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cond-mat.mtrl-sci

Our experimental results are in good qualitative agreement with the results presented in [2] and confirm the important role of electron-electron scattering on transport properties of 2D electron systems [2,[13][14][15][16][17]. We are grateful to A.V. Chaplik, M.V. Entin, and L.I. Magarill for useful discussions. This work was supported by RFBR Project No.

cond-mat.mes-hall

Polytype structures corresponding to different stacking of the ab-plane have been reported to exist in KCuF 3 [19]. Our single crystal was carefully prepared so that it only contains the (a)-type structure. This was confirmed by a magnetic susceptibility measurement where we observed a single antiferromagnetic transition at 38 K [20]. We use the Miller indices in the tetragonal unit cell of the primitive perovskite structure (a = 4.1410 Å and c = 3.9237 Å) to represent the momentum transfer (Q). The propagation vector of the orbital order is (1/2, 1/2, 1/2). All the spectra were measured at room temperature.

cond-mat.str-el

A description of their numerical values for AA7010-T6 is shown in Table I. The main aspects of a phenomenological strength model can be characterized by a yield criterion representing a surface that separates the elastic and plastic regions of the stress space, a flow potential gradient that represents the direction of plastic strain rate, a strain hardening rule and that plastic flow is incompressible. An anisotropic yield surface Following the research of Spitzig and Richmond [31], and Stoughton and Yoon [32], the mathematically consistent yield function of a fully anisotropic material based on generalized decomposition of the stress tensor is developed : F Sij = Ψ Sij (1 + χp * ) ≤ Y (ε p ) , p * = 1 α 2 σ ij α ij ,(23) where Ψ Sij is described by generalized Hill's yield functions: Ψ 2 Sij = F α 3 S2 -α 2 S3 2 + G α 1 S3 -α 3 S1 2 + +H α 22 S11 -α 11 S22 2 + 2N S2 12 + 2L S2 23 + 2M S2 13 , (24) where Sij is the generalized deviatoric stress tensor ( Si = Sii , i = 1, 2, 3); α ij is the generalized Kronecker's symbol [10] (α i = α ii , i = 1, 2, 3). The material constants χ, F , G, H, N , L, M are specified in terms of selected initial yield stresses in uniaxial tension, compression, and equibiaxial tension. It is important to note that plasticity model ( 24) is naturally independent from the generalized hydrostatic pressure and therefore, the following equality can be written: where σ ij is the stress tensor. In this paper, a uniaxial strain state (one-dimensional reduced mathematical formulation in strain space) and the adiabatic approximation assumptions are considered for modelling shock waves propagation in anisotropic solids.

cond-mat.mtrl-sci

The latter plot reveales that in x direction, being perpendicular to the mirror reflection plane m 1 , the circular photogalvanic effect overweight the linear photogalvanic effect. The data are in a good agreement with Eqs. (9). VII. SUMMARY We have studied photocurrents in n-doped zinc-blende based (110)-grown QWs generated by Drude absorption of normally incident terahertz radiation in the presence of an in-plane and out of plane magnetic field. The results agree with the phenomenological description based on the symmetry.

cond-mat.mes-hall

(49) Equation (49) implies that the position of the microcantilever can be very sensitive to the incoming ac signals if their frequency is close to one of the plasma resonant frequencies and the quality factor of the plasma oscillations Q p ∝ Ω p /ν ≫ 1. Hence the micromashined HEMT under consideration can serve as a mechanical resonant detector of microwave and terahertz radiation. One may expect that at sufficiently strong ac signals, the microcantilever can be pulled-in to the surface of the isolating layer. Assuming, for simplicity that V 0 = 0, we obtain the following condition of the microcantilever pull-in under the effect of the ac voltage:δV V 0 2 ≥ 8 27F ω . (50) Using the estimate for maxF ω , we obtain min δV V 0 2 ≥ 4π 2 27 ν Ω p 2 ∝ 1 Q 2 p ,(51) so that the minimum ac pull-in voltage can be estimated as min δV (pull-in) ≃ ν Ω p V 0 . (52) Equation ( 54) shows that when the quality factor of the plasma oscillations is large, the microcantilever pull-in might occur at fairly modest ac signals.

cond-mat.mes-hall

We also discussed the results of analyses by comparing them with those of iron-pnictide superconductors. Experimental Methods We synthesized polycrystalline samples of LaCoAsO by solid-state reaction methods from powders of La (purity: 99.9%), As (99.99%), and CoO (99.99%). The detailed synthesis conditions are described in our previous report. 14) By powder X-ray diffraction measurements, we confirmed our polycrystalline sample to be in a single phase of LaCoAsO with the crystal structure shown in Fig. 1(a). We present the temperature dependences of magnetizations (M ) at various magnetic fields (H) and inverse magnetic susceptibilities (χ -1 ) in Fig.

cond-mat.str-el

These states compete with magnetically or orbitally disordered phases dominated by VB correlations on the bonds, which are investigated in Sec. IV. The analysis suggests strongly that all long-range order is indeed destabilized by quantum fluctuations, leading over much of the phase diagram to liquid phases based on fluctuating dimers, with spin correlations of only the shortest range. In Sec. V we present the results of exact diagonalization calculations performed for small clusters with three, four, and six bonds, which reinforce these conclusions and provide detailed information about the local physical processes leading to the dominance of resonating dimer phases. In each of Secs.

cond-mat.str-el

An interesting feature is the presence of a crossing point in the critical temperature curves around U = 2.3V for z = 3. In the plane (n, T ), at fixed U , the CO phase is observed in the interval n 1 < n < n 2 ; the width ∆ = n 2 -n 1 varies with the temperature, following different laws according to the value of U . At T = 0 a complete CO state is established in the regions 2/z ≤ n ≤ 2(z -1)/z for U < 0 and 1/z ≤ n ≤ (2z -1)/z for U > 0. For U < 0 (see Fig. 9a), ∆n first increases with T , then decreases vanishing at n = 1, where the maximum critical temperature is reached; a reentrant behavior characterizes this region. As it is shown in Fig.

cond-mat.str-el

Since there are two real axes on the Σ g=1 (k x ), correspondingly, there is g=1 zero point at the up-edge-state energy µ j . The above considerations are for the fixed k x . Now, let us consider a family of the RSs Σ g=1 (k x ) parametrized by k x changing in one of its periods. Σ g=1 (k x ) can be modified by this change. However, all the RSs Σ g=1 (k x ) with different k x are topologically equivalent if there are stable energy gaps in the 2D energy spectrum. On the genus g=1 RS, the first homotopy group is generated by 2g=2 generators, α i and β i , i=1.

cond-mat.mes-hall

This means, the Ir 5d character enhances in the bonding bands and subsequently, relative O 2p character in the antibonding band appearing near ǫ F enhances. Thus, the Ir 5d-O 2p covalency is significantly influenced by the electron correlation. Secondly, the up spin feature in the vicinity of ǫ F (antibonding band having primarily Ir 5d character) gradually moves towards lower energies and have marginal contributions at ǫ F for U ≥ 4 eV. Distinct signatures of the coherent feature (delocalized electronic states in the vicinity of ǫ F ) and incoherent features (electron correlation induced localized band) are not observed in the up spin channel. The down spin DOS, however, splits into two distinct features presumably representing the incoherent features. Again, the signature of the coherent feature at ǫ F is absent.

cond-mat.str-el

Note that the observed value of 0.6 eV is much smaller than half the optical gap of undoped TiOCl, which is ≈ 2 eV. In addition, with further doping one would expect the formation of a coherent quasiparticle peak at the chemical potential concomitant with a decrease of the LHB (and UHB) spectral weight, indicating a strongly correlated metallic state [16]. In-intensity (arb. units) -10 -8 -6 -4 -2 0 E-µ exp (eV) stead, the doping-induced spectral weight develops in a broad hump, partly overlapping with the original spectral weight of the LHB. As we will see later, the latter two observations, the inconsistent gap value and the absence of a quasiparticle peak, can be explained by a simple single-particle effect. Na:TiOCl -3 -2 -1 0 E-µ exp (eV) What is more remarkable, though more inconspicuous at first glance is the development of the relative spectral weight of the two peaks at the chemical potential.

cond-mat.str-el

The correct normalization is obtained after division by the partition function, also measured in the space C W , i.e. by δ Z W = x z x with z x = 1 if x ∈ C Z and z x = 0 otherwise. Thus,G ab = G ab W δ Z W . (2) The sum over all terms in C W is performed using a diagrammatic Monte Carlo method: diagrams in C W are generated, accepted, or rejected stochastically by inserting and removing local operators and hybridization lines according to their contribution to Z W and integrated stochastically, in analogy to Ref. 4 . This summation is exact if all bold diagrams are included.

cond-mat.str-el

Below 100 nm, the result is in good agreement at the 10 % level with theory including contribution from measured optical properties and surface roughness of gold coatings. This was made possible by using stiff cantilevers to reduce jump to contact problems. Using more advanced metal deposition techniques such as atomic layer deposition (also for metal coating other than Au, which are used in NEMS/MEMS) [20] further possibilities arise to extend these measurements below 10 nm, and therefore to further extend our knowledge with respect to force effects in the operation of NEMS/MEMS (e.g., switches). For the roughness parameters we used w sphere =1.8 nm, w plane =1.3 nm, ξ sphere,plane = ~20 nm, H sphere, plane =0.9. Figure captions Acknowledgements: The research was carried out under project number MC3.05242 in the framework of the Strategic Research programme of the Netherlands Institute for Metals Research (NIMR). Financial support from the NIMR is gratefully acknowledged.

cond-mat.mtrl-sci

The approach is based on Chebyshev moment expansion, applied to the time evolution operator. We focused on the process of small polaron formation in finite lowdimensional quantum structures described by a generalized Holstein Hamiltonian. Both electron and phonon quantum dynamics were treated exactly. We first started from a non-interacting ground state and analyzed the real-time dynamics of the particle density and phonon number after a sudden switching-on of the electron-phonon coupling at a single oscillatory (molecular quantum dot) site. As a consequence of this interaction quench the originally free particle can be trapped at the "impurity" site after a while. The selftrapping process differs in nature for the adiabatic and anti-adiabatic regimes of small and large phonon frequencies, respectively.

cond-mat.str-el

The linewidth of the Kondo resonance is well described by an energy scale T K (Kondo temperature) given by T K ∝ DΓ 4 1 2 exp - π|ǫ dot | Γ ,(3) where D is a high energy cutoff equal to half bandwidth of the conduction electrons and Γ corresponds to the value of coupling between the dot and the contacts Γ(ǫ) at ǫ = ǫ F . The purpose of this paper is to theoretically investigate a case in which the dot level is displaced from its equilibrium level sinusoidally by means of a gate voltage. This results in a de facto time dependent Kondo temperature and causes the instantaneous conductance to exhibit periodic modulations with a minimum when the dot level is farthest from the Fermi level and a maximum when the dot level is closest. The period of conductance oscillations is equal to the driving frequency. In particular, we will investigate a system which has been analyzed in zero bias before. Its dot level is given by ǫ dot (t)=-5Γ+4Γ cos Ωt.

cond-mat.mes-hall

In the low-energy limit, the lattice operators may be linearized about the Fermi points and expressed in terms of chiral fields. For the first sublattice, the chiral-field decomposition is rather standard, d q1 (y) ≈ √ b ψ Rq (y)e ik F y + ψ Lq (y)e -ik F y . (10) For the second sublattice, one may expect the finite offset δ should give rise to some phase factor in the chiral-field decomposition. However, a careful analysis leads to a somewhat surprising result, d q2 (y + b -δ) ≈ √ b ψ Rq (y + b)e ik F (y+b) + ψ Lq (y + b)e -ik F (y+b) . (11) The above result states that the chiral-field decomposition is the same as when the finite offset δ is ignored. The detailed derivation can be found in Appendix A.

cond-mat.str-el

We expected interdiffusion between Ag and Al to lead to greater intermixing, because extrapolation of higher temperature diffusion data 5 to room temperature suggested that interdiffusion might occur at room temperature. 6 Our hope was three-fold. First, to try to measure 2AR Ag/Al (111) in the presence of the expected intermixing. Second, to see if 2AR Ag/Al (111) was as sensitive to intermixing as predicted. Third, to see if the intermixing was large enough to reduce the orientation dependence to where it would be harder to confirm. We checked for evidence of intermixing using measurements of both AR and x-rays.

cond-mat.mtrl-sci

Secondly, by studying HoMn 2 O 5 , we can investigate the influence of a magnetic R ion on the arrangement of the Mn moments and determine the magnetic ordering of the Ho sublattice itself. Comparison with YMn 2 O 5 , which has the same propagation vector but a non-magnetic R site is of particular interest, since the values of the electric polarization in the commensurate regime of the two systems are significantly different. [110] and [001] directions. For the HoMn 2 O 5 crystal, additional faces (100) and (010) were also visible. Single crystal diffraction measurements were performed on the four-circle diffractometer D10 at the ILL (Grenoble, France). Samples were checked for quality and pre-aligned with the (001) direction oriented along the vertical axis using the OrientExpress facility (ILL).

cond-mat.mtrl-sci

The fluid beyond a distance 10σ from the particle surface is thermostatted at T0 = 0.75, again using velocity rescaling. Temperature, density and pressure fields have been obtained by averaging the corresponding quantities during 10000 time steps in nanoparticle centered spherical shells of width ≃ 0.15σ, after a steady state is reached. Finally, we calculate the heat flux density flowing through the solid particle, by measuring the power supply needed to keep the nanoparticle at the target temperature Tp. For the highest temperatures, the temperature field inside the particle is not shown, in order to limit the amplitude of the scale of the vertical axis. Figure 6 displays steady state temperature profiles close to the nanoparticle surface, for different temperatures Tp of the nanoparticle. For low Tp, the temperature field in the liquid is practically indistinguishable from the form A/r + B (eq.

cond-mat.mtrl-sci

In particular, other effects (presently not taken into account) such as anharmonic interactions may be neglected in this temperature regime (and for lower temperatures). The measurements from Ref. 1 have been transformed into conductivities per unit length by assuming that the CNTs used for the experiments have a diameter of 1 nm. The authors of Ref. 1 indeed precise that the CNTs used have a diameter in the range 1-2 nm, occasionally 2-3 nm. If the diameter is indeed 1 nm, then the experimental results are close to the ballistic conductance curve, which means that the thermal transport is nearly ballistic.

cond-mat.mtrl-sci

I. INTRODUCTION Many of the phenomena in condensed matter physics can be understood as consequences of electronic correlations. Superconductivity, magnetism, and the quantum Hall effects are just a few examples of how collective behavior of electrons leads to macroscopic effects. In many cases the main effects can be ascribed to some kind of longer-range order. It is thus an important task of condensed matter theory to shed light on the question why and how electrons order in different ways. If the order parameter is known or restricted to a few possibilities, much progress can been made within mean-field approaches like the BCS theory of superconductivity.

cond-mat.str-el

These included samples at different temperatures, but also samples which were scaled and strained in different ways. The approximants were carefully selected, so that all relevant local environments are represented. For those reference structures, the forces, stresses and energies were computed with ab-initio methods, and a first version of the fitted effective potential given by sampling points with cubic spline interpolation was fitted to the reference data. In a second step, molecular dynamics simulations with the newly determined potential were used to create new reference structures, which are better representatives of the structures actually appearing in that system. The new reference structures complemented and partially replaced the previous ones, and the fitting procedure was repeated. This second iteration resulted in a significantly better fit to the reference data.

cond-mat.mtrl-sci

Results and Discussion Fig. 1 shows an energy path between coherent and dislocated configurations [19]. The misfit f = 8% and κ = 0. The initial chain of states is obtained by simple linear interpolation. This chain is minimized with NEB method [20]. The results show an energy barrier for the initial detachment of the dislocation from the island-wetting film contact point.

cond-mat.mtrl-sci

Long pi orbital are both located out of the plane of the nuclei in the molecule and they are relatively diffuse compared to the in plane sigma type orbitals. Thus one or more unoccupied or partially occupied orbitals can provide channels that permit the transport of additional electrons from one end to the other end. The sparse unoccupied pi orbitals can be named as conduction band. Molecular Insulators The aliphatic molecules contains only sigma bonds which will not form an uninterrupted channel outside the plane of the nuclei. The positively charged nuclei are obstacles to negatively charged electrons traveling along the axis of the plane. For this reason aliphatic molecules are used as insulators.

cond-mat.mtrl-sci

Let us move to the analysis of experimental results of Ref. [12]. In general, the dynamics of the magnetization m 1 determined by Eq. ( 10) is very complicated; thus, we cannot obtain the analytical expression of the critical current of STT-driven magnetization dynamics of the magnetization m 1 . However, in the experiment of Ref. [12], the system, and therefore the dynamics of m 1 , have axial symmetry along the direction normal to the film plane because the high magnetic field (about 7 T) is applied along this direction.

cond-mat.mes-hall

According to our results, most of the Raman and far-infrared modes are present up to the highest applied pressure. Therefore, we can rule out an amorphization of the sample between 10 and 12 GPa. Furthermore, our results show that the structural units, i.e., the V-O polyhedra, remain intact up to the highest applied pressure. In the pressure range 10 -12 GPa several Ramanactive modes show a significant change in their pressuredependent frequency shifts. In general, the force constant and hence the frequency of a Raman mode are affected by the amount of charge on the ions involved in the vibrations. 18,23 Accordingly, we interpret the changes observed in our Raman data in terms of a transfer of charge between the different V sites, setting in at 9 GPa and being completed at around 12 GPa.

cond-mat.str-el

This can be seen in detail in the Fourier transform of the symmetrized occupation in panels (c) and (d). There is a clear peak at k = ±2k F (dashed vertical lines). oscillations more or less average out, resulting in an essentially monotonic decay with r, as expected according to (1.5). We will next apply the analysis proposed in section 4.2 to the respective symmetry sectors (which will provide more exact fits of the exponents of the power-law decays). The analysis in any sector consists of two stages. First, following section 4.2, we try to find an optimal truncated basis which describes best the dominant correlations.

cond-mat.str-el

Further insight into the pseudo-inverse is gained by introducing the set of N ≤ 6 fourth order tensors associated with A ∈Sym, (2-7) A I = A I ⊠ A I , I = 1, . . . , n, A i ⊠ A j + A j ⊠ A i , I = n + 1, . . .

cond-mat.mtrl-sci

The atomic electron densities are computed as ρ a(k) i (r ij ) = ρ i0 exp -β (k) i r ij r 0 i -1 ,(10) where r 0 i is the nearest-neighbor distance in the singleelement reference structure and β (k) i is element-dependent parameter. Finally, the average weighting factors are given by t(k ) i = 1 ρ (0) i j =i t (k) j ρ a(0) j S ij ,(11)where t (k) j is an element-dependent parameter.The pair potential is given by φ ij (r ij ) = φij (r ij )S ij (12) φij (r ij ) = 1 Z ij 2E u ij (r ij ) -F i Z ij ρ (0) j (r ij ) Z i ρ 0 i -F j Z ij ρ (0) i (r ij ) Z j ρ 0 j (13) E u ij (r ij ) = -E 0 ij 1 + a * ij (r ij ) e -a * ij (rij )(14) a * ij = α ij r ij r 0 ij -1 ,(15) where α ij is an element-dependent parameter. The sublimation energy E 0 ij , the equilibrium nearest-neighbor distance r 0 ij , and the number of nearest-neighbors Z ij are obtained from the reference structure. The screening function S ij is designed so that S ij = 1 if atoms i and j are unscreened and within the cutoff radius r c , and S ij = 0 if they are completely screened or outside the cutoff radius. It varies smoothly between 0 and 1 for partial screening. The total screening function is the product of a radial cutoff function and three-body terms involving all other atoms in the system: S ij = Sij f c r c -r ij ∆r (16a) Sij = k =i,j S ikj(16b) S ikj = f c C ikj -C min,ikj C max,ikj -C min,ikj(16c) C ikj = 1 + 2 r 2 ij r 2 ik + r 2 ij r 2 jk -r 4 ij r 4 ij -r 2 ik -r 2 jk 2 (16d) f c (x) =      1 x ≥ 1 1 -1 -x) 4 2 0 < x < 1 0 x ≤ 0 (16e) Note that C min and C max can be defined separately for each i-j-k triplet, based on their element types.

cond-mat.mtrl-sci

One can show 19 that demanding: a) that the probability current normal to the boundary be zero; b) that the boundary should preserve the electron-hole symmetry of the bulk; c) and finally, assuming that the boundary conditions do not break the time reversal symmetry, leads to the following form of the matrix M : M = ντ ⊗ nσ , where σ = (σ x , σ y , σ z ), τ = (τ x , τ y , τ z ) and σ i , τ i are Pauli matrices acting in the sublattice and valley space, respectively. Furthermore, ν and n are three dimensional unit vectors, restricted to two classes: zigzag-like (ν = ±ẑ, n = ẑ, where ẑ is the unit vector perpendicular to the plane of the graphene sheet) and armchair-like (ν z = n z = 0). Additionally in both classes n ⊥ n E , where n E is a unit vector in the plane of the graphene sheet and it is perpendicular to the edge. Let us now consider the reflection from an edge of a nanoribbon in more details. It follows from the form of the boundary conditions described earlier that the wavefunctions Ψ ± E on the boundary is proportional to the eigenvectors Z ± corresponding to the doubly degenerate unit eigenvalue of the matrix M . In other words, Ψ ± E = η ± Z ± e ikx where Ψ + (Ψ -) and Z + (Z -) correspond to isospin vector ν (-ν), η ± are amplitudes and k x is the wavevector component along the (translationally invariant) edge.

cond-mat.mes-hall

Shot noise in graphene Now we focus our work on shot noise. We used the experimental set-up and the technique to extract the Fano factor presented in Section 3. We have divided this section in three parts. In the first part, we will show that our measurements are well described by the evanescent wave theory and demonstrate that transport in graphene can be ballistic. In the second part, we will see how disorder affects the Fano factor and we will compare our findings with the existing theories modeling disordered graphene. Finally, we will show how non-parallel leads affect shot noise.

cond-mat.mes-hall

On the other hand, Re, ω(k) describes the rate at which the amplitude of a perturbation with wave-vector k grows or decays with time. Given that at small angles of incidence [13] ν x (θ) < 0 and ν y (θ) < 0, any spatial perturbations on the initial surface grow exponentially in time. Since ∇ 2 h is positive at the bottoms of the valleys, at these points the rate of erosion is larger than at the top of the crests where ∇ 2 h < 0. Therefore, the negative signs of ν x and ν y are the mathematical expression of Sigmund's morphological instability. At these small incidence angles, moreover, ν x (θ) < ν y (θ) and perturbations grow faster along the X axis than along the Ŷ. Hence, at these angles, the ripples crests are perpendicular to the projection of the ion beam onto the surface as observed experimentally.

cond-mat.mtrl-sci

(B2a): A(x, y) ≡ - a 4 0 2πh Āν = 1 h (A 1 + A 2 + A 3 ) , A 1 = Θ + (h) 2π lim r ⋆ →0 |r-r ′ |>r ⋆ d 2 x ′ h 0 dz (2z 2 -ρ 2 )(h -z + a 0 ) (ρ 2 + z 2 ) 5/2 , (B4) A 2 = - a 4 0 8π µ rnm =0 1 ρ 3 νµ ≈ a 2 0 8π 2π 0 dα P - a 0 4 , A 3 = a 2 0 8π d 2 x ′ 2h 2 -ρ 2 (ρ 2 + h 2 ) 5/2 ≈ a 2 0 8π 2π 0 P 2 dα (P 2 + h 2 ) 3/2 - a 4 0 4(a 2 0 + h 2 ) 3/2 . Here ρ = (x -x ′ ) 2 + (y -y ′ ) 2 and we used a local reference frame (16) and the Heaviside function Θ + (x) takes the unit values for any positive x and zero values for x ≤ 0. The Heaviside function is added here to fulfil the condition A 1 ≡ 0 in a 2D case, when for h = 0. There is a singularity in A 1 , due to the nonintegrability of the kernel K z at r nm = 0. To regularize it we use a method similar to the one in Ref. 23.

cond-mat.str-el

(5) Here, E = 1 means the unit electrical field and the scalar product of two functions Φ k and Ψ k is defined as Φ, Ψ = k Φ k Ψ k . In fact, in Eq. ( 5) the k-integration over the actual FS is implied, which follows from the property of the scattering operator W kk ′ and the explicit form of X k = e(Ev k )(-df 0 k /dǫ k ). A way to search for a variational solution of Eq. ( 5) for the deviation function Φ k is to expand it in a set of the Fermi-surface harmonics (FSH) φ L (k):Φ k = L η L φ L (k),(6) where η L are variational parameters and L is a convenient composite label that includes numbering of different sheets of the FS in LiV 2 O 4 . The FSH's are defined 25,26 as polynomials of the Fermi-velocity Cartesian components v α k .

cond-mat.str-el

Since only the whole Hamiltonian provides these ground states, these not emerge given by a specific band structure, nor appear as interaction selected ground states from existent eigenstates of other parts of the Hamiltonian, but are created by both kinetic and interaction contributions, hence their eigenstate nature disappears when the interactions are turned off, or when the kinetic part is neglected (e.g. in the localized limit). The remaining part of the paper is structured as follows. Section II. describes the model used, Section III. presents the exact transformation of the Hamiltonian in positive semidefinite form, Section IV.

cond-mat.str-el

For a good understanding of the underlying physics we will prefer an analytical formulation easier to discuss than simulation results. Thus we only consider the case of epitaxial deposit that consists in periodic 1D ribbon (one monolayer thick) where lateral growth takes place at constant steps density (excepted at coalescence). We believe that such model allows us to capture the essential physics. In section II we compare the experimental data to theoretical one. First, we demonstrate experimentally that the full-width at half maximum (FWHM) is actually connected with the nucleation density. Second, we show that the amplitude of the detected relaxation effect actually depends on the nucleation density, or in other words, on the 2D islands size, in agreement with the theory.

cond-mat.mtrl-sci

The elastic material properties of 7010-T6 can be found in [34]. Material properties of plates 6082-T6 and PMMA can be found in [19]. Using a finite-difference wave propagation code [35], numerical simulations of plate-impact test were performed with a 5 mm thick target plate, 2.5 mm thick flyer plate and 5 mm PMMA plate. Based on the characteristics of this plate impact problem, the plates (numerical domains), which are used in the numerical simulation, are modelled as 1D bars [35]. The mesh resolutions were sufficient to allow the resolution of all the relevant elastic and plastic waves in the target and flyer. The stress time histories were recorded in the middle of the target plate and at the back of the test specimen (the first FD element in the PMMA connected to test plate).

cond-mat.mtrl-sci

We will use this fact for the analysis of dephasing. Physically, when electron tunnels, it excites two collective modes associated with two edge channels, and they carry away a part of the phase information. On the other hand, charging effects reflected in the parameter ∆t lead to the bias dependent shift of the AB phase, ∆φ AB . As it follows from Eq. ( 35), the phase slips by π at points where the visibility vanishes. Away from these points, in particular at zero bias, the phase shift is a smooth function of the bias.

cond-mat.mes-hall

Our result for γ 2 linearly decreases as the filling gets smaller and appears to approach 1 2 only in the limit ν → 0. We also explicitly calculated the same correlation function as investigated in [2] but found a stronger decay than the r -1 2 suggested there. We do not know whether the deviation is an artifact of the boundaries of our finite system, or whether the mapping used in [2] to a set of hardcore bosons might have omitted an important contribution. Moreover, it may be noted that by extrapolating the exponents in a linear fashion towards large fillings (ν → 1 2 ), it appears that for fillings larger than ∼ 0.35 eventually the CD correlations dominate over 2P correlations (see figure 13). This conclusion has also been found in [9] which similarly addresses diatomic real space pairing in the context of superconductivity. Their discussion, however, is not specifically constrained = 1 2 + 5 2 ( 1 2 -ν) γ CH 2 = 1 2 Figure 13 .

cond-mat.str-el

From the experimental point of view, this is especially evident for the case of nanodot patterns due to their relative novelty. For the case of nanoripples, in spite of the abundant avaliable data, there are also gaps to be filled. Perhaps, the least systematically investigated aspects concern transverse ripple propagation and the relevance of shadowing effects on the morphological evolution. The former is difficult to address due to its evident experimental complexity since in-situ, real time monitoring of the ripple morphology has to be carried out. The second issue, although quite specific, is interesting because it can provide important data for theory refinement, which requires exploring systematically the continuum models beyond the customary small-slope approximation. With regard to nanodot patterns, there is still a certain lack of systematicity in the studies of the various targets that have proved amenable to such patterns when subject to IBS.

cond-mat.mtrl-sci

Therefore, to generate the mixing the electrostatic potential must be modulated at this momentum. So, the mechanism can produce a CDW with the wave vector K. Let φ k is a Fourier component of the external electrostatic potential. The component interacts with the corresponding matrix element of charge density ρ k = ψ * b↑ (r)e -ik•r ψ a↑ d 2 r = χ 2 (r)e i(K-k)•r d 2 r = 8κ 3 [4κ 2 + (K -k) 2 ] 3/2 . (30) We have used here Eqs. ( 16) and (13). We assume that β 1 = β 2 , this allows to evaluate the integral in (30) analytically.

cond-mat.str-el

related by an S-matrix b 1 b 2 = 0 e i(k-θ/L) Lu P u e i(k+θ/L) Lu P u 0 b ′ 1 b ′ 2 . (6) Similarly for lower arm Before going into the calculation of conductance and impact of dephasing due to the two dephasing-models we study, let us first discuss what we expect in the completely incoherent limit. The incoming beam transits electrons in the upper (lower) arm with transmission coefficient ǫ. Hence the upper (lower) arm have same resistances at the two junctions 1/ǫ. In the incoherent limit the resistances in upper (lower) arm add as in Ohm's law, R u = 2/ǫ. Now these resistances add in parallel leading to the total conductance G = 2/R u = ǫ. c 1 c 2 = 0 e i(k+θ/L) L d P d e i(k-θ/L) L d P d 0 c ′ 1 c ′ 2 .

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[54]), in the case of a classical solvent it is sufficient to consider a single effective solvent coordinate q. Effectively, this means that in the Hamiltonian, we make the following substitutions: 1 2 ν ω ν a 2 ν → λq 2 , ν ω ν g ν q ν → -2λq(16) The average over the solvent configurations can then be written as: I = 1 Z dqe -βE(q) I(q) Z = dqe -βE(q) (17) where the energy, as a function of the solvent coordinate q, is: E(q) = λq 2 + i ǫ c † i c i(18) Thus E(q) is obtained by performing a partial trace over the fermionic part of the total Hamiltonian. The quantity c † i c i , as viewed by Wingreen et al. [18], is the lesser component of the Keldysh Green's function, G < ii . If Γ L and Γ R are the imaginary parts of the self-energy arising from the interaction with the left and the right reservoirs (which in the view of wideband approximations is ∆), then for the present case G < ii = if (ǫ + e 0 V )[G r Γ L G a ] ii + if (ǫ)[G r Γ R G a ] ii(19) At this point, a few comments on the appearance for G < are needed. It is well known that in equilibrium the lesser Green's function takes the form of a product of spectral function times the occupation function.

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(Since all observed magnetic propagation vectors are along b*, in the following we will give τ values only as numbers). T M n N τ M n (T M n N > T > T ) T τ M n (T > T > T R N ) T R N τ M n (T < T R N ) τ R GdMnO3 43 K 0.24...0.2 23 K 0, 1/4 § § 7 K 0, 1/4 (?) § § 1/4 Both Dy-and GdMnO 3 exhibit interesting effects induced by external magnetic fields. Below 10 K DyMnO 3 shows a significant enhancement of the electric polarization P c by a factor of up to 3.5 for magnetic fields between 10 and 50 kOe applied along a, and between 10 and 20 kOe for fields along b. In the ground state of GdMnO 3 (T << T Gd N ), in turn, an electric polarization P a is observed only when a magnetic field H > 10 kOe is applied along b. In this report we present XRMS results of the R magnetic ordering in an applied magnetic field H a for DyMnO 3 and H b for GdMnO 3 which give an additional physical insight on the observed field-induced effects.

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Due to the occurrence of the structural phase transition 28,38 and the possible existence of an additional phase boundary (this work) the phase diagram of La 1-x Ca x CoO 3 is rather complex and it is therefore discussed separately in section V. Figures 3 and4 show the linear thermal-expansion coefficient α of La 1-x Ca x CoO 3 as a function of tempera- (i) Fig. 3 (a): Again, the pronounced maximum caused by the spin-state transition of the Co 3+ ions in the undoped compound is strongly suppressed with increasing x, but a shoulder remains visible up to x ≈ 0.1. (ii) For x = 0.125, α(T ) features a kink around 85 K, which is about 10 K below the transition temperature to ferromagnetic order (black circle). As shown in Fig. 3 (b), similar kinks are also present in α(T ) of the highly-doped compounds with 0.23 ≤ x ≤ 0.27. The kinks occur about 10 K below T c , too.

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It should be also mentioned that the symmetry of AFM state (corresponding group is generated by the rotation 2 [001] and translation [ 1 2 , 1 2 ,0] both combined with time inversion 1 ′ ) allows the existence of macroscopic electric polarization vector oriented along the [001] axis and forbids existence of macrosopic magnetization. The role of magnetoelastic coupling in the formation of AFM-III structure can be traced from the following qualitative considerations. It was already mentioned that the value of Mn-Te-Mn angle φ is the key quantity in determining the exchange coupling constant J d-d between the NN Mn 2+ ions: upon decreasing the φ the strength of AFM interaction increases. For small deflection from an ideal φ 0 = 109.5 • angle peculiar to fcc lattice, this dependence can be approximated as follows (from the results of Bruno and Lascaray 37 ) J d-d (φ) = -3.45 + 0.135(φ -φ 0 ), K.(1) Now, let us turn to Fig. 3 which illustrates the effect of tetragonal strain induced by the presence of ZnTe layers. In a nondeformed cubic lattice all the bonds make an "ideal" angle φ 0 and all NN interactions are equivalent.

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Definition (17) of the distribution generates Van Hove singularities (VHS), in the vicinity of values t = t 0 for which there exists extremal or saddle integration points x i such that a(x i ) = t 0 and ∂ x a(x i ) = 0. In 2D, depending on the eigenvalues of the matrix ∂ 2 xx a(x i ) being of same or of opposite signs, the singularity in P is either a discontinuity or a logarithmic divergence (Van Hove, 1953). "Extended" Van Hove 0.8 1.0 1.2 1. 4 P(t) P σ m (t) f = 0.1 PS load. P σ PS (t)SS load. P σ SS (t) SS load.

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7) confirmed the decrease of magnetic moment with La doping. The field (H) dependence of magnetization (M) at 5 K for x = 0, 0.2, 0. and the calculated slope showed decreasing trend (e.g., α ∼ 10.35 and 0.94 in10 -3 K -1 for x = 0 and 0.6, respectively) with the increase of La concentration. This gives further evidence of increasing disorder in Ca 2 FeMoO 6 structure as an effect of La doping. The effect of increasing disorder has been relayed to the low temperature (< 300 K) state and already reflected in the increasing temperature shift per decade of frequency value (∆) for La doped samples. In fact, the ∆ value of x = 0.4 sample is close to the insulating spinglass system (EuSr)S ~ 0.06 [22]. The breaking of large size ferromagnetic grains into smaller grains (in terms of different size clusters) was indicated from SEM picture and this may cause a significant increase of resistance in spite of metallic character, in the doped samples.

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We have argued that this phase has no spin-gap, and supports local two-level system excitations as well as singlet and triplet excitations that decompose into kink-antikink pairs that delocalize over a local network of corner sharing triangles. This phase provides a consistent picture of thermodynamic, neutron and Raman measurements in the Herbertsmithite materials. Significantly reduced concentration of impurities can help provide clearer signatures for the Valence Bond Crystal phase in the Kagome Lattice Heisenberg Model. We would like to thank Fabrice Bert, Mark de Vries, Joel Helton, Michael Hermele, Andreas Laeuchli, Peter Lemmens, Frederic Mila, and Oleg Tchernyshyov for many valuable discussions and to Phillipe Mendels for an invitation to Paris, where many of these ideas were crystalized. APPENDIX In this appendix, we address the recetly reported Neutron scattering data on the Herbersmithite materials by Helton et al. [27] We make the assumptions that the large number of free spins created by the impurities go into a random singlet phase, where the spins are coupled by a renormalized distribution of exchange constants, which has a power-law behavior P (J) = CJ -α .

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From bottom to top: Dashed lines are calculations for z = 0, 1, and 2 nm from Ref. [3]. corresponding τ t long /τ q long . To assess the likelihood of this scenario, we have calculated τ t long , τ q long , and τ t long /τ q long caused by charged impurities uniformly distributed within a certain distance d of the graphene sheet, and estimated the effective 2D density of the impurities n eff imp in this layer. Figure S5 plots experimental τ t long /τ q long and calculations based on the above model for samples B and D, for which we have determined z = 1 nm, n imp = 7.7 x10 11 /cm 2 (B) and z = 2 nm, n imp = 7x10 11 /cm 2 (D) previously assuming a δlayer of impurity. Our calculations show that the τ data in sample B can also be described by n eff imp = 8.5x10 11 /cm 2 and d = 3 nm and the τ data in sample D are consistent with n eff imp = 1.1x10 12 /cm 2 and d =10 nm (Fig.

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Two other aspects of the numerical results in Table I relate to exact constraints, hence deserve brief comment. First, the von Weizsäcker KE is the exact T s for two-electron singlets. We have not enforced that limit, yet the error from RDA (24) (24) functionals are N -representable or, in some operational sense, close. It is also important to remember that the narrow goal is a functional that can be parameterized to a small training set which is relevant to the desired materials simulations. This limitation of scope is a practical means for limiting the risks of non-N -representability. In addition, we have many RDD forms open for exploration other than RDA (24).

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Details of the growth conditions have been reported elsewhere 17 . The total thicknesses of the bilayered heterostructures were fixed at 240 nm and the individual LSMO layer thickness was varied between 48nm and 120 nm. Crystallographic and epitaxial characterizations of the heterostructures were performed using Phillips X'Pert MRD Pro X Ray diffractometer (CuK α , λ = 0.15418 nm). The magnetization hysteresis (M-H) was measured using a vibrating sample magnetometer in a PPMS system (Quantum design, USA). A Radiant Technology Precision ferroelectric workstation was used to measure the FE polarization hysteresis (P-E). In order to measure the dielectric response under an applied magnetic field, the samples were mounted on a sample holder inserted in close cycle cryocooled magnet and connected to an Agilent 4294A impedance analyzer using co-axial compensated cables.

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A gradient expansion will break down for phenomena with short length-scales, for example mass enhancement [28]. If electron density is smoothly varying then starting from Eqn. (3), the gradient correction to the energy for a MFEG is [3] E = E 0 + 1 8 (∇n) 2 n ,(5) where E 0 is the energy of a homogeneous MFEG with density n, see Eqn. (4). As discussed in Sec. I A, this gradient expansion would be useful for DFT calculations and so its computational verification is important.

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Also, the appropriate on-site energies are given by ǫ C = -1.40 t R and ǫ O = -1.40 t R . Hence, the effect of this adsorbed molecule on the electronic structure of the system can be calculated numerically. The band structure and the average LDOS of 10-AGNR with CO adsorption are shown in Figs. 2(b) and 3, respectively. The band structure, which corresponds to gas concentration x = 0.05, has been calculated for a configuration in which the molecule is connected to one of the ribbon edges. In comparison with Fig.

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This basis has the advantage of revealing the symmetry properties of the Lie group SU (2). The following analysis is made for a square pulse of duration p t and height E 0 starting at t=0. Using the unitary transformation ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ - = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ 3 2 1 3 2 1 2 cos 0 2 sin 0 1 0 2 sin 0 2 cos r r r R R R ϑ ϑ ϑ ϑ (6) where 2 2 2 2 2 sin , 2 cos Ω + Δ Ω - = Ω + Δ Δ = ϑ ϑ , we get the Bloch equations in the basis of dressed states. They have exact solution given by the roots of a quaternary equation corresponding to the system of differential equations (1)-( 2). An interesting case is when the pulse is in resonance with the QD transition energy (Δ=0). In this situation we obtain 1 M1 M2 M1 M1 M2 2 1 ) ( 2 1 ) ( 2 1 R R dt dR Γ + Γ - Γ Ω Ω - Ω Ω Γ - Γ - Ω - = λ (7) 2 M1 M2 1 2 ) ( 2 1 R R dt dR Γ + Γ - Ω = (8) λ λ ) ( 2 1 ) ( 2 1 M1 M2 1 M1 M2 M1 Γ + Γ - Ω Ω Γ - Γ - Γ = R dt d (9) ) ( 2 1 M2 R e I L Ω Ω + Γ = λ (10) where λ is invariant under unitary transformation (6).

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3 for two values of the boson number in the ring, and at varying interaction strength. As a general feature (see the inset of Fig. 3), we observe that at intermediate values of q the momentum distribution displays a power-law behavior n(q) ∼ q 1/(2K)-1 with the same power predicted for a homogeneous ring (see e.g. [7]). This result is readily understood as the different power laws described in Sec. IV A only occur at the edge of the integration region with a negligible weight with respect to the bulk contribution.

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In both circuits, a positive sign of the current corresponds to electrons flowing to the left. Below we present the results for a double quantum dot (DQD) or a QPC used as the detector-nanostructure. Double-dot quantum ratchet A schematic measurement layout for the case of the DQD-detector is shown in Fig. 2a. The DQD is formed by negatively biasing gates 1 to 5 and represents two quantum dots tunnel-coupled in series. The electron occupancies of the right and left dots are mainly controlled by voltages applied to gates 2 and 4, respectively.

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This has been addressed by several authors in the past. Solving a D-fold degenerate Hubbard model using the Gutzwiller approximation as well as slave-boson approach, it was observed that the critical value of U (= U c ) required for metal-insulator transition increases monotonically with the band filling, n. U c is maximum at half filling, [20] where U c ∼ (D + 1)W . The calculations based on dynamical mean field theory [21] suggested U c = 1.85 × W . Exact calculations [22] at half filling also suggest U c = √ DW . Consideration of inter-band hopping [23] indicated significantly more pronounced dependence of U c on the degeneracy. It is apparent that the lifting of degeneracy due to spin orbit coupling will push U c towards smaller values.

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15. Again there is a qualitatively similarity, with a peak at a similar energy, but now the NLσM peak is about 3 times too low and there is far too much spectral weight at high energies. The total spectral weight in the 3-magnon peak compared to that in the single magnon is found from DMRG to be 2.7%. The lower edge of the multimagnon band is given by the three magnon edge, c.f. Fig. 10. ing momentum k/3 is at 3ǫ( k/3) ≈ 3 ∆ 2 + (v k/3) 2 .

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22 These data agree well with our values of f H = 0.670(3) and 0.19287(2) for σ = 0 and 1, respectively. IV. PDF'S IN BIEXCITONS The PDF's of electrons and holes in biexcitons reveal important information about the physics of biexciton binding. The electron-electron PDF is defined as g ee (r) = 1 2πr δ(|r e↑ -r e↓ | -r) ,(4) where r e↑ and r e↓ are the positions of the up-and downspin electrons and the angled brackets denote the average over sets of electron and hole coordinates distributed as the square of the ground-state wave function. The holehole PDF is defined in a similar fashion. The electronhole PDF is defined to be where r eσer hσ h is the in-plane separation of an electron and a hole.

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The observability of beatings, predicted by the quantum approach, is also discussed in the end of the section. A. Experimental procedure Hereafter we present results obtained at the working point (I b = 2.222 µA, Φ b = -0.117 Φ 0 ). The experimental low power spectroscopy measurements (Fig. 2(a)) present a resonant peak centered at 8.283 GHz with a full width at half maximum ∆ν = 110 MHz. The resonance is interpreted in a quantum description as the transition from |0 to |1 at the frequency ν 01 .

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The experimental dependences (see Fig. 5b) also demonstrate the maximum with decrease. Thus it turns out that the behaviour of experimentally observed H c (T, t sweep ) dependence is qualitatively similar to results of our modeling for the case when intergranular interaction generates the state with correlated directions of particles magnetic moments and with a coercive field independent from measuring time. The above results illustrate the case when temperature T sf ("dimensional T ord ") of transition to such "superferromagnetic" state exceeds blocking temperature T b . The decreasing of intergranular interaction parameter λ can lead to opposite situation, when T sf < T b . In this case the variations of dependence H c ( √ T ) also occur near T sf .

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Each [G η sys (ω)] i,N is expressed in terms of [G η sys (ω)] i+1,N as [G η sys (ω)] i,N = F i [G η sys (ω)] i+1,N . Denoting by B = ω 2 + iη -A sys - Σ η L (ω) -Σ η R (ω) and f i = [G η sys (ω)] i,N , it holds, for 2 ≤ i ≤ N -1, B i,i-1 f i-1 + B i,i f i + B i,i+1 f i+1 = 0, f i = F i f i+1 . It is then easily shown that (2) Set [G η sys (ω)]1,N = g (BN,N + BN,N-1FN-1) -1 . F 1 = -B -1 1,1 B 1,2 , F i = -(B i,i + B i,i-1 F i-1 ) -1 B i,i+1 (2 ≤ i ≤ N -1) while f N = (B N,N + B N,N -1 F N -1 ) -1 , so that [G η sys (ω)] 1,N = f 1 = F 1 F 2 . . .

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( 8) implies that the potential energy is simply represented by a vector of dimension n b . The operator of the kinetic energy is non-local as it involves information of different points in physical space. As a consequence, t i1i2 m1m2 is not diagonal. Particularly, any finite difference method applied to approximate the second derivative, cf. Eq. (10), must be carried out with great care, since the basis functions χ i m (x) given in FE-DVR representation are continuous but do not have continuous derivatives at x i .

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Assuming the coherent coupling between the optical and acoustic phonons and using a mean-field approximation, the Hamiltonian (1) describing the interacting polaron can be reduced to H = H pol + ∆H with ∆H given by Eqs. ( 7), ( 13) and (18). Note that ∆H is temperature dependent and [apart from the parameters of the "non-interacting" Hamiltonian (2, 3)] entirely determined by the thermal expansion coefficient and the Grüneisen parameter. The term ∆H corresponds to a (pseudo-) relaxation time τ ∼ 1 ns, i.e., 2-3 orders of magnitude larger than the previous predictions based on the Fermi's Golden rule. This renders the anharmonic decay channel virtually irrelevant, at least for nanocrystal QDs where the polaron is formed by a small number of confined optical phonon modes most strongly coupled to the electron or exciton. Instead, the temporal evolution of the photoinduced polarization in a QD can proceed much faster just because of the quantum beats resulting from coherent many-body interactions.

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6 We used in the simulations the same materials parameters as those found for sample A except for ν D = 0.5. The result of our simulations for ∆E = 100, 200, and 300 meV is shown as symbols in Fig. 5. The curves were analyzed with a sum of activated processes as described by Eq. 2. All curves are well reproduced with the activation energies given in Table II.

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Note that for the width of the gap the vertical axis goes up to 0.7 eV while for the position of the Fermi level up to 0.5 eV. In table 2 we present the majority density of states exactly at the Fermi level. These results show the possibility of engineering the properties related to the gap just by changing the concentration in the low-transition metal and the sp atoms. For realistic applications we need three conditions (i) we should have a quite large gap in order to have stable half-metallicity, (ii) the Fermi level should be as close as possible to the center of the gap for the halfmetallicity to be robust since impurities and defects induce states at the edges of the gap [29], and (iii) the majority DOS at the Fermi level should be also high in order to produce significant spin-polarized current in real experiments. The first remark concerning figure 10 is that all three methods give almost identical results for the width of the minority-spin gap. This enhances even further our argument in section 3 that short-range interaction taken into account in the supercell calculations are not significant for the full-Heusler alloys.

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Born approximation and Markoff approximation are applied, and H T is treated by perturbation up to the second order. 53 The rate equation can be expressed in a compact form, ∂ t P l = l ′ R ll ′ P l ′ ,(12) where 0 ≤ P l ≤ 1 are the probability to find the state l ≡ |N, S, S z . The diagonal and off-diagonal terms of the coefficient matrix of the rate equations are, respectively, R l ′ =l = ασi R ασi l ′ =l , R ll = - l ′ =l R l ′ l ,(13)where R α↑i l ′ =l = Γ α cos 2 θ α 2 [| l ′ |d i↑ |l | 2 f (E l -E l ′ -µ α + ) +| l|d i↑ |l ′ | 2 f (E l -E l ′ + µ α + )] +Γ α sin 2 θ α 2 [| l ′ |d i↑ |l | 2 f (E l -E l ′ -µ α -) +| l|d i↑ |l ′ | 2 f (E l -E l ′ + µ α -)],(14) and one just replaces ↑ with ↓ and exchanges + and -to obtain R α↓i l ′ l . Note that the Fermi distribution f (x) = 1/[exp(x/k B T ) + 1] is spin-resolved. The param- eter Γ α = 2π k |V kαi | 2 δ(ω -ǫ kα ) represents the spinirrelevant coupling between lead α ∈ {(4, 5), (6)} and the grain. For simplicity, we assume that Γ (4,5) = Γ (6) = Γ, and Γ are assumed to be independent of the specific single-particle level i.

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Next, the Fermi energy is tuned to E F = 18meV , sitting slightly above the bulk gap. A positive gap parameter M = 2meV , for which there is no helical edge states inside the bulk gap for the clean sample, is chosen in the following simulations. The conductance G vs. disorder strength W shown in fig. 2(a) can be classified to four regions (i) without disorder, (ii) before the anomalous plateau, (iii) on the anomalous plateau, and (iv) after the anomalous plateau. The typical configurations of local-current-flow vector in such four regions are plotted in fig. 4.

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1 (c)). Finally, the PS spheres were removed by sonication in chloroform for a few seconds, resulting in periodic graphene nanodisk arrays (Fig. 1 (d)). To clean the graphene nanodisks, a vacuum (x10 -3 Torr) post-annealing process was conducted at 500 o C for 30 min by a Linkam thermal stage. Optical and SEM images are shown in Fig. 2 to demonstrate the result of each step described above.

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For direct comparison with experiments and other theoretical results, the experimental lattice constants of GaN (a = 4.50 Å) and InN (a = 4.98 Å) were used, while the lattice parameter of the alloy was determined by linear interpolation. Table I shows the reference states and cut-off radii used to construct the pseudopotentials used in this study. All pseudopotentials were generated using the OPIUM code 21 . Unlike with traditional density functional theory, Hartree-Fock pseudopotentials require extra care in their construction. This arises from the non-local form of the Hartree-Fock exchange potential 22,23,24,25 . The presence of the non-local exchange potential in Hartree-Fock or Hartree-Fock/DFT hybrids will often yield pseudopotentials with an unphysical, long-range tail.

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As we will see in following sections this creates interesting ingredients in the wave packet dynamics but initially, we will describe the semiclassical theory free of these complications assuming that electrons do not interact with the crystal potential and with each other [23]. The impurity free Hamiltonian of such an electron system has plain wave eigenstates ψ k (r, t) = 1 L D/2 e ik•r-i k 2 2m t ,(2) where L is the size of the system, D is its spatial dimension and k = |k|. To construct a wave packet with a well defined average momentum k c , plain waves (2) should be superposed with the envelope function a(k), sharply peaked near the point k = k c so that d D k|a(k)| 2 k = k c , then the wave packet vector can be written in the coordinate representation as follows Ψ kc (r, t) = d D k L D/2 a(k)exp i k • r - k 2 t 2m . (3) The normalization condition requires that Ψ kc |Ψ kc = d D rΨ * kc (r, t)Ψ kc (r, t) = d D k|a(k)| 2 = 1 (4) and the index k c tells that the wave packet has this average momentum, namely, switching to the momentum representation one can find that k c = Ψ kc | k|Ψ kc = d D k d D k ′ a(k)a * (k ′ ) k ′ | k|k = d D k|a(k)| 2 k.(5) The velocity of the free wave packet center of mass can be derived as follows ṙc = d dt Ψ kc |r|Ψ kc = d dt d D r L D d D k d D k ′ a(k)a * (k ′ )e -ik ′ r re ikr e i (k ′ ) 2 t 2m -i k 2 t 2m = d dt d D k d D k ′ a(k)a * (k ′ ) d D r L D e -ik ′ r -i ∂ ∂k e ikr e i (k ′ ) 2 t 2m -i k 2 t 2m = d dt d D k d D k ′ a * (k ′ )δ(k -k ′ )e i (k ′ ) 2 t 2m i ∂ ∂k [a(k)e -i k 2 t 2m ] = d dt d D k|a(k)| 2 kt m + d dt d D ka(k) * -i∂ ∂k a(k) = kc m . (6) In the external uniform electric field, the Hamiltonian operator is Ĥ = k2 /2+eE•r and the average of the momentum is changing with time kc = d dt Ψ kc | k|Ψ kc E = d dt d D k d D k ′ a(k)a * (k ′ ) k ′ |e i Ĥt ke -i Ĥt |k = d D k d D k ′ a(k)a * (k ′ ) k ′ | k, -ieE•r |k = -eE,(7) where k and r are respectively quantum mechanical momentum and coordinate operators. From (7) it follows that under the action of only the electric field the wave packet will accelerate indefinitely.

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Substituting the solution of Eq. ( 40) in the form u(r, t) = A α exp[i(mϕ + qζ -ωt)] (q and ω are the phonon wave vector and frequency, respectively, and α is the phonon mode) and keeping only leading terms in qR (qR 1), we get for TM phonons (m = 0): ω T = c t q, A T = A T (1, 0, 0),(42)for SM phonons (m = 0): ω S = c S q, A S = A S (0, 1, -iqRη) ,(43)and for BM phonons (m = 1):ω B = c S Rq 2 / √ 2, (44) A B = A B √ 2 i + iη(qR) 2 2 , -iqR, 1 - η(qR) 2 2 , (45)where c S = 2(c t /c l ) c 2 l -c 2 t , η = (c 2 l -2c 2 t )/c 2 l ; A j = /2M ω j (M is the NT mass). We see that TM and SM show linear dispersion, whereas BM exhibits quadratic dispersion. Note that these results are only valid for long-wavelength phonons (qR 1 and ω < ω RBM ). The electron-phonon coupling is expressed by the operator V el-ph = V 1 V 2 V * 2 V 1 + H.c.,(46)where for the K-point V 1 = g 1 (u ϕϕ + u ζζ ), V 2 = g 2 e 3iθ (u ϕϕ -u ζζ + 2iu ϕζ ),(47) u ϕϕ = 1 R ∂u ϕ ∂ϕ + u r R , u ζζ = ∂u ζ ∂ζ , 2u ϕζ = ∂u ϕ ∂ζ + 1 R ∂u ζ ∂ϕ ,(48) g 1 ≈ 30 eV is the deformation potential constant (which appears in diagonal elements of V el-ph ), and the off-diagonal coupling constant g 2 ≈ 1.5 eV (which is caused by change in the bond-length between neighboring carbon atoms). 36 Using Eqs.

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( 7) is such that , the applied potential to the tip. The conical part potential is modeled by the linear charge of length q D L ϕ + ϕ + ϕ ) 0 , 0 ( ) 0 , 0 ( L ϕ L with a constant charge density       θ - θ + πε = λ cos 1 cos 1 ln 4 0 V L q ϕ z ρ ϕ ) , ( Vr q 0 4πε ≈ , where θ is the cone apex angle. Additional point charge potential is chosen to reproduce the conductive tip surface as closely as possible by the isopotential surface . The contact area potential is modeled by a disk of radius, r (see Appendix B). Numerical calculations proved that the charge q is located at the end of the line at a distance of approximately the disk radius r from the surface, and that for a wide range of cone angles θ. It is clear from the Figure 6 that for a chosen geometry, the isopotential surfaceV = V z = ρ ϕ ) , ( reproduces the conductive tip shape in the vicinity of the surface for a wide range of cone angles θ.

cond-mat.mtrl-sci

(8) Combined with the completeness relation of the projectors, P 1 (i, j) + P n(n-1)/2 (i, j) + P (n+2)(n-1)/2 (i, j) = 1,(9) we can express the bond projection operators with the SO(n) generators as   P 1 (i, j) P n(n-1)/2 (i, j) P (n+2)(n-1)/2 (i, j)   =   -1 n(n-2) 0 1 n(n-2) n-1 2(n-2) -1 2 -1 2(n-2) n-1 2n 1 2 1 2n   ×   1 a<b L ab i L ab j ( a<b L ab i L ab j ) 2   . (10) Now we define our model Hamiltonian as H SO(n) = i P (n+2)(n-1)/2 (i, i + 1),(11) which is a bilinear-biquadratic Hamiltonian in terms of the SO(n) generators according to Eq. (10). This model has exact matrix product ground states, which will be extensively studied below. Although the exact excited states are not known, we argue that there is a finite energy gap above the ground states. For a projector Hamiltonian such as Eq.

cond-mat.str-el

For a given E F the interference of the edge states, labelled by n ± in Eqs. ( 6) and ( 7), is determined by the phase factors exp(ik ± n L). Here the wave numbers k ± n are given by k ± n = k F sin β ± n and L is the distance between the (very narrow) injector and collector. Both in the armchair and in the zigzag case one can show that around n ± = n ± max /2, which corresponds to |β ± n | ≪ 1, in good approximation the angles β ± n depend linearly on n ± . Expanding Eq. ( 6) around β ± n = 0 one finds that k ± n L ≈ πL R c n ± ± 1 4 -C a + k F L 3 π 4 n ± max -2n ± n ± max 3(8) where C a = π 4 k F L. This result means that if L/2R c is an integer (or equivalently, B/B f ocus is integer, where B f ocus = 2 kF eL ) some edge channels, with quantum numbers n ± centred around n ± max /2, can constructively interfere at the collector.

cond-mat.mes-hall

( 4) will be positive, which may converge to a sufficiently large value capable of overturning the satisfied criterion for single impurities. In addition, in the case of nanotubes, we have shown that the coupling magnitude tends to decay rather slowly as 1/D, where D is the separation between magnetic impurities [9]. Such a slow decaying rate will turn the summation of Eq. ( 4) into a non-convergent series in the limit N → ∞, meaning that the correction will always surpass the magnitude of ∆E 1 . The striking implications of this mathematical analysis are that spurious nonmagnetic solutions may be obtained if existing magnetic moments are artificially constrained to adopt a parallel alignment when they would spontaneously prefer to be antiparallel. This raises the question whether the recently reported absence of magnetic moments for Fe in graphene could be one such case [1].

cond-mat.mtrl-sci

Therefore, the screening of the antidot, and related metallic-like behavior of the system, is provided solely by the f c states, not by the (f c + 1)-th transport state. The latter crosses E F steeply and mediates the conductance oscillations in a similar fashion to that in the semi-classical Thomas-Fermi approximation. Fourth, the number of electrons N in an annulus around the antidot shows saw-tooth oscillations that reflects pinning and depopulation of f c edge states. Intervals of magnetic field with linear negative slopes of N and pinned states are marked by shaded regions in Fig. 5. The negative slopes of N in Fig.

cond-mat.mes-hall

The most common methods used for the structure prediction of solids are simulated annealing [6,7,8], genetic algorithms [9,10,11,12], basin hopping [13,14], or the recently introduced metadynamics [15]. Structure prediction usually involves a huge amount of CPU time, and therefore efficient ways to keep the calculations tractable have to be found. Thus, the procedures were initially split in two steps: first, a global search on the potential surface was performed. The energy was evaluated with empirical potentials, e.g. Coulomb and Lennard-Jones potentials, or chemically/physically motivated cost functions. After the global search, e.g.

cond-mat.mtrl-sci

[28]. A. CO on 10-AGNR We first emphasize that, according to the DFT calculations [21], the size of charge transfer between the molecules and the ribbon depends on the orientation of the molecules with respect to the ribbon surface. Moreover, the highest occupied molecular orbital in CO molecule is located on the C atom. Therefore, CO molecule is attached to a single atom of the ribbon via its carbon atom with the bond distance d C-C = 1.35 Å, while the bond length of the adsorbed CO is d C-O = 1.18 Å [28]. Inserting these values into Eq. 13, we obtain τ = 1.11 t R , and t C-O = 1.45 t R .

cond-mat.mes-hall

Our best estimate for the sublattice magnetization in this case, M = 0.20 ± 0.02, is in complete agreement with the best available by all other methods. The good agreement, both with respect to internal consistency checks using different extrapolations and with respect to other methods, for the gs properties of both the above models, gives us considerable confidence in our results for the spin-1/2 J 1 -J ′ 2 model for all values of κ ≡ J ′ 2 /J 1 . We also comment on the κ → ∞ (decoupled spin-1/2 1D HAF chains) limits of Figs. 4 and5. Firstly, Fig. 4 shows that at large J ′ 2 the extrapolated energy per spin approaches the value E/N = -0.4431J ′ 2 which is the same as the exact result 33 from the Bethe ansatz solution.

cond-mat.str-el

33 and summarized in the appendix) lead to effective diffusion terms for the amplitude (D - eff ) and phase (D + eff ) of the resonator about the limit-cycle, where the effective diffusion constants are valid on timescales long compared to the resonator period, but short compared to the damping rate. We find 36 that as well as the direct phase diffusion D + eff , we must also take into account another mechanism of phase diffusion. The frequency shift Ω ′ = Ω R -Ω depends on the amplitude, so any change in amplitude will lead to a change in frequency. 3 This means that a term describing amplitude fluctuations appears in the equation of motion of phase, and thus there are both direct and indirect contributions to the phase diffusion. We combine the terms arising from direct phase diffusion and the contribution from amplitude fluctuations (neglecting cross-correlations) to obtain the total linewidth γ φ = γ φ φ + γ n φ , γ φ = D ext + D + eff (E) 4 n + Ω lin γ lin 2 D ext + D - eff (E) n (21)whereΩ lin = E 0 dΩ ′ (E) dE E=E0 is the frequency shift linearized about the limit-cycle, and D ext = γext 2 at zero temperature. In Fig.

cond-mat.mes-hall

At the same time, the S z S z part of the interaction gives rise to the interaction term proportional to cos √ 8πϕ --πM whose scaling dimension is 2K -and which favors n-type spin-nematic (or XY2 in the nomenclature of Ref. [ 24]) correlations [ 25]. The transversal part of the zigzag exchange yields the so-called "twist term" sin √ 2πθ -(∂ x θ + ) that has a nonzero conformal spin and the formal scaling dimension 1 + 1/(2K -). The twist term favors states with spontaneous spin current [ 9]. If K < 1, as is the case for S = 1/2, the two interaction terms compete, which leads to the Ising-type transition between the nematic and spin-current state [ 12]. For S = 1 it is known that K > 1 [ 20,21,23], thus the nematic-favoring term is irrelevant and the spin-current favoring term dominates.

cond-mat.str-el

It is a remarkable observation that whereas the in-plane parameters are clamped to those of the substrate up to large film thickness, the out-of-plane parameter relaxes gradually when increasing thickness [5,12,13], indicating that the Poisson ratio changes with thickness. Thus, a simple model of elastic deformation under biaxial strain of the manganite lattice does not hold to this system. The common assumption of elastic deformation of lattices under strain was proven to be true in simple systems such as heteroepitaxies of metals and some semiconductors, although we recall that in some cases (SiGe, for instance) it has been recently shown that strain is relaxed via compositional changes [14]. It remains to be demonstrated that the assumptions of elastic unit cell deformation, constant unit cell volume and invariable composition as a function of film thickness still hold in the case of manganese perovskites. It is important to note that the elastic energy induced by epitaxial strain can also be relaxed in other ways depending on the real structure of the bulk manganite (rhombohedral or orthorhombic), the growth mode or the eventual chemical fluctuations [5]. Moreover, it has been proposed that interface effects, either due to symmetry breaking or strain, are prone to induce chemical [15] or electronic phase separation [13].

cond-mat.mtrl-sci

A representative curve for decreasing field at base temperature is plotted revealing the same qualitative behavior. For falling fields the field derivative is smaller, resulting in a worse signal to noise ratio. The data also show a second peak to the right (left) of H c1 and H c3 (H c2 and H c4 ). These peaks do not mark phase transitions but rather signify a zero temperature crossover between two distinct phases observed in our earlier work [18]. Inspection of Fig. 2 reveals that at lowest temperature the peak at H c4 is significantly higher than the peaks at the other three critical fields.

cond-mat.str-el

First, even though we have not performed a PSG study on rotation operators, intuition on rotation symmetry suggests that there should be four states (with S z = 1, -1, 0, and 0) located at k = (π, -π/ √ 3). Second, although our Chern-Simons theory is formulated with a fixed quantization axis for spin, the SU (2) spin-rotation symmetry should remain unbroken. Therefore, the S z eigenvalues should organize into SU (2) representations for each k value. While this is true for k = (π, π/ √ 3) and k = (0, 2π/ √ 3), where the "elementary" SQP form 1 ⊕ 0 representations, the same does not hold for k = (π, -π/ √ 3) and k = (0, 0). The two issues mentioned above indicate that some topological excitations are lost in our formulation. In other words, there are topological excitations that have trivial S z quantum numbers but non-trivial S quantum numbers.

cond-mat.str-el

Also, the pseudopotential results in Table II are in good agreement with the all-electron values for both the RRKJ and TM methods. On average the difference is less than 0.5 milli-Hartree (mHa) and the largest deviation is less than 1.5 mHa. This is a clear indication of the good quality of the pseudopotentials. Finally, the results obtained using the TM construction scheme are in excellent agreement with the equivalent results obtained by Trail and Needs [13]. Any small differences could be attributed to the different grids used, or the slight differences in the self-consistent HF procedure. In Table III, we show a similar study for the electron affinity of the first-and second-row elements.

cond-mat.mtrl-sci

VII for a typical experimental situation. On the other hand, at even higher temperatures the optical phonon power becomes dominant. To estimate also the temperature for this crossover, we consider some simplified models for optical phonons that may be relevant. The most obvious ones are the intrinsic in-plane longitudinal (LO) or transverse (TO) modes. For graphene on a dielectric substrate, the surface optical phonons of the dielectric must also be considered. 15,16 We find that the latter can begin to dominate the energy relaxation already at much lower temperatures than the intrinsic phonons.

cond-mat.mes-hall

Follow- ing Refs. [21,22], the average number of electrons is determined by the lesser Green function G < (t 1 -t 2 ) = i d † (t 2 )d(t 1 ) as n = -i G < (ǫ) dǫ 2π . The calculation of the Green function is a nontrivial task even in the single-level model. It is simplified in the important limit of low vibron frequencies, ω 0 ≪ Γ < ǫ p , where the Born-Oppenheimer approximation holds true. We used the equation-of-motion approach in this case. In Fig.

cond-mat.mes-hall

The phonon spectrum is affected by the transition only for momenta fairly close to π. The situation is different for larger ω 0 . Fig. 3 displays a density plot with ω 0 = 1.0 and g = 1 which is close to but above the critical coupling. There is a central peak branch, which is now separated from the Einstein phonons, even above the transition. No softening was observed at this larger ω 0 , even at a large coupling of g = 1.6.

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VI. OPTICAL PHONONS For graphene, its multilayers, and graphite the phonon spectra have been studied in detail both experimentally and theoretically. [29][30][31][32][33] In order to describe the crossover from acoustic phonons to optical phonons as the dominating phonon type for heat dissipation, we use some simplified optical-phonon models. For the description of the intrinsic optical modes an atomistic description is needed as a starting point. However, we skip the details here (see App. B), as similar calculations have been reported earlier.

cond-mat.mes-hall

[7]. Namely, the thermodynamic characteristics (like specific heat, magnetization etc) consist of the low temperature LFL scale characterized by the fast growth and the high temperature one related to the NFL behavior and characterized by the slow growth. These scales are separated by the kinks in the transition region. Obtained theoretical results are in good agreement with experimental facts and allow us to reveal for the first time a new scaling behavior of both magnetoresistance and kinks separating the different energy scales. ACKNOWLEDGEMENTS This work was supported in part by the grants: RFBR No. 09-02-00056, DOE and NSF No.

cond-mat.str-el

The mechanism of this additional channel of the radiation absorption and the resulting MPGE are out of scope of this paper. VI. MICROSCOPIC MODELS AND DISCUSSION The most surprising result obtained in the experiment is that in samples with L W = 12 nm and L W = 22 nm, as well as in the sample with L W = 8 nm at low temperature, the cubic-in-B contribution to J is strong and may overcome the linear-in-B contribution at the magnetic field of 4÷5 T. Therefore, we focus below on possible microscopic mechanisms of such a non-linear behavior which is observed in QWs with the inverted band structures only. Since to the best of our knowledge the band structure of HgTe/HgCdTe QWs in in-plane magnetic fields is not available, we perform here only a qualitative microscopic analysis of the effect. First we discuss the terahertz spectral range where radiation absorption is dominated by Drude-like processes. In this case, the photocurrent is mainly caused by asymmetry of the electron scattering by phonons and static in the magnetic field.

cond-mat.mes-hall

Keeping the best third neighbor l and assuming R i = 0, we obtain a quantum interference contribution ∆σ 0 (B) = σ 0 2t il t lj t ij (ε i -ε l ) cos e B • (R l × R j ) -1 . (30) The average in Eq. ( 30) is over the percolation network and gives a negative magnetoresistance, according to Schirmacher 44 . In general, one has to note that all hopping contributions below 1T are at best a few per cent, and nowhere near the large values observed by Van Esch et al. 7 . This completes the hopping analysis.

cond-mat.mtrl-sci

We fix γ using the coordinates at which γ passes through a Poincaré surface of section taken at A. Following Refs. 47,48,49,50, we parameterize a position on the Poincaré surface of section using the stable and unstable coordinates of the classical dynamics at A. The phase space point A is taken to be the origin of the coordinate system; The stable and unstable phase space coordinates of the point where γ passes through the Poincaré surface of section at A are labeled s A and u A , respectively. The precise values of s A and u A will depend on where we choose the reference point A along the encounter. Moving A along the encounter, s and u change ∝ exp(±λt), where λ is the Lyapunov exponent of the classical dynamics in the sample.

cond-mat.mes-hall

We suggest our finding may be related to the rarity of solids in nature having spontaneous currents in their ground state 39 .A. Summary The central results of this paper are as follows. We emphasize first that our microscopic Hamiltonian was limited to (mainly spinless) models with interactions and one-fermion hopping terms. We did not explore the possibilities of correlated hopping, which were already known to be conducive to the "d-density-wave" current order 4,36 . Ultimately such terms come microscopically from higher-order processes in fermion hops; thus, within our picture, related terms might be accessed by expanding our canonical transformation (Sec. III and Appendix A) to higher orders, producing effective interactions with higher powers of pseudospin.

cond-mat.str-el

Figure 2 shows some of the representative SHPM images as a function of magnetic field with increasing and then subsequent decreasing field at 120K when reached from 300 K (i.e. reached by cooling). All the images, shown in figure 2, are plotted on same scale after subtracting the applied magnetic field. The labels on these images are marked on corresponding ρ -H and M -H curves (plotted in the middle row of figure 2) to correlate these results. Image (a) of figure 2, taken at 0.5 Tesla shows inhomogeneous magnetic state where both FRI (blue) and AFM (red) phases co-exists. The image contrast remains almost same with further increase in magnetic field to 1 Tesla, image (b), which is consistent with almost constant ρ and M between these field values.

cond-mat.str-el

One begins at high energies and short wavelengths and works one's way down to low energies, taking into account the modes that are integrated out through changes in the parameters of the action of the remaining modes. This process is called renormalization, and the change of the parameters from high to low energies is called the RG flow. Later, Polchinski 2 formulated the renormalization group as an exact flow equation for the partition function of the theory. In the following, this was generalized to other generating functionals, such as the one for one-particle irreducible (1PI) vertices that will be used in this work. The flow equations for this generating functional were first derived for scalar fields by Wetterich 3 , and later for fermionic systems 4,5,6 . By now it has been widely used to investigate many-fermion systems in various contexts (e.g.

cond-mat.str-el

To our knowledge, there is no effective mechanism of inhomogeneous broadening of the spin dephasing rate for free electrons in this sample system. Hence, a strictly monotonic increase of the Q-factor with the magnetic field is expected in sample B. Last, we study the magnetic field and temperature dependence of g * . To our knowledge, similar investigations were only carried out for undoped or very low n-doped bulk GaAs samples [20,21]. Figure 3 shows the magnetic field dependence of g * for sample A and B at 25 K. A linear fit to the magnetic field dependence of g * between 0.5 T and 3 T yields a very small magnetic field dependence of g * A = -0.4292(2) + 0.0003(1) T -1 • B for sample A and g * B = -0.4100(2) + 0.0003(1) T -1 • B for sample B at T = 25 K. The gradient dg * /dB is by more than one order of magnitude smaller than for free electrons in undoped GaAs [20] or for donor-bound electrons at higher magnetic fields [21], where g * (B) increases in both cases by 0.005 T -1 due to the energy shift of the lowest Landau level which is occupied by all electrons. At the doping densities examined in this work, either Landau quantization is suppressed because of momentum scattering or several Landau cylinders are occupied since the cyclotron energy is rather low compared to the Fermi energy.

cond-mat.mes-hall