven insulator-metal transition using a combination of first-principles density-functional and many-body calculations. We report a striking result: the finding of an orbital-selective Mott transition in a pure p-band elemental system. We apply our theory to understand extant structural and transport data across the transition, and make a specific two-fluid prediction that is open to future test. Based thereupon, we propose a novel scenario where soft multiband modes built from microscopically coexisting itinerant and localized electronic states are natural candidates for the pairing glue in pressurized O2.Unusual metallic states involving breakdown of the standard Fermi-liquid picture of long-lived quasiparticles in well-defined band states emerge at low temperatures near correlation-driven Mott transitions. Prominent examples are ill-understood metallic states in  Particularly interesting examples of intriguing physics in solidized molecular phases of gases are dense hydrogen3 and solid oxygen5, as well as the most recent report of very high-Tc superconductivity in solid H2S under very high pressure6. H2 is predicted to metallize under high pressure, while solid O2 even shows a superconducting phase (Tc = 0.6 K) at the border of a pressure-driven transition from a non-magnetic insulator to paramagnetic metal, joining the long list of materials exhibiting superconductivity proximate to metal-insulator transitions.The unique properties of high-pressure induced solid phases of molecular gases continue to evince keen and enduring interest in condensed matter physics. Beginning with early ideas of Mottα, δ, ε and ζ phases7. At lower pressure, the antiferromagnetically ordered α phase transforms into another antiferromagnetically ordered δ phase at 5.4 GPa, followed by a non-magnetic ε phase at 8 GPa. Higher pressure, 8, followed by emergence of superconductivity below 9. This astounding behavior in a molecular system, reminiscent of strongly correlated, doped Mott insulators in d-band oxides like cuprates, presents a significant challenge for theory. The high-P ε–ζ phase transition is also accompanied by significant volume reduction10, with a contraction of about 10% of the lattice parameter along the b direction. The ε phase retains the layered nature of the lower pressure phases4, and the monoclinic (C2/m) structure11 as shown in Fig. Pressurized molecular oxygen forms various low-temperature solid phases under pressure, labelled mentclass2pt{minimα–β transition at moderate T is dominantly magnetic has been established in a series of careful studies14. Indeed, early work of da Silva and Falicov15 already explained the measured heat of formation at the α–β transition in terms of the entropy difference computed from cluster analysis of a multi-orbital Hubbard model . Observation of very different magnetic orders in the α, β phases, correlation between magnetic and structural changes along with ferromagnetic coupling between the off-plane near neighbors in the δ phase are reminiscent of those found in classic multi-band systems like V2O316, taken together with the above, favor a multi-orbital description. Additional evidence for multi-orbital effects is provided by the anisotropic and partially discontinuous pressure-induced changes in the lattice parameters in the different phases17. In such a scenario, increasing pressure is expected, in the simplest approximation, to decrease lattice spacings and increase the carrier itinerance. The result would then be to suppress antiferromagnetic order along with insulating behavior, and to induce metalization. In solid O2, antiferromagnetic order is destroyed well before metalization occurs18, and so, within the p4 configuration of oxygen, the insulator-metal transition across the ε–ζ transition must be regarded as a Mott metal-insulator transition. This suggests that on the one extreme, a Heisenberg model description is only valid in the insulating α, β, δ phases, and that a more general multi-orbital Hubbard model must be used, at least for the ε phase. At the other extreme, one-electron band structure calculations for the antiferromagnetically ordered phases do provide qualitatively correct ground states19. In addition, electronic structure calculation based on generalized gradient approximation (GGA) shows that the nonmagnetic insulating state is energetically favored at pressures corresponding to the ε-phase21. However, by construction, ab initio density-funtional calculations have intrinsic difficulties in describing non-magnetic insulating phases, and in particular the ε phase23, for reasons described in detail in ref. That the driving force for the e.g., by holes, creates two available states at the Fermi energy. This is at the heart of spectral weight transfer, a phenomenon ubiquitous to Mott, as opposed to band, insulators. In both cases, electron hopping might still be prevented by inter-orbital Coulomb interactions in a multiband system. The resulting metallic state upon doping can vary from a Fermi liquid at weak coupling to an exotic orbital-selective, non-Fermi liquid metal for stronger electron-electron interactions, as doping and temperature25 are varied. This fundamental difference between band and multi-orbital Mott-Hubbard insulators is of basic and practical interest. Below we show that sizable multiband electronic interactions are the clue to the insulating state of the ε-phase of solid oxygen and its evolution to a non-Fermi liquid metallic state at high pressures.Before presenting our local-density-approximation plus dynamical-mean-field (LDA + DMFT) results, we point out essential differences between band and Mott insulators. In conventional semiconductors (or band insulators) all bands below the Fermi energy are filled and, therefore, inert. Removing an electron leads to an empty state which can be thought of as a hole moving freely through the solid. The same is true for an added electron, which occupies the first empty band. In a multi-orbital Mott-Hubbard insulator, the insulating state arises because electron hopping from one site to another is inhibited by intra- and inter-orbital Coulomb repulsions. In these systems, when the band filling is slightly reduced from its commensurate value, a small number of unoccupied states are created; similarly adding electrons creates locally doubly occupied electronic states. The crucial difference in this case is that since the doped carriers can have either spin  with equal probability, doping a Mott insulator, p29 or s30 band systems is very intriguing, since the naive expectation dictates that the itinerance  is appreciable compared to the electron-electron interactions, as distinct from d-band systems, where the d electrons reside in much narrower bands 31. Thus, understanding Mottness (or the proximity to a Mott-Hubbard insulating state) in materials with active p or s bands is undoubtedly an issue of great contemporary interest32. In light of the discussion above, we study how an orbital-selective interplay between appreciable p-band itinerance and sizable, on-site Coulomb repulsion, U, plays a central role in this unique Mott transition in solid O2.Possibility of Mott-Hubbard physics in purely 2, we start with the C2/m structure 35 scheme in the atomic sphere approximation36. The corresponding LDA density-of-states of the three (symmetry) inequivalent atoms11 is shown in Fig. pz, i.e., the σ-orbital37 in the energy level diagram of O2. However, due to inter-molecular orbital overlap in the monoclinic structure, the pz states acquire some itinerance, explaining the small amount of pz states found at the Fermi energy. As seen in Fig. π-bands cross the Fermi energy, providing a metallic state within LDA.To quantify the correlated electronic structure of solid Oure Fig.  with lata = x, y, z label the three diagonalized p orbitals and the Δa are on-site orbital energies in the real structure of solid O2. In light of antiferromagnetic insulator15 phases and the non-magnetic Mott transition, local multi-orbtial interactions are mandatory to understand O2. These constitute the interaction terms JH is the Hund’s rule term. Following da Silva and Falicov15, we use U = 11.6 eV and JH = 0.45 eV, along with the LDA bands of the three inequivalent oxygen atoms described above. In this work, the correlated multi-orbital problem of solid O2 encoded in H = H0 + Hint is treated within the state-of-the-art local-density-approximation plus dynamical-mean-field-theory (LDA + DMFT) scheme31. The DMFT self-energy, 31. We use the multi-orbital iterated-perturbation-theory (MO-IPT) as an impurity solver for DMFT38: This analytic solver has a proven record of successes in describing finite temperature Mott transitions39 as well as unconventional behavior in correlated p-band systems42.Within LDA, the one-electron part of the many-body Hamiltonian for solid oxygen is now p-bands in different ways. Generically, one expects partial (Mott) localization of a subset of bands, leading to orbitally selective Mott transitions, and bad metallic states43. Within LDA + DMFT, this orbital-selective mechanism involves two renormalizations: static  renormalization shifts the p-bands relative to each other by amounts depending upon their bare on-site orbital energies (Δa) and occupations (na). In addition, dynamical effects of U, 43. The large, anisotropic changes in dynamical spectral weight transfer in response to small changes in bare one-particle (LDA) parameters 39 are known to drive the orbital-selective Mott transition in real multi-orbital systems. As we show below, precisely such an orbital-selective Mott transition, accompanied by an incoherent metallic phase in solid O2, occurs at very high pressures.With orbital orientation-induced anisotropic LDA one-particle energies and hoppings, multi-orbital correlations renormalize various U, U′, JH as obtained in ref. ε phase is a Mott insulator, as shown in Fig. px band compared to the other two. Large spectral weight transfer, characteristic of dynamical local correlations, is explicitly manifested in the qualitative difference between LDA and LDA + DMFT spectra. At first sight, derivation of a Mott insulator with U < W in solid O2 seems a bit puzzling. The reason, however, is that, in this multi-orbital system, both U, U′ are appreciable, and the combined effect of both acting in tandem is to (i) reduce the band-width of each band , and (ii) the dominant effect of U′ on a reduced bandwidth is to split the bands via the Mott mechanism. In the actual multi-orbital problem, both effects are simultaneously operative, and reinforce each other.Using δa) and occupations (na) within LDA and LDA + DMFT. Within LDA, we find 44, is an interesting manifestation of correlation-induced orbital rearrangement, and controls structural changes across the Mott transition (see below).From our results in Fig. 2 at high P, and adopt the following strategy to derive this transition. Instead of reverting back to the LDA to use a different LDA density-of-states corresponding to the metallic ζ-phase, we search for an instability of the insulating, ε phase to the paramagnetic-metal by varying δa, found for the Mott insulator above. To proceed, consider the orbital-dependent on-site energy term, x = −Δ, Δy = Δ, to simulate the structural  changes upon pressure. Here, Δa acts like an external field in the orbital sector , sensitively controlling the occupations of each orbital in much the same way as the magnetization of a paramagnet as function of an external magnetic, Zeeman field. However, in order to draw a qualitative interpretation of HΔ in our total model Hamiltonian 2, we recall that the pressure derivative of crystal-field splitting is given by K is the bulk modulus and ξ is a constant value45. This in turn suggests that in the pressure range of interest in this work solid O2 could be in a linear regime as observed in other materials under external pressure conditions47. As for V2O339, YTiO343 and, more recently, for FeS48 we search for the second self-consistent LDA + DMFT solution by solving the multi-orbital DMFT equations for each trial value of Δ keeping U, U′ fixed. As seen in Fig. px and py are most severely affected. At a critical Δc = 0.3 eV, the px density-of-states remains Mott insulating, while the py band undergoes an insulator to bad-metal  transition. Thus, our results imply that the paramagnetic, metallic phase of ζ-oxygen is an orbital-selective incoherent metal without Landau quasiparticles, characterized by a pseudogap at EF in the py, and hence, in the total spectral function, at EF. Our simulations (not shown) indicate that Kondo-like resonance found below EF for Δ = 0.4 eV will cross the Fermi level at extremely high pressures, driving solid O2 into (quasi)coherent Fermi liquid-like metallic state at even higher  pressures. The underlying theoretical reason for this is as follows: At Δc, strong scattering between the effectively (Mott) localized and itinerant components of the matrix DMFT propagators produces an incoherent metal because strong interband scattering indeed operates in a sizably orbitally polarized metallic system. However, at very high pressure (large Δ > Δc), the px band becomes almost fully polarized  localized and itinerant components of the full DMFT matrix propagators. This behavior is intimately linked to orbital-selective Mott-like physics within DMFT50.Our results in Fig. δa across the insulator-metal transition. The features are well understood as follows. In a multiband situation, Δ acts like an external “Zeeman” field43 in the orbital sector. The insulator-metal transition is characterized by a sudden jump in the renormalized δz, and in the px and py populations as a consequence, suggesting that anisotropic structural (and volume) changes will accompany the orbital-selective Mott transtion. Here, we propose that these changes in na control anisotropic changes in lattice parameters (a–c) across the insulator-metal transition: indeed, the changes in a–c are expressible in terms of na as g is the electron-phonon coupling constant, M the ion mass, and vsa is the velocity of sound along a. Changes in γa across the insulator-to-metal transition thus follow those in the na. Though values of vsa and g in the ε phase are unknown, we deduce that the lattice parameter a increases, while b,c descrease across the orbital-selective Mott transition as in Fig. 10 provides further support for our Mottness scenario in solid O2.In Fig. 51. In our theory, the observed features in ρdc(T) originate from changes in the correlated spectral functions with Δ. Showing how this provides a compelling description of the admittedly limited available data is our focus in what follows. In Fig. ρdc(T) for three values of Δ in solid O2, computed using the LDA + DMFT orbital resolved spectral functions . Various interesting features immediately stand out. First, ρdc(T → 0) in the ε phase (Δ = 0) shows semiconducting behavior, in accord with the insulating classification at lower pressures, when Δ < Δc. Secondly, at all T, no Fermi liquid T2-like contribution is detectable in the metallic phase with Δ = 0.4 eV: instead, ρdc(T) is approximately constant up to 10 K. For intermediate pressure , ρdc(T) crosses over from semiconductor-like (at high T) to bad-metallic (at low T) behavior. Remarkably, the detailed T-dependence closely resembles that seen in experiment9, in the normal state up to 2 K  for both values of Δ = 0.2, 0.4 eV is characteristic for carriers scattering off dynamically fluctuating and coupled, short-range spin and charge correlations. On general grounds, we expect this effect to be relevant near a correlation-driven Mott transition. Since an external magnetic field will generically quench spin fluctuations, we predict that destroying the ε Mott insulating state by a magnetic field52 might reveal this behavior. We emphasise that resistivity measurements as a function of pressure over extended T scales is a smoking gun for our proposal, as would be the study of the T-dependence of the dc Hall constant. These can distinguish a band-versus-Mott scenario for the pressure-induced insulator-metal transition: in the band-insulator-to-metal transition, there is no reason why, e.g., ρdc(T) should show the above form, since neither orbital selectivity nor local antiferromagnetic spin fluctuations are operative there. More detailed transport work to corroborate our prediction are thus called for in future.To illustrate the importance of correlation-induced changes in the orbital “Zemman” field Δ under high pressure in our theory, we now discuss our results for the normal state resistivity computed within the Kubo formalismpx sector, this electronic system is inherently unstable to soft two-particle instabilities53. In solid O2 at high pressure, lack of conditions supporting magnetic and charge-density instabilities in the correlated electronic structure near the insulator-metal transition opens the door to superconductivity as the only two-particle instability that can quench this finite normal state entropy. In fact, the situation is quite similar to that considered by Capone et al.54 in the fulleride context, where the pseudogapped, bad metal arose from an unstable (intermediate coupling) fixed point in the impurity problem, corresponding to the Kondo unscreened phase: in our case, precisely the same effect results from selective localization of the px band at the orbital-selective Mott phase. In fact, in the orbital-selective metal, the low-energy physics is selfconsistently controlled by strong scattering between quasi-itinerant py,z and Mott localized px orbital states, implying low-energy singularities in one- and two-particle propagators55. This suggests soft, multi-orbital electronic modes at low energy, which can potentially act as a pair glue. In a way similar to the fulleride case, we then expect that multiband spin-singlet s-wave superconductivity (notice that S = 0), driven by such soft inter-orbital electronic fluctuations in this unstable phase, will cut off the incoherent metal found above, and that the superconducting transition temperature Tc will rise to values larger than those obtained for the weakly correlated case54. Interestingly, the variation of Tc with decreasing U/W (increasing pressure) found by Capone et al. does bear uncanny resemblance  observed in solid O2 under high pressure. This is suggestive, but out of scope of the present work. We leave details for the future.Insofar as superconductivity arises at the boundary of the Mott transition, our analysis provides tantalizing insight into sources of the pairing glue. Since the incoherent metal has a finite residual entropy (2. In view of the complexity of the problem (as discussed below), we only restrict ourselves to a qualitative discussion. Given selective incoherent metallic state within DMFT in our case, residual, inter-site and inter-orbital (in multiband systems) two-particle interactions can generate ordered states directly from the bad metal. Following the philosophy used earlier53 for the iron-pnictides superconducting systems we restrict ourselves to the y, z orbital sector. In this situation the interaction in the Cooper channel reads a, b = y, z and the scattering vertex is Hpair in the particle-particle channel using Gorkov’s formalism56 gives 2. A plausible assuption to be made here is that the superconducting gap function has no nodes and therefore it can be taken to be momentum independent, i.e., s-wave case of solid O2. However, as shown below this assumption has profound effects in the multiband excitation spectrum withing the s-wave superconducting phase.Our findings put constraints on mechanisms of superconductivity in solid O2 across the superconducting phase transition we have extented our normal state electronic structure calculation to treat Hpair above within LDA + DMFT formalism for the superconducting state53. In fact, using our assumption for the s-wave superconducting gap function ΔSC the LDA + DMFT equations are readily extendable to the superconducting regime. As in ref. Gab) have normal and anomalous components yielding remormalized Gaa propagators, which are solved by extending the normal state LDA + DMFT solution to include an explicit pair-field term. Including the pair-field, the DMFT propagators are writen as ref. p-orbitals of oxigen, the opening up of a superconducting gap in a particular p-band might induce secondary gaps in the remaining p orbitals, in a way reminiscent of the inter-band proximity effect induced by U′ and JH in multiband supeconductors. With this caveats in mind, we now describe our results within the superconducting state of solid O2. Using the normal state LDA + DMFT solution for Δ = 0.4 eV ] prevents opening up of a clean superconducting gap in the electronic spectrum. Remarkable as well is the fact that the insulating px channel is not affected at low energies by the superconducting instability, and this is strictly related to the fact that in this electronic channel the excitation spectrum is already gapped in the normal state. Moreover, weak spectral weight transfer from low- to high-energies occurs in all p bands as seen in Fig. 57. Future tunneling spectroscopy (dI/dV) measurements are also called for to corroborate our predition for the changes in the total one-particle spectral function  and Mott localized (px) states arising at this orbital-selective Mott transition act as the pairing glue for the superconducting state found at low T in solid O2. Our work underlines the importance of local dynamical correlations in this molecular-solid system, and holds promise for understanding similar physics in other solidified gases.In conclusion, we have theoretically studied the insulator-metal transition in highly pressurized solid O31, which correctly takes disorder, temperature and pressure effects into account in numerous strongly correlated multiband systems39. Within our scheme, the LDA band structure calculations were performed for the experimental crystal (C2/m) structure of solid O2 using the non-fully relativistic version of the PY-LMTO code35. To incorporate the effects of dynamical electronic correlations in solid O2, we use the multi-orbital iterated-perturbation-theory (MO-IPT) as an impurity solver of the many-particle problem in DMFT58. This method has recently been benchmarked by comparison with merically exact continuous time quantum Monte Carlo method (CTQMC) as an impurity solver in DMFT58. These authors find very good accord between MO-IPT and CTQMC for both one-band and multi-band Hubbard models when realistic, non-negligible crystal field splittings are included. Thus, with sizable effects of the real crystal field splitting in solid O2, our IPT solver is sufficiently accurate for quantifying the effects of sizable electronic correlations in solid O2. LDA + DMFT is thus to be viewed as a combined density functional plus dynamical mean-field (DMFT) scheme31, and adequately describes the effect of local dynamical interactions in the limit of large lattice dimensions (DMFT)59. Thereby, practical calculations become feasible even for complex multiband systems like solid O2. The basic idea in a DMFT solution involves replacing the lattice model by a self-consistently embedded MO-Anderson impurity model, and the self-consistency condition requiring the local impurity Green’s function to be equal to the local Green’s function for the lattice. The full set of equations for the MO case can be found in refs ansatz that connects the two exactly soluble limits of the one-band Hubbard model60, namely, the uncorrelated (U = 0) and the atomic (εk = 0) limits. At intermediate U, it ensures the correct low-energy behavior of the self-energies and spectral functions by strict observance of the Friedel-Luttinger sum rule in the impurity solver (we have used MO-IPT). It thus accounts for the correct low- and high-energy behavior of the one-particle spectra by construction. It ensures the Mott-Hubbard metal-insulator transition from a correlated FL metal to a Mott-Hubbard insulator occurs as a function of the Coulomb interaction U. Compared to numerically expensive QMC solvers, IPT-based schemes are known to be computationally very efficient, and readily yield real frequency data at zero and finite temperatures without the need to perform numerical analytic continuations, which are known to be a very delicate matter in QMC schemes. Finally, we have carried out the computation of electrical transport within the Kubo formalism51.To unveil the electronic reconstruction at the border of the Mott metal-insulator transition in solid Oxygen, we employ an implementation of the local density plus dynamical mean-field (LDA + DMFT) scheme


The lentiviral protein Viral Infectivity Factor (Vif) counteracts the antiviral effects of host APOBEC3 (A3) proteins and contributes to persistent HIV infection. Vif targets A3 restriction factors for ubiquitination and proteasomal degradation by recruiting them to a multi-protein ubiquitin E3 ligase complex. Here, we describe a degradation-independent mechanism of Vif-mediated antagonism that was revealed through detailed structure-function studies of antibody antigen-binding fragments (Fabs) to the Vif complex. Two Fabs were found to inhibit Vif-mediated A3 neutralization through distinct mechanisms: shielding A3 from ubiquitin transfer and blocking Vif E3 assembly. Combined biochemical, cell biological and structural studies reveal that disruption of Vif E3 assembly inhibited A3 ubiquitination but was not sufficient to restore its packaging into viral particles and antiviral activity. These observations establish that Vif can neutralize A3 family members in a degradation-independent manner. Additionally, this work highlights the potential of Fabs as functional probes, and illuminates how Vif uses a multi-pronged approach involving both degradation dependent and independent mechanisms to suppress A3 innate immunity. Restriction factors are cellular proteins that inhibit viral replication and represent a first line of defense against viral pathogens. The APOBEC3 (A3) family of restriction factors plays an important role in blocking retroviral infections. HIV-1 encodes the Vif protein to antagonize A3, which allows spread of virus in host and ultimately development of AIDS. Prior studies indicate that Vif hijacks host proteolysis pathways to degrade A3 restriction factors; however, our work demonstrates that Vif can neutralize A3s in a degradation-independent manner. These findings suggest viral suppressors of innate immunity work by multiple mechanisms to ensure robust replication. Knowledge of such mechanisms is critical for development of therapeutic strategies to restore the ability of the immune system to cripple viral infections. Despite tremendous advances in control and prevention, HIV has remained a persistent worldwide health concern. Current anti-retroviral treatments often use a combination of drugs that target key viral enzymes such as the protease, integrase, and reverse transcriptase . The exiThe HIV protein Viral Infectivity Factor (Vif) has become recognized as a promising therapeutic target –3. The pin vivo, inhibition of Vif is an attractive strategy to restore the restrictive function of A3 family members and in turn cripple HIV infection. We and others have demonstrated that pharmacological inhibition of Vif unleashes the restriction potential of A3 family members [As Vif is required for viral replication both in cell culture and  members –20; howe members ,22. TherVif, the transcription co-factor CBFβ, and adapter proteins ELONGIN B and C  to the minimal Vif complex capable of binding A3 family members. This complex, termed VCBC, consists of HIV-1  B and C . Through10 to identify Fabs against VCBC [D) in the low nanomolar range as determined by BioLayer Interferometry (BLI)  , S2 Fig.in vitro using either the Vif-binding, C-terminal domain of A3F (A3F-CTD) or full-length A3G  were generated for intra-cellular expression and tested for their ability to disrupt Vif-mediated degradation of A3C, A3F, and A3G  assays and found that the presence or absence of 3C9 had no affect on the VCBC/A3F-CTD interaction. For the direct binding assay, fluorescently labeled A3F-CTD was titrated with either VCBC or VCBC-3C9, and the Kdentical . For thedentical . Second,dentical .Cullin-RING E3 ligases catalyze ubiquitin transfer by orienting substrate lysines toward an activated E2~Ub thioester that is bound by the RING-Box subunit ,28. One Taking a similar approach as we did with 3C9, we assessed the Vif-mediated ubiquitination of Myc-tagged A3F-CTD in the presence of Flag-tagged 1D1. In contrast to 3C9, 1D1 was not ubiquitinated even though it inhibited A3F-CTD ubiquitination . 1D1 mayMultiple groups have shown that disrupting A3 ubiquitination by mutating the A3 binding surface on Vif, by expressing a dominant negative CUL5 variant, or by pharmacologically inhibiting the E3-ligase restores cellular A3 levels and results in A3 packaging ,29. Simi2+ to help stabilize this inter-domain region of Vif.To determine the structural basis for VCBC antagonism by 3C9 and 1D1, we used negative stain electron microscopy (NSEM) to define the VCBC-3C9-1D1 complex at low resolution . InitialIn constructing a molecular model, the crystal structure of VCBC (PDB: 4N9F) and homology models of 3C9 and 1D1 were fitted into the EM map . The speThe NSEM data revealed the 3C9 and 1D interacting patches on the surface of VCBC, and both Fabs appear to bind VCBC across composite protein-protein interfaces . The 3C9To identify structural regions that may contribute to 3C9 “shielding” we modeled full-length CUL5/RBX2 on the VCBC-3C9-1D1 structure and highlighted Vif residues known to be important to A3F binding . Indeed,Several studies have indicated that inhibition the Vif E3-ligase complex can restore A3 restriction and block viral replication, but there are no known drugs to date that directly target Vif. In this study, we developed Fabs that bind to the HIV-1 VCBC complex and demonstrated the utility of these Fabs as selective reagents to probe Vif function. Our panning campaign resulted in six Fabs that bound to VCBC with high affinity, of which 3C9, 3F12, and 1D1 were selected for additional studies as they recognize unique epitopes on VCBC. We initially categorized the Fabs based on their ability to disrupt Vif-mediated A3 ubiquitination, as Fabs that disrupt A3 ubiquitination would provide valuable information regarding Vif inhibition strategies, and Fabs that do not perturb A3 ubiquitination may be useful reagents for structural studies. Indeed, we have isolated Fabs that have no effect on A3 ubiquitination (3F12), inhibit A3F/A3C ubiquitination (3C9), or inhibit all A3 ubiquitination (1D1).We show that 3C9 is able to selectively inhibit the ubiquitination of A3F/A3C, but not A3G, indicating the feasibility of targeting specific A3 sites on Vif . ImportaWe identified a second biologically relevant Fab, 1D1, which acts as a pan-inhibitor of A3 ubiquitination. Structurally and biochemically, we have shown that 1D1 disrupts the VCBC-CUL5 interaction, thereby preventing A3 ubiquitination and degradation. Initially, this seemed like a promising strategy to antagonize Vif as it would 1) restore the levels of all A3 proteins degraded by Vif, 2) be potentially amenable to small molecule inhibition as the Vif-CUL5 interface is the smallest protein-protein interface in the Vif complex, and 3) may avoid off-target effects as Vif uses a non-canonical Cullin-binding motif to interact with CUL5 –33. To oThe prevalent mechanism for Vif-mediated antagonism of A3 is through ubiquitination and proteasomal degradation. Previous studies investigating A3 mutants and cell-to-cell variability have suggested that a degradation-independent mechanism exists ,34–37. DIn summary, we have developed a diverse panel of Fabs for use as biochemical probes to better understand Vif antagonism of the innate immunity provided by A3 restriction factors. These studies support the feasibility of pursuing Vif as a therapeutic target, but indicate that inhibition of ubiquitination by the Vif E3-ligase alone may not be sufficient to rescue A3 packaging. Importantly, our data establish an degradation-independent mechanism by which Vif prevents A3 packaging, and this together with previous studies show that Vif repression of A3 packaging is a multilayered process involving both degradation dependent and independent mechanisms ,29,38,39All constructs were generated by standard PCR and restriction-based cloning methods unless otherwise noted. For mammalian expression, scFv3C9 and scFv1D1 with C-terminal 3x-Flag tags were cloned into pcDNA4 (Invitrogen). Human A3C, A3F, and A3G expression constructs with C-terminal 3xHA tags have been previously reported . Env-defE. coli. Recombinant Fabs were expressed from phagemid as described [6-thioredoxin (Trx)-tagged CBFβ/Vif and ELOC/ELOB were co-expressed from pET-Duet and pCDF-Duet plasmids, respectively. HIS6-GB1-tagged CUL5-RBX2 was co-expressed from a pRSF-Duet plasmid. SOCS4 and ELOC/ELOB were co-expressed from pET28a and pCDF-Duet plasmids, respectively. HIS6-Trx-myc-tagged A3F-CTD was expressed from a pHisTRX plasmid. For E. coli expression, plasmids were transformed into E. coli BL21(DE3) (Invitrogen) cells and grown at 37°C to an optical density of 0.6–0.8 and induced with 0.5 mM IPTG overnight at 18°C (or 1mM IPTG at 20°C for Fabs).All proteins, except A3G, were expressed in escribed . HIS6-thVif-CBFβ complex, and the SOCS4-ELOBC complex were obtained as described previously [Purified VCBC, 6-protein CRL5eviously ,22. Fabseviously . BrieflyA3G was C-terminally myc-tagged followed by a TEV cleavage site and GFPII and expressed in baculovirus infected Sf9 cells. Purification was carried out as previously described . Minor m10 to identify Fabs against VCBC (23). Fabs were isolated using a phage display panning protocol descirbed in detail by Kim et al, 2011 [We used a previously published human naïve B cell phage library with a diversity of 4.1 x 10al, 2011 . Brieflyal, 2011 . A fullynst VCBC . Fabs weal, 2011 . The panal, 2011 . Clones The ELISA experiments were done as described previously . All theKinetic constants for VCBC Fabs were determined using an Octet RED384 instrument (ForteBio). Four concentrations of each Fab were tested for binding to the biotinylated VCBC complex immobilized on ForteBio streptavidin SA biosensors. All measurements were performed in 20 mM HEPES pH 7.4, 0.5 M NaCl with 0.1% (w/v) bovine serum albumin (BSA) and 0.02% (v/v) Tween 20 at room temperature in 384-well microplates. Data were analyzed using a 1:1 interaction model on the ForteBio data analysis software 8.2.in vitro ubiqutination of A3F-CTD and A3G were done as previously reported [NL4-3 E3 holoenzyme, 2–4 μM myc-tagged A3F-CTD or myc-tagged A3G, and the ubiquitin activating system containing: 1.2 μM ATP, 1.2 μM ubiquitin activating enzyme (UBE1), 45 μM ubiquitin, 4.8 μM E2 (CDC34). Ubiquitination reactions done in the presence of Fabs contained 0.1 μM, 0.5 μM, or 1μM of indicated Fab. Ubiquitinated A3 proteins were detected using a monoclonal anti-c-myc antibody (Sigma).Vif-mediated reported . BrieflyHuman Embryonic Kidney (HEK) 293T cells (ATCC) were maintained in Dulbecco’s Modified Eagle Medium (DMEM) containing 10% fetal bovine serum (FBS) and 0.5% penicillin/streptomycin (P/S).At 50% confluency, HEK293T cells were transfected  with 1 μg Env-deficient HIV-1 NL4-3 proviral construct in the presence or absence of 25 ng of the indicated C-terminal HA-tagged APOBEC3 expression construct, and either 0, 50, 100, or 250 ng of the Flag-tagged scFv expression construct. Alternately, cells were transfected with 1 μg Env-deficient HIV-1 NL4-3 proviral construct in the presence or absence of 50 ng of the C-terminal HA-tagged APOBEC3G expression construct and in the presence or absence of 100 ng of the Flag-tagged CUL5 or ELOC expression construct. After 48 hours, viral supernatants and the cells were processed for immunoblotting. Cell lysates were prepared by resuspension of washed cell pellets directly in 2.5x Laemmli Sample Buffer , and homogenization at 95°C for 30 minutes. Virus-like particles were isolated from culture supernatants by purification through 0.45μm PVDF filters (Millipore) followed by centrifugation  through a 20% sucrose, 1x PBS cushion and lysis directly in 2.5x Laemmli Sample Buffer.Samples were run on 4–20% Tris-HCl SDS-PAGE gels (BioRad Criterion) at 150V for 90 minutes. Proteins were transferred to PVDF membranes by methanol-based electrotransfer (BioRad Criterion Blotter) at 90V for 2 hours. Membranes were blocked in 4% Milk in PBS, 0.1% Tween-20 overnight prior to overnight incubation with primary antibody against HA , Vif (NIH ARRRP 809), Flag (Sigma F7425), GAPDH (Sigma G8795), p24/capsid (NIH ARRRP 3537 courtesy of B. Chesebro and K. Wehrly). Anti-mouse and anti-rabbit horseradish peroxidase (HRP)-conjugated secondary antibodies (BioRad) were detected using Hyglo HRP detection reagents (Denville Scientific). Blots were incubated in a 1xPBS, 0.2M glycine, 1.0% SDS, 1.0% Tween-20, pH 2.2 stripping buffer before reprobing.A3F-CTD was labeled with maleimide–conjugated fluorescein at 4°C for 12 hrs in 20 mM HEPES pH 7, 300 mM NaCl, 1 mM TCEP. For the direct binding assays, labeled A3F-CTD was diluted to 20nM and incubated with increasing amounts of VCBC or VCBC/3C9 for 20min at 25°C in 20 mM HEPES pH 8, 300 mM NaCl, 5% glycerol, 1 mM DTT. For the competition assays, VCBC was pre-bound with labeled A3F-CTD, and unlabeled A3F-CTD or 3C9 were titrated into the pre-assembled complex. Fluorescence polarization measurements were made using an Analyst plate reader (LJL Biosystems) with excitation and emission wavelengths of 485 nm and 530 nm, respectively. Titration assays were performed in duplicate, and all data were analyzed in SigmaPlot using equations derived as previously described .−9 M. For all experiments, 3 μL of the sample was applied to a glow-discharged, carbon-coated, 400 mesh Cu grid and stained with 2% (wt/vol) uranyl formate as previously described [1D13C9-VCBC was diluted to a final concentration of 50 × 10escribed . Images escribed  at a nomData was processed in one of two ways. For initial 2D class averages of VCBC fab combinations images were binned by a factor of two for particle picking and subsequent image processing. Individual particles were manually picked, extracted at a box size of 64 pixels and normalized to have a mean of 0 and a standard deviation of 1. Particles were subject to two-dimensional classification using Relion . For 3D The PIGS server for the automatic prediction of antibody structures was used to identify fab structures with the highest sequence homology to 3C9 and 1D1 and to generated a predicted structure for the variable regions of 3C9 and 1D1 . To obtaPulldown assays were performed in buffer containing 20 mM HEPES pH 8, 300 mM NaCl, and 10% glycerol at 25°C. MBP-tagged VCBC WT or mutant proteins were immobilized on amylose resin. Resin bound MBP-tagged VCBC was incubated with excess purified CUL5-NTD and/or 1D1 protein and subsequently washed. Pulldown samples were separated on a SDS−PAGE gel and stained with coomassie blue dye.S1 Fig(A) Sequence alignment of HIV-1 NL4-3, HXB2, and consensus Vif. (B-C) HIV-1 infectivity data comparing WT and consensus Vif in the absence or presence of (B) A3G and (C) A3F.(TIF)Click here for additional data file.S2 FigPrimary sequences for the (A) light and (B) heavy chain CDRs for Fabs 1D1 and 3C9.(TIF)Click here for additional data file.S3 FigIn vitro ubiquitination of Myc-tagged A3F-CTD or A3G in the absence or presence of increasing amounts of (B) 3C9 and scFv3C9 or (C-D) 1D1 and scFv1D1.(A) Cartoon depiction of an antibody, a fab, and a scFv. The heavy (blue) and light (orange) chain constant and variable regions are highlighted in the fab and scFv. (B-D) (TIF)Click here for additional data file.S4 FigEnv-deficient NL4-3 HIV (either Vif+ or Vif-) was co-transfected with A3C and a gradient of (A) scFv3C9 or (B) scFv1D1.(TIF)Click here for additional data file.S5 Fig(A) Fluorescence polarization competition assay. Pre-bound fluorescently labeled A3F-CTD with VCBC was titrated with either 3C9 (red) or unlabeled A3F-CTD (black). (B) Simulated competition curves establish that 10 μM of 3C9 and 100 μM of A3F-CTD are sufficient to compete with the labeled A3F-CTD bound to VCBC. (C) SEC elution profile for VCBC/3C9/Trx-A3F-CTD (black), VCBC/3C9 (red), VCBC/Trx-A3F-CTD (blue), VCBC (green), Trx-A3F-CTD (orange). SDS-PAGE gel of peak fraction for VCBC/3C9/Trx-A3F-CTD.(TIF)Click here for additional data file.S6 Fig(A) SEC profile and corresponding SDS-PAGE gel for VCBC-3C9-1D1. (B) Representative NSEM micrograph and (C) 2D class averages for VCBC-3C9-1D1.(TIF)Click here for additional data file.S7 FigEM maps aligned on (A) 1D1 or on (B) 3C9 reveal that the two conformations arise due to flexibility in VCBC. (C) The CBFβ and ELOC binding regions of Vif are boxed off. Postulated “hinge” connects these two regions and is comprised of the Zn+ binding motif and three interdomain loops.(TIF)Click here for additional data file.S8 Fig(A) NSEM 2D class averages and corresponding cartoon depictions of VCBC-Fab complexes show that 3F12 and 1D1 bind the same side of VCBC, and that 3C9 binds the opposite side of VCBC from 1D1 and 3F12. (B) SD200 elution profile and corresponding SDS-PAGE gels show that 3F12 is able to form a stable complex with SOCS4/ELOBC. (C) Purified VCBC complex resolved by SDS-PAGE gel. Myc-tagged Fabs were used as a primary antibody to WB for individual VCBC components. 3F12 is able to detect ELOB in a WB. The asterisk indicates a non-specific protein.(TIF)Click here for additional data file.S9 Fig(A) SD200 elution profile and corresponding SDS-PAGE gels for (B) SOCS4/ELOBC and SOCS4/ELOBC in the presence of (C) 3C9 or (D) 1D1. (E) SD75 elution profile and corresponding SDS-PAGE gels for (F) CBFβ and CBFβ in the presence of (G) 3C9 or (H) 1D1.(TIF)Click here for additional data file.