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The two arrows indicate the energy levels that avoided cross when the electron is removed of the dot in which the hole is localized. Letters (a,b) mark the bright energy levels of the same family (with the hole localized in the same dot) that appear for F << 0, F ≃ 0 and F >> 0, respectively. II. MODEL AND METHOD The model and the computational method are those as were presented in Ref. 27 for two coupled dots. This approach accounts for the electron-hole correlation in the external electric field assuming the single valence band approximation and a simple confinement potential model. | cond-mat.mes-hall |
(ii) In the previous QSHE, the edge states only carry a spin current while at equilibrium; in this QSHE system, the edge states carry both spin and charge currents at equilibrium with the two edges states being CT partners of each other (see the inset in Fig. 1a). Thus, this is a new kind of QSHE and the system is a new type of topological insulator. Due to the topological invariance, the plateaus of the spin Hall resistance are robust to disorder or impurity scattering. So the plateau is very stable and its value can be used as the standard value for the spin Hall resistance. In the tight-binding representation, the four-or sixterminal ferromagnetic graphene device (see the insets in Fig. | cond-mat.mes-hall |
2,4,15,16 IV. FAST SPIN ROTATION VIA NON-ADIABATIC PASSAGE THROUGH BENDS As a second example of spin manipulation, we consider the geometry in Fig. 4(a), consisting of two straight segments on either side of a single bend, with radius of curvature r, forming an angle 2θ. Two quantum dots, denoted a and b, are defined by gates on the straight segments of this "coat hanger" shape, and the external field is applied in the plane, at an angle ϕ with respect to the symmetry axis. Effective fields B * a and B * b in the two dots differ in both magnitude and direction. In particular, the angle η between B * a and B * b , given by sin η = (g -g ⊥ ) 2 cos(2θ) + (g 2 ⊥ -g 2 ) cos(2ϕ) sin(2θ) 2b(θ + ϕ)b(θ -ϕ) ,(11) can reach η = π/2 for realistic device parameters. | cond-mat.mes-hall |
Recent experiments report an agreement with the theoretical predictions of Refs. [6,7] for either the conductance [9] or the Fano factor [10]. Furthermore, the temperature dependence of the conductivity [11] also shows an approximate agreement with the ballistic theory generalized to finite temperatures [12]. However, even for low temperatures, the convergence with W/L → ∞ is much slower than predicted. In particular, for the largest aspect ratio W/L = 24 studied in Ref. [10] the deviations from the limiting values GL/W = σ 0 and F = 1/3 are close to 10%, whereas results of Ref. | cond-mat.mes-hall |
I. INTRODUCTION Hole-doped manganites, such as La 0.67 Ca 0.33 MnO 3 , have been widely studied, not only because they exhibit colossal magnetoresistance (CMR), but also because of interest in the coupled metal-insulator (M -I) and ferromagnetic-paramagnetic transition they demonstrate. One unanswered question is how electronic phase separation (PS) occurs, that is its spatial structure as function of temperature and magnetic field, and how that connects to the CMR effect observed in transport measurements. Local-probe techniques, such as scanning tunneling microscopy (STM) and magnetic force microscopy, would seem to be ideal tools to explore this, and a number of groups have studied thin-film manganites using these methods. 1,2,3,4,5,6 Some reports find PS on the scale of many nanometers up to micrometers. Because of the electrostatic energy cost of domains on the order of micrometers, phase separation should be limited to nanometers, unless large disorder is present, 7,8 suggesting that disorder must play a role in such large-scale PS. | cond-mat.str-el |
The frequency variable in Π(q) is omitted from now on. The bare polarization bubble (without any interaction lines in the loop) is known to be Π (0) (q) = -i k dω 2π Tr{ Ĝ(k, ω) Ĝ(k + q, ω)} = -|q|/(4v). (6) From now on the trace stands for summation over spin (s), valley (v) and pseudospin (Pauli matrix σ) indices, i.e. Tr = s,vTr σ = 4Tr σ .A) B) FIG. 1: First order interaction corrections to the polarization bubble: (a.) self-energy correction, (b.) | cond-mat.str-el |
In the region of 0 < θ < π 2 , 1q-and 3q-modulations emerge from the first and second terms of Eq. (3), respectively. In reciprocal lattice space, the satellite peaks corresponding to the 1q-modulations appear at τ even ± (0, q, 1 2 ) and τ odd ± (0, q, 1 2 ), and the satellite peaks corresponding to the 3q-modulations appear at τ even ± (0, 3q, 1 2 ) and τ odd ± (0, 3q, 1 2 ), as shown in Fig. 9(b). According to the results of recent magnetization measurements, 29 the canting angle θ at H b = 4T is roughly estimated to be 5 • ∼ 10 • . In the region of θ < 10 • , |P (τ odd ± (0, 2q, 0))| 2 decreases slightly with increasing θ, and the intensities of the other Fourier spectra are quite small compared with |P (τ odd ± (0, 2q, 0))| 2 , as shown in Fig. | cond-mat.str-el |
Note that P is defined as the sum of K1 and K2, but the latter are not drawn to avoid clutter. available to K 3 once K 2 and K 1 have been selected are given by the thick gray lines in the figure. Notice that while k 3 can still take any values -Λ < k 3 < Λ within the annulus, the angle of K 3 has become highly constrained. However, it is clear that even when K 4 = 0 the value of Λ/K F can still be nonzero. We now know the dimension [u f ] when we restrict to K 4 = 0. However, the three cases corresponding to K 4 = 0 constitute only a small portion of ( K 1 , K 2 , K 3 )-space. | cond-mat.str-el |
In contrast to the wide range of values found for ρ 3D , the same data plotted as ρ 2D (Fig. 2 (b)) shows that the data for all of the metallic samples essentially collapse to a narrow range of ρ 2D values. This indicates that the LaVO 3 film itself is indeed insulating, and that the interface forms the conducting channel. For LaAlO 3 /SrTiO 3 interfaces, several groups have reported that the conducting interfaces they have studied may arise from growth induced oxygen vacancies in the SrTiO 3 substrate [17,18]. This is particularly important to address for the LaVO 3 /SrTiO 3 interfaces studied here, since oxygen post-annealing is generally unavailable due to the further oxidation of the film (forming LaVO 4 ). Already the scaling of ρ 2D shown in Fig. | cond-mat.str-el |
The crucial difference between the two is that one-site DMRG is strictly variational in the sense that the energy is monotonically decreasing with each step,, whereas in two-site DMRG the energy may (slightly) increase in some steps, but with the advantage that the cutoff dimension can be chosen dynamically in each step. Two-site DMRG Two-site DMRG arises when variationally optimizing two sites at a time. We consider two current sites, say k and k + 1, and we may choose the cutoff dimension site-dependent: D → D k ≡ dim(H l k ). Following section A.2.4, we assume site k to have an orthonormal left basis and site k + 1 to have an orthonormal right basis. After contracting the indices connecting A [σ k ] and A [σ k+1 ] (see figure A6), the state is described byA [σ k σ k+1 ] l k r k+1 . In this description we may optimize the ground state locally by variationally minimizing the ground state energy with respect to A [σ k σ k+1 ] l k r k+1 (see section A.3.1). | cond-mat.str-el |
The ferromagnetic ordering along the b-axis is indeed evident in magnetization measurements under similar conditions [21]. The work we present here unambiguously proves that the commensurate P a phase in TbMnO 3 coincides with an ab Mn spin cycloid for H b=5T. The antisymmetric DM interaction in this case does yield a ferroelectric polarization along the a-axis as indeed is observed (P s a = τ × (S i × S i+1 ) = c × b). We may thus identify the inverse DM interaction as the main mechanism for the magnetic-field induced flop of ferroelectric polarization. In a perfect cycloidal magnetic arrangement the exchange mechanism proposed in references [13,14] does not yield any ferroelectric polarisation, as the scalar product (S i • S i+1 ) of neighboring spins is everywhere the same. This still holds for the commensurate perfectly circular spiral. | cond-mat.str-el |
21). In a Taken as M(50 kOe)-M(30 kOe) 20 kOe ,in unit 10 -3 emu/mol b in unit mJ/molK 2 c Eqn. 2 is invalid for T = Os and Rh; see text the same Fermi level position as YFe 2 Zn 20 because of the same valence electron filling. However, its total, and partial-Ru, DOS are lower than those for YFe 2 Zn 20 . This difference is not unexpected, since the 4d band is usually broader than the 3d band in the electronic structure of intermetallics. Calculated N(E F ) of YCo 2 Zn 20 is half of the value of YFe 2 Zn 20 , whereas the value of YRu 2 Zn 20 is slightly larger than YCo 2 Zn 20 (Table IV). | cond-mat.str-el |
The specific feature of the resonant CPGE in GaN heterojunctions is that the symmetric and asymmetric components of the photocurrent have comparable strengths. j spin /j orb ∼ Λ ξ (α 1 -α 2 )ωτ( Acknowledgments We thank E.L. Ivchenko, V.V. Bel'kov and S.A. Tarasenko for their permanent interest in this activity and the many discussions that helped to clarify the problem under study. The financial support from the DFG and RFBR is gratefully acknowledged. Work of L.E.G. is also supported by "Dynasty" Foundation -ICFPM and President grant for young scientists. | cond-mat.mes-hall |
For free fields, the normal ordering (19) coincides (up to an overall constant) with the normal ordering : • • • : used to define the vertex operators in (1). That P(η) as defined above is an eigenstate of the total charge follows directly from the commutator, [Q,H -1 (η)] = -1 m H -1 (η) , while the quasilocal nature of the charge is revealed by studying the commutator with the localized charge operator Q(η; ǫ) = 1 √ m 1 2π η dz ∂ϕ(z),(20) where the contour is a circle of radius ǫ around η. We get [Q(η; ǫ), P(η)] ≈ -1 m P(η) up to an exponentially small correction for ǫ ≫ ℓ. Since J p is expressed in the shifted field φ, it is convenient to use the relations (12) to express the original vertex operators, V , in terms of the Ṽ 's, with the understanding that the expectation values are now taken using the action S[ φ] (11), and with the modified charge neutrality condition (14). In this way we directly calculate the polynomial part, Ψ (hol) 1qp (η; z 1 . . | cond-mat.mes-hall |
However, for a very small Z, η has to be really small before the peak is seen. As in the 1D case, we also observe the fractionalization of the spectrum for moderate and large effective couplings, with a succession of discrete peaks and continua at higher energies. We expect similar behavior to be observed in 3D as well. Clearly, the changes in going from MA to MA (1) and MA (2) are quantitatively much smaller in 2D than in 1D, because the continua have so little weight. We expect the trend to continue in going to 3D, meaning that in 3D, the difference between MA (2) and MA should be quantitatively even less. Indeed, all the comparisons of MA results with available 3D numerics, shown in Ref. | cond-mat.str-el |
The difference in magnitude from our result may in part originate from the fact that the 75 A hf values for both directions are estimated using χ ab and χ c , not χ of the powder sample. Since the single crystal is hard to obtain (and the obtained crystal is small compared with that of the 122 system 27) ) and both microscopic and macroscopic magnetic susceptibilities are small, the precise anisotropy of the hyperfine coupling constant in the FeAs-based 1111 system seems to be hard to obtain as argued above. For this reason, our results must aid in the study of the FeAs-based 1111 system, though they contain ambiguities in the magnitude of the hyperfine coupling constant. Finally, we would like to discuss the spin fluctuations. To observe the ferromagnetic spin fluctuations of the sample, we must study the temperature dependence of nuclear spin-lattice relaxation rate (1/T 1 ), as reported by Sugawara et al. in the case of 31 P NMR in LaCoPO. | cond-mat.str-el |
However, Hilton and Tang [3] recently showed that pump-probe techniques could be used to probe the hole spin dynamics in bulk GaAs. They found a time of τ h = 110 fs for the hole spin relaxation time, which has spurred theoretical investigations [4]. All such techniques measure optical orientation indirectly by monitoring, after excitation, the population in various bands, or its effect on luminescence or Faraday rotation [5,6]. In this manuscript we present an approach for the direct measurement and study of ultrafast optical orientation. While we focus on GaAs, the technique is applicable to a wide range of semiconductors. It relies on the magnetization that accompanies the injected spin density in optical orientation: Under ultrafast excitation this magnetization varies rapidly over a sub-picosecond timescale, and radiates in the terahertz (THz) regime. | cond-mat.mtrl-sci |
According to Fig. 10, the stability of the QW networks scale with their size M similarly to the case of random scatterers: given values of F 2 is reached at temperatures that decrease as a function of M slower than linearly. FIG. 9: (Color online) The measures of functionality given by Eqs. ( 13) and ( 14) for rectangular 3 × 3 and 5 × 5 quantum ring arrays as a function of temperature. The ring sizes and the SOI strengths correspond to the ideal operation described in the text. | cond-mat.mes-hall |
I. INTRODUCTION In the last decade the possibility of a superfluid alkali atom Fermi gas has attracted much attention both theoretically [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and experimentally 15 because this phenomenon opens a new opportunity to study strongly correlated quantum many-particle systems and to emulate high-temperature superconductors. Optical lattices are made with lasers, and therefore, the lattice geometry is easy to modify by changing the wavelength of the intersecting laser beams. Near the Feshbach resonance the atom-atom interaction can be manipulated in a controllable way because the scattering length a s can be changed from the BCS side (negative values) to the BEC side (positive values) reaching very large values close to resonance. We focus our attention on the BCS transition (negative scattering length) of degenerate fermionic gases to a superfluid state analogous to superconductivity. In particular, we consider an equal mixture of 6 Li atomic Fermi gas of two hyperfine states |F = 1/2, m f = ±1/2 > with contact interaction loaded into an optical lattice. | cond-mat.str-el |
We summarize in Table 2 the total moments per formula unit (M ), half-metallic gaps (G HM ) [27], and the energy differences per formula unit (∆ E = E AF -E FM ) for all the three sulvanite Cr 3 4 phases (X=S, Se, and Te), where E AF and E FM are the total energies for the AF and FM spin configurations. Here we define G HM as the smaller of E cb and E vt , where E cb is the bottom energy of the minority-spin conduction bands with respect to the Fermi level and E vt the absolute value of the top energy of the minority-spin valence bands. Our GGA G HM values should be rough estimates for the minimal energies for spin flip excitations. We obtain 10µ B for the magnetic moment per formula unit in all the three cases. This is because we have ten Cr d electrons to contribute to the moment after eight of the eighteen Cr electrons of the three Cr atoms are bonding with the sixteen X p electrons of the four X atoms. The half-metallic gaps are larger than the corresponding zb-CrX phases because the Fermi levels move toward lower energy level due to the fact that there are one less Cr atom for Cr 3 X 4 , compared with the cubic zb unit cell including four Cr and X atoms. | cond-mat.mtrl-sci |
Although the current is well below the threshold, the wall can shift slightly as we see below (for about a distance of µm, but this would be an overestimate). Under small current, φ 0 remains small, and the equation of motion reduces to that of a "particle"; M w Ẍ + M w τ Ẋ + M w Ω 2 X = F (t),(88) where M w is the wall mass, τ ∝ α -1 is a damping time, Ω is the (extrinsic) pinning frequency, and F (t) is a force due to current. For AC current, I(t) = I 0 e iωt , where ω is the frequency, the force is given F (t) = I(t) e 2 S λ β -iP 2 ω K ⊥ λ , where β, given by Eq. ( 73), is from momentum transfer and spin relaxation (β sf ), and the last term proportional to ω is from the spintransfer torque. The wall under weak current thus shows a forced oscillation of a particle. By measurering the energy dissipation (from complex resistance), a resonance peak would then appear when ω is tuned closely around Ω. | cond-mat.mes-hall |
The two dashed blue lines represent (i) an interpolation λ Ĥeff + (1λ) ĤRK between the RK model and the effective model for the Heisenberg quantum antiferromagnet and (ii) a cut at γ = 1 along J12, and correspond to the simulations performed in reference 7. Red lines are qualitative phase transitions. Note that for γ > 0.9 a finite J12 lifts the degeneracy between two VBC's with identical 36-site unit cells but opposite parities P± of their resonating pinwheels (in yellow). tice as well as other numerical studies of a generic QDM on the triangular lattice 39 strongly support such a scenario. Even though the Z 2 phase has no broken symmetry, it does have a topological order. In principle, the topological order can coexist with the VBC, and so their disappearance at a common critical point without fine-tuning, can be considered as a non-LGW (Landau-Ginzburg-Wilson) transition 40 . | cond-mat.str-el |
In all samples where the kinks in α(T ) can be identified the corresponding temperatures T α kink appear about 10-20 K below T c , see Figs. 3 and4 andTable I. This suggests some correlation between ferromagnetism and the kinks. However, for a conventional ferromagnetic order with a pressure-dependent T c one would expect a clear anomaly in α(T ) at T c , similar to the corresponding anomaly of the specific heat c p . However we do not observe clear c p anomalies at T c , either, as discussed below. This suggests that the ferromagnetic order in La 1-x Ca x CoO 3 is rather unconventional as has been proposed recently based on relaxation time measurements of the dc magnetization, too. | cond-mat.str-el |
2). Furthermore, by applying field µ 0 H c, the two kinks become separated to form two peaks, providing clear evidence for the successive transitions. Here, we define T N1 and T N2 by the locations of the lower and higher tempera-ture kinks or peaks, respectively. Under field µ 0 H c, the IMP in between T N1 and T N2 becomes stabilized, while under µ 0 H ab, T N1 approaches T N2 with increasing field, and finally the IMP disappears under µ 0 H > 4 T (Fig. 2(b)). A broad tail of the peak seen at T ≥ T N2 suggests an enhanced 2D spin fluctuations. | cond-mat.str-el |
( 70)] with its spin counterpart where h is a local magnetic field that enters an additional Hamiltonian term Ĥs,loc = h 2 (n d↑ -nd↓ ). χ s,loc (T ; ω = 0) = -lim h→0 nd↑ -nd↓ 2h ,(89)(90) In particular, characteristic energy scales for the spin and charge Kondo effects are expected to be 1/χ s,loc (ω = 0, T = 0) and 4/χ c,loc (ω = 0, T = 0), respectively [where the factor of 4 accounts for the difference in conventions that φ couples to nd -1, whereas h couples to (n d↑ -nd↓ )/2]. Figure 21 plots the λ dependence of these quantities for the parameter set illustrated in Figs. 18 and 19. The Kondo resonance width 2Γ K crosses over from paralleling 1/χ s,loc (0, 0) for small λ to loosely tracking 61 4/χ c,loc (0, 0) as λ approaches λ c . In the intermediate region near λ = λ c0 , 2Γ K is much smaller than either inverse static susceptibility, indicating that the Kondo effect has mixed spin and charge character. | cond-mat.str-el |
Standard techniques based on measurements of the Hall conductivity are obstructed by the considerable anomalous contribution which can be much greater than the standard Hall conductivity. Recent advances in spintronics, especially the creation of new types of diluted magnetic semiconductors, revived the interest in the AHE as a useful tool to control spinpolarized currents and to characterize the magnetization. In addition, the recent theoretical interest has been fueled by the new interpretation of the anomalous Hall conductivity in terms of Berry phases and topological defects in the crystal band structure. Many theoretical constructions that usually had been considered of relevance mainly in high energy physics such as noncommuting coordinates and magnetic monopoles, became useful and even measurable in experiments on the AHE [1,2,3,4]. Despite the long history and the considerable practical importance, the theory of the anomalous Hall effect has remained controversial. The first steps to explain the AHE in ferromagents were made more than 50 years ago. | cond-mat.mes-hall |
11. For small angles between H and S ′ m or S ′′ m , only one peak is observed. At larger angles, the positions of two peaks can be resolved. Two different symbols are used to represent the two different spin substructures, while for spectra with single peaks, a third symbol is used. Since the angle between the spin direction and the b-axis is much less than one radian, cos α i in Eq. ( 3) for the field in the a-b plane can be approximated by cos α 1,2 ≈ cos(θ ′ m ± ∆θ ′ /2 -θ ′ H ),(4) where α 1,2 are the angles between the field and the two spin directions S 1 and S 2 , respectively. | cond-mat.str-el |
[1][2][3] Accompanying this transition, the electronic state also changes: above T MI , a metallic shortrange charge order (CO) characterized by a diffuse rod, q = (1/3, k, 1/4), is observed in X-ray measurements, 4 while below T MI , an insulating long-range CO characterized by a diffuse rod, q = (0, k, 1/2) ≡ q 1 , is observed in NMR, X-ray, Raman scattering, and optical conductivity experiments. [4][5][6][7][8][9][10][11][12] The latter CO is called the horizontal CO, which has two-fold periodicity in real space. On the other hand, when X is CsM ′ (SCN) 4 (M ′ =Co, Zn), the crystal remains θ type down to low temperature and no phase transition is observed. 1 Above 20K, it is metallic and a short-range 3-fold diffuse rod, q = (2/3, k, 1/3) ≡ q 2 , is observed. At about T = 20K, the resistance starts to increase by 10 4-6 times accompanied by an appearance of the short-range diffuse rod at q = q 1 , which coexists with q 2 . 13,14 The wave number, q 1 , is same as that observed in Rb salts below T MI i.e., the horizontal CO. | cond-mat.str-el |
To demonstrate this we show in Fig. 5(a) and (b) a comparison of the equilibrium monoclinic lattice calculated from MEAM and used throughout this paper with that obtained by Rietveld refinement of the X-ray powder diffraction measurements [29], respectively. Clearly, the positions of atoms calculated from the MEAM potental for Pu do not correspond to the experiment. The most notable feature is an unphysical hexagonal symmetry that can be seen clearly by rotating the unit cell about the horizontal a axis. The origin of this discrepancy is presumably the inability of the potential to account for strong directional bonding arising from the overlap of the f orbitals as the volume of the crystal is decreased and the symmetry of the parent fcc phase (48 symmetry operations) is broken into 12 variants of the monoclinic lattice (4 symmetry operations). The observation that the current MEAM potential for Pu does not represent with reasonable accuracy the positions of atoms in the α phase of Pu raises serious concerns when calculating the transformation pathway between the δ and α phases. | cond-mat.mtrl-sci |
3b) is much larger than that obtained from XRD data (~ 22 nm). This represents the fact that SEM is not the suitable tool to estimate the particle size, as the scale (micrometer range) of SEM data is larger in comparison with the particle size in nanometer range. This means the SEM picture indicates the size of multigrained particles. The mapping (Fig. 3c-e) suggests a uniform distribution of Cr, Fe, O atoms over the zone. Achieving some basic knowledge of the structural properties (i.e., size, shape, composition, and crystal structure) of the samples, we have attempted below to understand the magnetic properties of the samples. | cond-mat.mtrl-sci |
Introduction.-Interference phenomena are the most prominent feature of quantum mechanics. Of particular interest are interference effects in multi-particle states. For example in optics, the Hanbury Brown-Twiss effect [1] and the Hong-Ou-Mandel (HOM) effect [2] both result from two-particle interference of photons emitted by two independent sources. In mesoscopics, electrons can play a role similar to photons in optics. In an electrical circuit with currents incoming from different (uncorrelated) equilibrium contacts the noise can show interference even if the currents exhibit no interference contribution [3]. Recently a single-particle emitter [4] was experimentally realized on the basis of a quantum capacitor in a two-dimensional electron gas in the integer quantum Hall effect regime. | cond-mat.mes-hall |
In 2003, vertically aligned single-walled carbon nanotubes (VA-SWNTs) were realized 2 by using alcohol catalytic CCVD (ACCVD). 3 VA-SWNTs have now been achieved using several CVD methods and conditions. [4][5][6][7] As a result, CCVD from substrates now has potential as a process in the mass production of SWNTs. Among those growth methods, the water-assisted method, so-called "super growth", 4 realized an outstanding growth rate of a few micrometers per second, leading to millimeter-thick VA-SWNTs forests. However, many research groups have failed in reproducing "super growth", and the underlying mechanism of the growth rate enhancement by water remained unclear. By using our combinatorial method for catalyst optimization, 8,9 we recently reproduced the "super growth" method and showed the important role of catalyst supports. | cond-mat.mtrl-sci |
(40) At the end, we interpolate to have the Green's function for the next iteration, G n+1 β α (ω) = αG n+1 β α (ω) + (1 -α)G nβ α (ω) ,(41) In the iteration procedure we iterate this loop until the ǫ n become small enough, in some nth order, which means that the Green's function is converged. When we reach this point we can extract spectral functions from the resulting Green's function from ρ iσ (ω) = - 1 π Im G R iiσ (ω) ,(42) in the followings in many of the cases, we will use the total spectral function, ρ T (ω) = i,σ ρ iσ (ω), or a spectral function only summed up for the spins. D. Limitations We have seen in paper I that the IPT suffers from instability at large values of U/Γ and J/Γ parameters. Similar kind of instability exists in the FLEX scheme: from arbitrary starting Green's function the iteration converges only at small values of U/Γ and J/Γ. The error caused by the not satisfactory behavior of the self-energy contributions for large U/Γ and J/Γ parameter rates, if we use the hybridized Green's function to obtain the selfenergy. But in opposition to IPT, starting from a converged Green's function, high enough interaction parameters can be reached by increasing the interaction parameter in small steps. | cond-mat.str-el |
Small threshold current at 140K would be due to reduction of magnetization close to T C = 150K. The threshold current is about 2 orders of magnitude smaller than in other metals. This high efficiency would be due to a very narrow domain wall, λ ∼ 3nm, as a result of very strong uniaxial anisotropy energy (K) corresponding to a field of 10T. They defined a parameter determining the efficiency as a ratio of depinning field and depinning current density, Λ ≡ B c /j c . Their results were Λ = 10 -12 Tm 2 /A. They compared this value with threshold current of extrinsic pinning, 9 given by Eqs. | cond-mat.mes-hall |
This behavior can be easily understood: (i) if S ox = S oy = 0 and S oz ≠ 0, in zero magnetic field, the hh spins and nuclear fields are aligned, so that no dephasing can occur, whatever the magnitude of the nuclear field fluctuations; (ii) in presence of a small magnetic field, of the order of the typical nuclear field fluctuation 0 ∆ , the hh spins precess around total magnetic fields out of the z-axis, so that the spin components are sensitive to the nuclear field fluctuations, and a decrease of the average spin amplitude then occurs; (iii) in a strong magnetic field, the hyperfine nuclear field is screened, so that the dephasing time // τ increases and for finite values of τ , the R X 1 (t) spin amplitude tends to 1: in this regime, an initial ( S ox ≠ 0, S oy = S oz = 0 ) spin essentially remains constant in time. Finally, let us compare the time dependence of the transverse components ( R x 1 and R y 1 ) for pure hh or lh spins, at high field, shown in Figure 5 and6. One clearly observes a Gaussian decay of the oscillations for lh ( 2 = α ) spins, and a power-law decay for hh ( 0 = α ) spins. The lower part of Figure 4 shows the behaviour of R x 1 (τ), R y 1 (τ) and R z 1 (τ) for a mixed heavy-light hole spin. These components follow the general trends already given for the case of a lh spin ( 2 = α). In the last section we will connect the above commented theoretical results with expected experimental observations. | cond-mat.mes-hall |
In previous studies, the trapping of photoexcited charges on QDs has been used as a detector of single-photons or as a "floating gate" for counting the number of photons in a single pulse of light. However, in these experiments the step-like changes in the tunnel current through the quantum well of a resonant tunneling diode 8 or in the conductivity of a two-dimensional (2D) electron gas 9,10 were small, typically 1% of the current, or less. Persistent photoconductivity effects caused by hole trapping effects have also been observed in studies of narrow onedimensional (1D) constrictions in a 2D electron gas 12 . In our work, we use devices in which the current over a narrow range of bias arises from resonant tunnelling through a single "active" QD state. The positive charge of the bound photoexcited holes shifts the resonance condition to lower applied bias thus providing a means of switching the current-carrying channel from fully open to fully closed, an effect which has potential for charge-sensitive photon counting detectors 8,9,10,11 . In our tunnel diodes, a layer of self-assembled InAs quantum dots is incorporated in an Al 0.4 Ga 0.6 As tunnel barrier and gives rise to a planar ensemble of discrete atom-like states with energy levels close the conduction band minimum of GaAs 13 . | cond-mat.mes-hall |
SERS measurements were performed with a LabRam confocal Raman system. Excitation at 633 nm was provided by a 12 mW He-Ne laser. A 50× long-working-distance objective was used. In situ spectroelectrochemistry was carried out in a cell with a vertical polycrystalline Cu disc working electrode of diameter 5 mm embedded in a Teflon cylindrical holder. The counter electrode was a Cu cylinder, coaxial with the working electrode holder. An Ag/AgCl (KCl 3M) reference electrode was used, placed in a separate compartment; potentials are reported on the Ag/AgCl scale. | cond-mat.mtrl-sci |
In particular, the logical states of an individual (physical) qubit can be presented by two single-electron orbital states localized in the spatially separated potential minima of a double quantum dot (DQD) [14] - [22]. The quantum operations on that socalled charge qubit can be accomplished via adiabatic variation of the DQD confinement potential [14] - [17] or by the electromagnetically induced resonant transitions between the DQD states [18] - [22]. In order to perform some non-trivial two-qubit operation on an arbitrary pair of qubits in a quantum register one should organize the interaction between those qubits for a finite period of time. In general, after interaction is off, the qubits become entangled with each other, i. e., their total wave function cannot be presented as the product of an individual qubit wave functions. The charge qubit entanglement via electrostatic control over the tunnel coupling between two neighboring qubits has been studied in Refs. [4], [6], [11], [14] - [17]. | cond-mat.mes-hall |
The D 1 symmetry of the eccentric nanoring implies that there is one symmetry axis, let us say the x-axis, with reflection operator Tx . The wave function transforms in the following way Tx Ψ α (x e , y e , x h , y h ) ≡ Ψ α (x e , -y e , x h , -y h ) = ±Ψ α (x e , y e , x h , y h ). (20) With respect to this symmetry operation, all states can be grouped into even and odd ones. The odd states have zero oscillator strength which follows immediately from Eq. (20). The doubly degenerate states of the concetric nanoring at B = 0 T can form an even and odd linear combination with respect to Tx . | cond-mat.mes-hall |
The CCD selects a small plane of the reciprocal lattice and intercepts the (111) direction with an angle θ. The direction q ⊥ is horizontal and q is in the vertical diffracting plane can be observed if the irradiated volume has the size of the coherence volume. A good transverse coherence length is obtained by using suitable slits, in order that the product of the beam size at sample φ by the beam divergence ǫ is of the order of the wavelength λ [18]. The longitudinal coherence length Λ l is fixed by the beam monochromaticity Λ l = λ 2 /2∆λ, and the path-length difference ∆L of the beam in the sample must not exceed this limit. This latter condition is contradictory with the asymmetric geometry. As scattering far enough from Bragg peaks is discussed here for the observation of surfaces, only interferences between surface atoms are relevant. | cond-mat.mtrl-sci |
We present a theoretical analysis of graphene's optical conductivity σ(ω), extending previous studies 32,33,34,35,36,37,38,39,40 to the situation with finite SOI. SOI effects on the DC conductivity were investigated in a recent theoretical study for a bipolar graphene pn junction, 41 and the effect of intrinsic SOI on the polarisationdependent optical absorption of graphene was considered in Ref. 42. Our study presents the analogous scenario for the richer case of the optical conductivity when both intrinsic and extrinsic types of SOI are present. Since ∆ R can be tuned by external fields, we will analyze various situations distinguished by the relative strengths of ∆ R and ∆ I . Our findings suggest that optical-conductivity measurements can be useful to identify and separate different SOI sources. | cond-mat.mes-hall |
(69) The ratio of j Q and the electric current I = env d gives the Peltier coefficient Π = π 2 6e T 2 µ L l eq + L . (70) Similar to our main result (60) for the conductance, Eq. ( 70) is applicable at L ≫ l 1 . It shows how Π grows from exponentially small values at L ≪ l eq to π 2 T 2 /6eµ at L → ∞. The thermopower and thermal conductance are defined in a system with a small temperature bias ∆T . To find these transport coefficients we revise our analysis of the conservation laws ( 41) and (45) to add finite ∆T . | cond-mat.mes-hall |
[4] that the interface between the substrate and this asperity is in the weak pinning limit if σ 0 < c 1/2 a K, where σ 0 is the mean load per unit interface area supported by this asperity and c a is the fraction of the surface atoms of this asperity that are in contact with the substrate. Assume that a fraction c 0 of the zeroth order asperities have atoms belonging to them in contact with the substrate. Let c 1 represent the fraction of next order (first order) asperities whose zeroth order asperities are in contact with the substrate, c 2 , the fraction of second order asperities whose first order asperities have their zeroth order asperities in contact with the substrate, etc., up to n th m order. Then σ 0 = σ/(c 0 c 1 c 2 ...c nm-1 ), where σ is the load per unit apparent area of the surface of the whole solid. Then, we conclude that the criterion for the atoms at the interface between the zeroth order asperity and the substrate to be in the weak pinning regime is that σ < (c 1/2 a c 0 c 1 c 2 ...c nm-1 )K. We see from this inequality that the more fractal the surface is, the more difficult it is for the zeroth order asperity to be in the weak pinning regime. The cost in elastic energy due to the shear distortion of the asperity can be determined by the following scaling argument: The elastic energy density for shear distortion of the asperity is proportional to (∂u x /∂z) 2 , where u x represents the local displacement due to the distortion, the x-direction is along the interface and the z-direction is normal to it. | cond-mat.mtrl-sci |
The rotor Hamiltonian, H θ , reduces to a set of coupled Harmonic oscillators on the pyrochlore lattice. It is easily diagonalized: each of x Ri and y Ri leads to four bands of "phonons" that have dispersions ) , and w 3,4 (k) = 2, such that the former two are dispersive, and the latter are dispersionless. w 1 (k) is the lowest band with min w 1 (k) = -6. Note also that U had to be rescaled, U → U/2, in order to keep the correct atomic limit [2]. Having solved the spinon and rotor sectors, we can determine the phase boundaries in a self-consistent manner. The Mott transition is characterized by the change from gapped, ρ > 6t|Q θ |, to gapless (and Bose-condensed) rotors, ρ = 6t|Q θ |. | cond-mat.str-el |
Yet, after heating the sample up to 700 • C (panel (c)) the slight p-doping vanishes and charge neutrality is retrieved (E F =E D ), so that we tentatively attribute the p-doping effect to the presence of chemisorbed species on the graphene surface and the subsequent downshift of the band structure to their desorption [20]. At temperatures above 700 • C the π-bands progressively weaken as indicated in panel (d). Since Si-H bonds are known to break at temperatures just above 700 • C [21], this effect can be correlated to progressive hydrogen desorption. Around 900 • C the hydrogen has completely desorbed and the zerolayer structure is re-established as seen from the absence of π-bands (Fig. 3(e)) and also from the LEED pattern which is similar again to the one shown in Fig. 2 (a). | cond-mat.mtrl-sci |
One observes that the number of localised spots increases with the index of the resonance level. In the energy-resolved transmission, twice the number of resonance energy levels in the pseudo-band is observed in the perfectly correlated case as compared to anti-correlated case. This is attributed to the reduced symmetry of the channel with a perfectly-correlated surface morphology, which lacks the x-axis mirror symmetry of the anti-correlated surface. The degradation of the energy-resolved transmission at higher energy is due to the appearance of the second mode at 0.3eV , which opens up a transmission through Φ 12 . Therefore the resonance peak has maximum transmission less than 1. IV. | cond-mat.mes-hall |
At α = 0 and 1, the correlation function is exactly the same with the analytical result. When α < 0.80, the correlation behaves similarly with the AKLT model, showing an oscillating behavior with respect the lattice separation. However, when α > 0.80, the correlation behaves similarly with the SZH model, showing an negative-definite behavior. At the critical point, the correlation function undergoes an qualitative change from AKLT to SZH. To get the ground state phase diagram, we also calculate the peak position α c of |d 2 E/dα 2 | as a function of β, as shown in Fig. 5. | cond-mat.str-el |
The corresponding experimental curves look similar, but their signs are opposite to the calculated ones. We do not find the origin for the opposite sign. Concluding Remarks We have studied the magnetoelectric effects on the x-ray absorption spectra in a polar ferrimagnet GaFeO 3 . We have performed a microscopic calculation of the absorption spectra Fig. 2. Average intensity I(ω q , q, e) as a function of photon energy ω q . | cond-mat.str-el |
[1] confirmed an earlier prediction [3] and demonstrated a charge relaxation resistance R q quantized at half a resistance quantum. A necessary condition is a contact which permits transmission of a single (spin polarized) quantum channel. As long as electron motion in the dot is coherent, the quantization of R q holds for arbitrary values of the transmission probability. This is remarkable. Whereas the quantization of the Hall resistance both in the integer [4] and fractional [5] quantized Hall effect, as well as the quantization of conductance in a ballistic contact [6] are due to perfect chiral transmission channels for which back scattering is suppressed [7], the quantization of the charge relaxation resistance has an entirely different origin. It is due to the fact that the mean square dwell time of a single scattering channel is equal to the square of the mean dwell time [8]. | cond-mat.mes-hall |
For the lowest lying subband, with s = 1 around k = ±k F , the energy band gap in the absence of the magnetic field is zero. Using eq. ( 5) one obtains ∆ g (Φ ρ ) = 3∆ 0 Φ ρ . As the field strength increases the line through the Fermi energy at zero magnetic field is shifted away further from the CNPs thus given rise to an increasing energy-gap. It is also worth mentioning that, the quantity µ orb = ev F r t /2, with v F = 3γ 0 a cc /2 ≈ 10 6 m/s, is the magnetic moment of an electron traveling in a loop of radius r t with velocity v F . Changes in the energy of electron states can be described by the interaction of this orbital magnetic moment with an axial magnetic field. | cond-mat.mes-hall |
Experimentally, Fano resonances have been observed first in QDs at the Kondo regime. 9,10 Subsequently, by embedding a Coulomb blockaded QD in an Aharonov-Bohm (AB) ring interferometer, a variety of Fano lineshapes were observed in the measured conductance spectra. Conductance measurements exploring different geometries, such as a quantum wire with a side-coupled QD, 11,12,13 a one-lead QD, 14 a ring with side-coupled QD, 15 as well as the parallel double QD structures, 16,17 provide more insight into the Fano problem in mesoscopic systems. The occurrence of conductance dips in ballistic AB rings was theoretically investigated almost 20 years ago. 18 Further, early theoretical works examined the possibility of Fano lineshapes in the transmission through one-dimensional waveguides and waveguides with resonantly coupled cavities. 19 Recently, inspired by the development of the relevant experimental works, there have been a lot of theoretical investigations devoting themselves to the Fano interference in electron transport through various QD structures, for example, one or two QDs embedded in an AB ring, 20,21,22,23 double QDs in different coupling manners. | cond-mat.mes-hall |
The QDs are separated by a distance much smaller than the relevant photon wavelength λ = 2π c/E, so that the spatial dependence of the EM field may be neglected (the Dicke limit). The Hamiltonian describing the interaction of carriers with the EM modes in the dipole and rotating wave approximations is H c-rad = Σ - k,λ e -iEt/ g kλ c † k,λ + H.c.,(3) with Σ -= |0 1|+|2 3|+|0 2|+|1 3| andg kλ = id•ê λ (k) w k 2ε 0 εrv , where d is the interband dipole moment, ε 0 is the vacuum permittivity, ε r is the dielectric constant of the semiconductor and êλ (k) is the unit polarization vector of the photon mode with the wave vector k and polarization λ. For wide-gap semiconductors with E ∼ 1 eV, zero-temperature approximation may be used for the radiation reservoir at any reasonable temperature. The system evolution In certain limiting cases, analytical formulas for the evolution of the DQD system may be found. For uncoupled dots (V = 0) interacting only with lattice modes (phonons), an exact solution is available [9]. If only the radiative decay is included, a solution in the Markov limit can be obtained [3]. | cond-mat.mes-hall |
Since F θ = 1 (or any constant in general) also yields a non-singular Pauli potential, we can form κ4 -dependent enhancement factors which resemble GGA forms and thereby enable connection with the modified conjoint GGA functionals discussed already. One form which we have begun exploring (see below) is F RDA(ij) θ (κ 4 ) = A 0 + A 1 κ4 1 + β 1 κ4 i +A 2 κ4 1 + β 2 κ4 j . (68) A i and β i are parameters to be determined. Even this simple form has two desirable properties: (i) the corresponding v θ is finite for densities with the near-nucleus behavior defined by Eq. ( 59), hence also Eqs. ( 25) or (26) (this has been checked by explicit analytical calculation); (ii) the divergence of κ4 near the nucleus (see Figure 5) cancels in Eq. | cond-mat.mtrl-sci |
. . 0 2 w 2 0 2 w 4 0 2 w 6 . . . . | cond-mat.mes-hall |
Specifically we consider a one-dimensional (1D) system consist- ing of an interacting region of length L int connected to two non-interacting leads (see Fig. 1). The interacting region is initially in the MI state and we focus on the strongly interacting regime with interaction strength on the order or larger than the bandwidth. The sudden application of a large external voltage drives the system out of equilibrium and causes a time-dependent electrical current to flow through the interacting region, destroying the MI state. Our goals are first, to calculate the nonlinear current-voltage (I-V) characteristics; second, to contribute to the characterization of the currentcarrying state; and third, to study the time-dependence of the entanglement entropy in this set-up. We employ the adaptive time-dependent density-matrix renormalization group (tDMRG) method, 28,29 which has been successfully used to compute the non-equilibrium dynamics of single quantum dots. | cond-mat.str-el |
In this case one expects a Q-independent spin gap to follow the Ce 3+ form factor squared, F 2 (Q). In case of inter-site (or lattice effects) one expects a modulation of the gap value and its intensity with Q. II. Experimental details The polycrystalline sample of CeOs 2 Al l0 was prepared by argon arc melting of the stoichiometric constituents with the starting elements , Ce 99.9% (purity), Os 99.9% and Al 99.9999%. The sample was annealed at 1000 o C for four days in an evacuated quartz ampoule. The sample was characterised using power X-ray diffraction and neutron diffraction and was found to be dominantly single-phase. The impurity phase was found to be about 3%, but its real composition is not known at present. | cond-mat.str-el |
Introduction The efficiency of thermoelectric devices is related to the figure of merit, ZT = 2 S GT , 1 where T is the temperature, S is the Seebeck coefficient, G is the electrical conductance, and κ is the thermal conductance, which is the sum of the electronic contribution, e , and the lattice thermal conductance, l . The use of artificially structured materials such as superlattices 2 and nanowires 3,4 has proven to be an effective way to increase the performance of thermoelectric devices by suppressing phonon transport. In addition to the success of phonon engineering, additional benefits might be possible by enhancing the electronic performance of thermoelectric devices. 5 Possibilities include reducing device dimensionality 6,7 and engineering the bandstructure. 5 Using the Boltzmann transport equation (BTE), 8 thermoelectric transport coefficients can be expressed in terms of the "transport distribution," E . 9,10 Note that the quantity, 2 qE , is sometimes called "differential conductivity," E , 11,12 where q is the electron charge. | cond-mat.mes-hall |
Within DMFT, which does not treat the spatial correlations, it is known that the Hund's coupling reduces the energy gap of the Mott insulator to U ′ -J. Therefore, in DMFT, the Hund's coupling reduces the effective Coulomb repulsion and tends to stabilize the metallic phase. The previous DMFT + NCA studies show that the quasiparticle peak in DOS get enhanced as J increases 10 . On the other hand, in our CDMFT, which properly incorporate spatial correlations, the Hund's coupling enhances spatial correlations of spin and orbital, which give rise to the NFL state with the pseudo gap. The NFL behavior is also seen in the renormalization factor Ẑ = 1 -∂Re Σ(ω + i0)/∂ω ω=0 -1 . In the inset of Fig. | cond-mat.str-el |
Hydrochloric acid removes surface iron from all samples, but when it is applied to metallic samples hydrochloric acid may also corrode the surface of the metal. To evaluate the rate that hydrochloric acid corroded the metal samples, each of the samples was immersed in hydrochloric acid for durations of 10 minutes, 70 minutes, and 24 hours. Table 3 shows some loss of mass from acid washing. In particular the corrosion in the aluminum sample after 24 hours produced a significant 7% reduction in the mass. Fig. 3 shows that immersing the metallic samples in acid for only 10 minutes removes nearly all the surface contamination and reduces the volume susceptibility by an order of magnitude. | cond-mat.mtrl-sci |
We will be particularly interested in the experiments in the copper oxide high temperature superconductors, in the ruthenate materials (notably Sr 3 Ru 2 O 7 ), and in two-dimensional electron gases (2DEG) in large magnetic fields. However, as we will discuss below, our results are also relevant to more conventional CDW systems such as the quasi-twodimensional dichalcogenides. A. High temperature superconductors In addition to high temperature superconductivity, the copper oxide materials display a strong tendency to have charge-ordered states, such as stripes. The relation between charge ordered states [55], as well as other proposed ordered states [56,57], and the mechanism(s) of high temperature superconductivity is a subject of intense current research. It is not, however, the focus of this paper. | cond-mat.str-el |
For ABINIT we use norm-conserving pseudopotentials generated using the method of Ramer and Rappe 19 as implemented in the OPIUM package, 20 while in LAUTREC we use projector augmented-wave (PAW) potentials. 21 In both cases, the semicore 3s and 3p orbitals of Ti, and the 5d orbitals of Pb are treated as valence electrons. Plane-wave cutoffs of 50 and 30 Hartree are chosen for ABINIT and LAUTREC respectively (the PAW potentials being softer than the norm-conserving ones). The Brillouin zone is sampled by a 4 × 4 × 4 Monkhorst-Pack 22 k-point mesh for ABINIT and a 6 × 6 × 6 mesh for LAUTREC. A stress threshold of 2×10 -2 GPa is used for cell relaxation, 23 and forces on ions are converged below 2.5×10 -3 eV/ Å. In ABINIT the electric polarization is calculated using the Berry-phase approach 24 and is coupled to a fixed electric field E. 25,26 In LAUTREC the electric polarization is computed using the centers of the "hermaphrodite" Wannier orbitals 26,27 and the electric displacement field D is used as the independent electrical variable. | cond-mat.mtrl-sci |
Figure 4 shows that the zero-temperature superfluid stiffness ρ 0 , denoted by dotted line, which obtained via extrapolation of values at T > 0, follows ρ 0 ∝ |t -t 0 c |, implying that x = 1.0. It is consistent with the hyperscaling argument [11] suggestingx = z/(d + z -2). We expect that this quantum criticality disappears as temperature rises, which means quantum fluctuations possibly leave some tracks in bulk properties at low temperatures. Figure 5 shows the specific heat, C V , and the energy expectation values, H , as a function of T for different t. Sharp rises of C V in the conducting regime or round up-rises in the insulating regime are followed by indents, regions indicated by , which apparently represent anomalous behavior due to quantum fluctuations and disappear at high temperatures for T 0.25. This feature strongly suggests a crossover in normal fluid from quantum mechanical to classical regime. Similarly the curves of H show bumps, indicated by , only in the range where quantum critical fluctuations are expected to have effects. | cond-mat.str-el |
4. V. CONDUCTANCE FLUCTUATIONS The same framework can be used to calculate the conductance fluctuations in arbitrary ballistic conductors in the semiclassical limit. Conductance fluctuations are characterized by the correlation functionK(t) = 1 2π dωK(hω)e iωt ,(59) K(ε -ε ′ ) = g(ε)g(ε ′ ) -g(ε) 2 . (60) The correlation function K(t) determines the variance of the conductance at finite temperatures, var g(T ) = dt (πT t) 2 sinh 2 (πT t) K(t). (61) At a finite temperature, dephasing from electron-electron interactions further suppresses the conductance fluctuations. The effect of thermal smearing considered here is dominant, however, since typically T τ φ ≫ h. 4 (See Ref. | cond-mat.mes-hall |
Then we use Eqs. ( 6) and (7) to writeÎ = i(A † -A). (25) We evaluate the average current to lowest order in tunneling and obtain I = ∞ -∞ dt [A † (t), A(0)] ,(26) where the average is taken with respect to ground state in quantum Hall edges. Finite temperature effects will be considered separately in Sec. IV C. It easy to see that the average current can be written as a sum of four terms: I = ℓ,ℓ ′ I ℓℓ ′ , I ℓℓ ′ ≡ dt [A † ℓ (t), A ℓ ′ (0)] ,(27) where I LL and I RR are the direct currents at the left and write QPC, respectively, and I LR + I RL is the interference contribution. In our model there is no interaction between upper and lower arms of MZI, therefore the correlation function in (27) splits into the product of two single-particle correlators: I ℓℓ ′ = t * ℓ t ℓ ′ dt × ψ † 1U (x ℓ , t)ψ 1U (x ℓ ′ , 0) ψ 1D (x ℓ , t)ψ † 1D (x ℓ ′ , 0) -ψ 1U (x ℓ ′ , 0)ψ † 1U (x ℓ , t) ψ † 1D (x ℓ ′ , 0)ψ 1D (x ℓ , t)(28) We note that the operator ψ † 1j applied to the ground state creates a quasi-particle above the Fermi level (with the positive energy), while the operator ψ 1j creates a hole below Fermi level (with the negative energy). | cond-mat.mes-hall |
With the exception of Cr and Fe, the agreement is quite satisfactory. The origin of such discrepancies may be due to large experimental uncertainties as well as the neglect of vibrational entropy in our calculations. In summary, using a combination of first-principles calculations and a statisticalmechanical Wagner-Schottky model, we predict the site preference of 3d, 4d and 5d transition-metal elements in L1 0 TiAl as a function of both alloy stoichiometry and temperature. At all alloy compositions and temperatures, Zr and Hf have a predominant preference for the Ti sites, while Co, Ru, Rh, Pd, Ag, Re, Os, Ir, Pt and Au have a predominant preference for the Al sites. For V, Cr, Mn, Fe, Ni, Cu, Nb, Mo, Tc, Ta and W, their site preference will depend quite sensitively on alloy stoichiometry as well as heat treatment, e.g., annealing temperature and cooling rate. ACKNOWLEDGEMENTS This work is financially supported by Director's postdoctoral fellowship at Los Alamos National Laboratory (LANL). | cond-mat.mtrl-sci |
( 9), one finds [21,22] Π(q, iΩ)= γ |Ω| q z-2 ,(15) where γ = N g 2 χ 0 k F /(πv 2 F ). Considering only the linear-frequency Landau term in the spin susceptibility, this writes χ -1 (q, iΩ) = χ -1 0 ξ -2 + |q -Q| 2 + |Ω| q z-2 . (16) In particular, we have z = 2 for an antiferromagnetic QCP and z = 3 for a ferromagnetic one. Using this expression, the singular part of the free energy (14) writes f s (ξ -2 , T ) = T iΩ,q ln ξ -2 + |q| 2 + γ |Ω| q z-2 = - 1 π ∞ 0 dν coth ν 2T d d q (2π) d tan -1 γν/q z-2 ξ -2 + q2 ,(17) where q = q -Q is the shifted momentum near the wave vector Q. Performing the frequency and momentum integrals in this equation, one finds the analytic expression of (17). Details of this evaluation for d = 3, z = 2 are given in appendix Appendix C. We would like to emphasize that the resulting effective free energy satisfies the following scaling relation f s (r, T ) = b -(d+z) f r (rb 1/ν , T b z ),(18) where f r (x, y) is an analytic regular function. | cond-mat.str-el |
The parameters b ψ , a ψ and c ψM are further constrained by the experimental temperature-magnetic field phase boundary. The fitting with account of these constraints is shown in the upper panel of Fig. 5. In the case of PrRu 4 P 12 , the anomaly of χ at the scalar transition is very small. We interpret the smallness in terms of the followings: (i) the system is far from the ferromagnetic instability characterized by T F in eq. ( 16), and (ii) the coupling constant c ψM is small. | cond-mat.str-el |
In [4], a cylindrical electromagnetic cloak constructed using specially designed concentric arrays of split ring resonators, was shown to conceal a copper cylinder around 8.5 GHz. The effectiveness of the transformation based cloak was numerically demonstrated solving Maxwell's equations using finite elements for an incident plane wave (far field limit) [5] and for electric line current and magnetic loop sources (near field limit) [6]. In [7], a reduced set of material parameters was introduced to relax the constraint on the permeability, necessarily leading to an impedance mismatch with vacuum which was shown to preserve the cloak effectiveness to a good extent. Other routes to invisibility include reduction of backscatter [8] and cloaking through anomalous localized resonances, the latter one using negative refraction [9,10]. To date, a plethora of research papers has been published in the fast growing field of transformation optics. However, transformation based invisibility cloaks applied to certain types of elastodynamic waves in structural mechanics received less attention, since the Navier equations do not usually retain their form under geometric changes [11,12]. | cond-mat.mtrl-sci |
It is also useful to distinguish the side-jump accumulation and the anomalous distribution effects. The side-jump accumulation is a rather direct consequence of coordinate shifts while the derivation of the anomalous distribution requires several extra steps in the semiclassical theory, which were unnoticed in a few former publications. Another confusing example from the recent terminology is the statement that the vertex correction, coming from a Gaussian correlated disorder in the Kubo formula is due to the side-jump effect only. Comparing the vertex correction with the semiclassical expression for the side-jump conductivity, discussed by Berger, Nozieres and others, one would find a discrepancy because the intrinsic skew scattering is also captured by the vertex correction and it was not considered by the older semiclassical theories that concentrated only on the side-jump effect. The classification into the "intrinsic" and "extrinsic" contributions was also understood quite arbitrarily by many authors. In the present review we coined the word "intrinsic" for the single special contribution, which is due to unusual trajectories of wave packets in the external electric field rather than any other mechanism that involves scatterings on impurities. | cond-mat.mes-hall |
In these models with shortrange valence-bond ground states, the simplest excitation is generated by breaking one of the valence bonds, promoting it to a triplet. An interesting and important question is how this excited state propagates. More specifically, does the triplet propagate coherently, or does it "break apart" so that the individual spins forming the triplet -referred to as spinons -propagate independently? In both the rung-singlet and Haldane phases, it is known that the triplet propagates coherently. The reason for this can be understood looking at Fig. 10 and counting the number of valence bonds crossing a vertical line. | cond-mat.str-el |
Therefore, the XOR gate operation time may be short enough in order to perform the sufficiently large number of operations during the spin coherence time [10]. We note that the two-qubit XOR logic gate is commonly defined as follows: |X |Y -→ |X |Z = X ⊕ Y , where ⊕ is the addition modulo two. This two-qubit XOR gate is equivalent to the CNOT gate [20]. However, according the present mechanism, the nanodevices A and B perform the following operation: |X l1 |Y l2 -→ |Z = X ⊕ Y r1 , where X, Y , and Z are defined in Fig. 3(a) and the output is detected by QPC1 as the charge of QD(r1) (cf. Fig. | cond-mat.mes-hall |
From a symmetry point of view, the ground states of doped Mott insulators are chargeordered phases, which share many similarities with classical liquid crystals, and should be regarded as electronic liquid crystal phases. [3] However, unlike classical liquid crystals, electronic liquid crystals are strongly quantum mechanical states whose transport properties range from insulating to metallic and even superconducting. In contrast with classical liquid crystals, whose ordered phases represent the spontaneous breaking of the continuous translation and rotational symmetry of space [4,5], the electronic liquid crystal phases of strongly correlated systems are sensitive to the effects of the underlying lattice and the symmetry breaking patterns involve the point and space groups, as well as to disorder. More complex ordered states, involving simultaneously charge and spin degrees of freedom, may also arise. [6] The sequence of quantum phase transitions described above, electron crystal → smectic (stripe) → nematic → isotropic fluid, representing the progressive restoration of symmetry, is natural from a strong correlation perspective. Indeed, the electron crystal state(s) are naturally insulating (much as in the case of a Wigner crystal), the smectic or stripe phases are either anisotropic metals or superconductors, and the charged isotropic fluids are either metallic or superconducting. | cond-mat.str-el |
We used facilities supported by the NSF Center in EUV Science and Technology. Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Author Contributions J. M. and K. S. R. conceived of ankylography. J. M. planned the project; K. S. R., S. S., H. J., J. A. R., J. D. and J. M. conducted the numerical experiments; S. S., K. S. R., R. L. S., H. J., H. C. K. and J. M. performed the analysis and image reconstruction of experimental data; J. M., K. S. R, S. S., J. D. and J. A. R. wrote the manuscript. | cond-mat.mtrl-sci |
For the tube, the interaction terms are just "degenerate" hops of Sec. III; they conserve spin as well as pseudospin. Actually, they conserve a combined flavor which includes both the spin and the pseudospin. Hence, the effective Hamiltonian possesses an SU (4) symmetry in which there is no distinction between the four combined flavors the hopping fermion might carry. The interesting behavior of such SU (4) chains is discussed in Ref. 32; in terms of the original fermions, it obviously corresponds to a high degeneracy between many kinds of order. | cond-mat.str-el |
32 have investigated the spin torque and spin Hall currents in generic 2D spin-orbit Hamiltonian H so =A(k)σ x -B(k)σ y also using the conserved spin-current operator and found that regardless of the detailed form of the energy dispersion [i.e. A(k) and B(k) coefficients], the conserved static (ω = 0) spin Hall conductivity changes its sign with respect to the conventional spin Hall conductivity. In this paper, using the definition for the spin-current operator reported by Shi et al. 27 we explore the behavior of the frequency dependent spin (Hall) σ sz µν (ω), and of the charge conductivity tensor σ ch µν (ω) for a 2DHG with k-cubic Rashba and Dresselhaus SOI. We show that the optical spectrum of the spin conductivity exhibit remarkable changes when this new definition of spin current is applied. A rather large response of the spin Hall conductivity is predicted to arise when using the conserved definition of spin current operator owing to a dominant contribution of the spin-torque term. | cond-mat.mes-hall |
However, since B = -dP/d ln V , where B is the bulk modulus and P the pressure, the pressure deformation potential α P can be expressed in terms of α V according toα P = -α V /B. Experimentally reported values for the bulk modulus of wz-GaN scatter between 1880 and 2450 kbar. 93,94,95,96,97 Using these values, our volume deformation potential of α V =-7.6 eV would translates into a pressure deformation potential in the range of 3.1 -4.0 meV/kbar, which is comparable to the experimentally determined range of 3.7 and 4.7 meV/kbar. 97,98,99,100,101,102 This large uncertainty has been partially ascribed to the low quality of earlier samples and substrate-induced strain effects. 101 The fact that the pressure dependence of the band gap is sublinear (unlike the volume dependence) further questions the accuracy of linear or quadratic fits for the extraction of the deformation potentials in the experiments. 101 For wz-InN experimentally reported values are sparse. | cond-mat.mtrl-sci |
Accordingly, the delamination takes place when: i F i i i w l γ 2 = ∂ Π ∂ - , W E - = Π , i=1,…,N(3a) where is the total potential energy, Π E is the elastic energy, W is the external work, i γ is the surface energy of the i th tape/substrate interface and is its width. i w The elastic energy variation can be calculated as: ( ∑ = - = Δ N i i i i i i Y l A E 1 2 2 / 2 1 ε ε ) (3b) The variation of the external work is:η Δ × = Δ F W (3c)The real critical force is:{ } j i C F F F = = min (3d) and corresponds to the delamination of the j th tape. The algebraic system is nonlinear but can be linearized considering the differentials instead of the finite differences (e.g.η η d → Δ ). However note that the physical system remains intrinsically geometrically nonlinear due to the existence of the orientation variations. Moreover, the energy balance remains non linear in the force F. Double peeling The developed treatment is here applied to study a double peeling system, Figure 3. From eq. | cond-mat.mtrl-sci |
In a continuum, the lifetime is determined by ImΣ(k, ω) and is independent of η if η is chosen small enough. In Fig. 4(a) we show results for the 1D spectral weight A(k = 0, ω) vs. ω for a relatively weak coupling λ = 0.6. The MA spectral weight shows two discrete states at low energies, and a continuum starting for ω > -1.5t. Within MA (1) , the second peak spreads into a continuum whose lower edge is at roughly Ω above the energy of the GS peak. In fact, since ḡ0 (ω) acquires an imaginary part when -2dt ≤ ω ≤ 2dt, from Eq. | cond-mat.str-el |
The λ(ω) of 3d correlated metal (Ca, Sr)VO 3 was reported to be approximately 3-4 [25]. Note that the λ(ω) of SrIrO 3 is comparable to or larger than those of the 3d and 4d TMOs. It is quite interesting that such a large value of λ(ω) was found for the 5d TMO compound. This large value implies that SrIrO 3 is a correlated metal close to the Mott transition. Our findings, the W-controlled IMT and the large effective mass of the resulting metallic compound in 5d system, challenge the conventional expectation that the electron correlation is insignificant in 5d system. These unique findings originate from the large SO coupling of 5d transition metal ions. | cond-mat.str-el |
2(f). In the Hall bar center the density is homogeneous and given by n 0 , whereas closer to the Hall bar edges, the density profile increases due to the action of the side gates. In order to simplify the analysis we approximate the induced density by a step function which gives rise to two parallel conducting channels: two thin regions of width W 1 /2 and density n 1 First we assume that for V SG = 0 V [middle trace in Fig. 2(a)] all regions have the same density. We proceed by regarding the channel widths (W 1 , W 2 ), as well as their lever arms (α 1 , α 2 ) with respect to the side gates as parameters. Together with the constraint W tot = W 1 + W 2 = 720 nm this results in three free parameters. | cond-mat.mes-hall |
(32) This is because the generator M given by Eq. ( 17) is in the normal form. This should be contrasted with systems of charges of opposite signs, where new squeezed vacuum states are generated. 17,24 The coordinate representations of the normalized vacuum state in the two set of coordinates are r 1 , r 2 |0 = 1 2πl 1 l 2 exp - r 2 1 4l 2 1 - r 2 2 4l 2 2 ,(33) R 1 , R 2 |0 = 1 2πL 2 B exp - R 2 1 + R 2 2 4L 2 B . (34) We construct a complete orthonormal set of states compatible with both axial and magnetic translational symmetries as follows: |n 1 , n 2 , m 2 , k = 1 (n 1 ! n 2 ! | cond-mat.mes-hall |
6 which presents the differ- ence ∆G between the measured G(τ ) and G(τ ) backcontinued from A(ω). The analytical approximations show clear deviations, in particular a larger gap. The difference in gap value can be seen directly as a difference in the imaginary-time data in the lower panel of Fig. 5: G(τ ) calculated using the two analytical methods falls below the numerically exact results in the imaginary-time range 2 < τ t < 5. VI. CONCLUSIONS In conclusion, we have presented a "bold" diagram method and applied it to an expansion around the noncrossing and one crossing approximations to the Anderson impurity model. | cond-mat.str-el |
That such questions can be reliably addressed with quantum chemical methods was shown before for the layered copper oxides [12] and ladder vanadates [13]. However, simple point-charge embeddings were used in previous work for representing the surroundings of the region where the correlation treatment is carried out. A newly developed, rigorous embedding technique [10,11] is applied here for the first time to a 3d-metal compound. LaCoO 3 has attracted considerable attention due to a number of puzzling phase transitions induced by changes in temperature [14,15], doping [15,16], and/or strain [17,18]. Up to now, most of the experimental work was aimed at understanding the nature of the phase transitions in the undoped compound, from a nonmagnetic insulator at low T to a paramagnetic semiconductor above 90 K and to a metal for T > 500 K. The low-T ground-state was assigned to a closed-shell t 6 2g e 0 g configuration [low-spin (LS), S = 0] of the Co ions [14]. For T 90 K, however, the available experimental results are rather contradictory. | cond-mat.str-el |
The above trend is clear in the left part of Fig. 2(b). We note that our simulations are performed at zero temperature and with an exact energy of the incoming carriers, this leading to the steep transitions in the transmission probability of Fig. 2(b). Such steepness is not expected in experiments due to the uncertainty of the incoming carriers' kinetic energy and the temperature dependence of bound levels' occupancy. In the simulations based on the mean-field approach, the universal behavior, i.e. | cond-mat.mes-hall |
Because of Γ 11 ≫ Γ 22 , one can well understand the result of ρ 2σ → 0. To be contrary, we can see that when φ = π, ρ 2σ = 1 π Γ22 (ω-ε2) 2 +Γ 2 22 , which leads to the clear peak of the LDOS spectrum, as shown by dotted line in Fig. 6(a). The further explanation about this result should fall back on the analysis of the quantum interference in this system by means of the language of Feynman path. 39 Next, for the reason alike, we can understand that at the zero magnetic field case, when U 1 = U 2 = Γ n 2σ begins to increase sharply at the point of ε 0 = -3Γ 2 , since the identical ε 2 and ε 1 + U 1 , as shown in Fig. 5(c). | cond-mat.mes-hall |
We stress that the particular choice of N = 3 allows to match precisely the phase boundary of the usual single-band Hubbard model for canonical spin-1/2 fermions [19], and is helpful to make quantitative comparisons when introducing other degrees of freedom (more orbitals for example) or new energy scales (random spin exchange as in the present work). We see from Fig. 1 that irrespective of J, there always exists an interaction range U c1 (T ) < U < U c2 (T ) bounding a coexistence region. With increasing temperature, the transition lines always merge onto a critical point that occurs at T c D/30 for J = 0, consistent with Refs. [2,19]. Interestingly, Fig. | cond-mat.str-el |
The details of theoretical descriptions can be found in Appendixes A-C, and will be specified in the following subsections. FIG. 2: The calculation steps of the magnetization of the grain and the non-local spin valve signal RNLSV as functions of Ic, the driving current. Rectangles represent calculation processes. Parallelograms represent inputs or outputs of the calculations. The region (1), (2), (3), ( 4) and (5) in Fig. | cond-mat.mes-hall |
Let us introduce the following diagrammatic notation :( ) n = n! ẑ(n) ,(76)and its cumulant counterpart,( ) c m = m! ẑ(m) c ,(77) Defining, for any s = {s 1 , . . . , s m } ∈ S n m , the combinatorial factor [s] = 1 m! | cond-mat.str-el |
Let us relax this constraint and introduce ( ) c * whose definition is the same as ( ) c but evaluated with at least one internal contraction. Obviously, the sum corresponds to a fully unrestricted evaluation where both internal and external contractions are allowed. In that case each term of equation (79) produces the same set of terms by contraction since all partitions become equivalent when the distinction between internal and external contractions is suppressed. Thus, the corresponding weight can be obtained by the formal identification ( ) ↔ 1 into equation (79) or, according to Eq. (76), ẑ(n) ↔ (1/n!) into equation ( 67). | cond-mat.str-el |
In the presence of the Hund's coupling, we find that the spatial correlations give rise to the pseudo gap in the quasiparticle excitation. In Fig. 4, we show the DOS for U/t = 4.0 at T /t = 0.1 with varying the Hund's coupling J. As the Hund's coupling J increases, the quasiparticle peak gradually shrinks and vanishes for J/t ∼ 0.7. As J further increases, a pseudo gap evolves and the system becomes insulating. We note that this behavior caused by the Hund's coupling J is qualitatively different from the results of single-site DMFT 14 . | cond-mat.str-el |
The calculated resistance ρ xx /ρ 0 (B) matches the experimental curve in low magnetic field B < 0.7 T. The correspondence breaks at higher magnetic field, since the calculations do not account the substantial interference between the MISO and PIRO. Additional analysis is required to explain and describe quantitatively the observed effect. In conclusion, we have found that the magneto-intersubband oscillations of dissipative resistance in single GaAs quantum wells with two populated subbands coexist with the phonon-induced oscillations. These two kinds of the quantum oscillations interfere constructively. The experiment demonstrates that the enhancement of the electron-phonon scattering increases the amplitude of MISO, indicating decrease of the linewidth of the intersubband resonance. We suggest that the effect is similar to the diffusive narrowing of spin resonance. | cond-mat.mes-hall |
Inversion symmetry then implies that for x < 0: φ L (x; kσ) = e i(k F +k)x -1 -T 0 e -i(k F +k)x (3) φ R (x; kσ) = -i T 0 e -i(k F +k)x . (4) Letting ĉL,kσ , ĉR,kσ denote the anhiliation operators for the scattering states, the field operator may be written as ψσ (x) ∝ k (φ L (x; kσ)ĉ L,kσ + φ R (x; kσ)ĉ R,kσ ). The current operator for x < 0 then takes the form: Î(x) = ÎD (x) + ÎOD (x) ,(5) with (R 0 ≡ 1 -T 0 ) ÎD (x) = e hν k,k ;σ ĉ † R,k σ ĉR,kσ [-T 0 e -i(k-k )x ] +ĉ † L,k σ ĉL,kσ [e i(k-k )x -R 0 e -i(k-k )x ] (6a) ÎOD (x) = e hν k,k ;σ (6b) ĉ † L,k σ ĉR,kσ [-i T 0 R 0 e -i(k-k )x ] + h.c. . Without Fermi liquid corrections, the average current would be determined by ÎD , while the zero-temperature current noise would be determined by ÎOD [12]. Similar to the N = 2 case [1,15], the effects of δ σ (ε) may be incorporated via the Hamiltonian: H ≡ k,σ,j=L,R ξ k ĉ † j,kσ ĉj,kσ + H α + H α + H β (7a) H α = - α 2πνT K k,k ,σ (ξ k + ξ k ) d † kσ dk σ (7b) H α = - α 2πν(T K ) 2 k,k ,σ (ξ k + ξ k ) 2 d † kσ dk σ (7c) H β = β 2πν 2 T K k ,q ,k,q σσ d † kσ dk σ d † qσ dq σ ,(7d) Here, ξ k = v F k and dkσ = (ĉ L,kσ + ĉR,kσ )/ √ 2 (only the symmetric combination enters due to inversion symmetry). H α + H α and H β represent, respectively, the elastic scattering from the impurity (to order (ε/T K ) 2 ) and the presence of two-particle scattering. | cond-mat.mes-hall |
3(b), which is in good qualitative agreement with experiment. We set the tunneling rate ∆ 0 = 2 K, and the energy splitting takes the form∆(T ) = ∆(0) 1 - T T SPT 2(15) where ∆(0) = T SPT = 150 K when T < T SPT . It should be noted that the overall behavior of the scaling flows and the resistivity are independent of the chosen parameters. This represents the explanation of the RA for the iron pnictides. IV. ORBITAL DRIVEN MAGNETISM Our model also offers a natural solution to the observed stripe-like anti-ferromagnetism. | cond-mat.str-el |
Gauge fields and topological insulating phases We start by focusing on the pattern shown in Fig. 1(b). First we set α = β = 0 implying that only hopping around square plaquettes on each point of the underlying square lattice have spin dependency. As depicted on the right hand of Fig. 1(b), the gauge fields can be selected so that the inversion symmetry is preserved or not. Three different patterns are depicted. | cond-mat.str-el |
Fig. 1(c) shows the excel-lent agreement between experiment and theory, even the magnitude of the inelastic signals is quantitatively reproduced. All the peaks appearing in the PDF in Fig. 2(c) can be identified with some group of peaks in Fig. 4(a): peak A corresponds to a C-C stretch with some contribution from CH 2 twist; B to C-S stretch with some CH 2 rock; C to CH 2 wag and twist; D to CH 2 scissor; E to Au-S-C stretch; F to Au-S stretch; and G to CH 2 rock and twist. The fact that the calculated peaks have the same intensities as the measured peaks [see Fig. | cond-mat.mes-hall |
I. INTRODUCTION In the last couple of decades, the growing world of nanotechnology put at our disposal several classes of lowdimensional materials. Particularly interesting examples are two-dimensional (2D) quantum dots 1,2 (QDs), formed at the interface between two semiconductors. These systems are not only important from a technological point of view, but are also remarkable from a purely theoretical perspective. In fact, as they can be built with different shapes and sizes, and with a varying number of electrons, they are the ideal system to study electronic correlation. The problem of electronic correlation is perhaps the most challenging in the field of condensed matter physics. | cond-mat.str-el |
For simplicity, we assume that the nematic order parameter is small enough so that a Landau-type expansion still makes sense, which is equivalent to assuming that the system is still "close enough" to the nematic-isotropic QCP. However, as we will show later, the critical theory we get using these assumptions has the only form allowed by symmetry, assuming analyticity. By symmetry, the coupling between the CDW and the nematic field is S int = -g d kdΩ (2π) 3 d qdω (2π) 3 N ( q, ω)e -2iθ k ρ( k -q, Ω -ω)ρ(-k, -Ω) + h.c. (4.12) whose tensor form is shown in Appendix A. Here, θ k is the polar angle of k. This term is irrelevant in the isotropic phase, but in the nematic phase, where N gets the expectation value N ; this term will be of the same order as S 2 , which was defined in Eq. (4.10), and hence it becomes important. Inside the nematic phase the amplitude fluctuations of the nematic order parameter are gapped while the orientational fluctuations, the nematic Goldstone modes, are gapless, at least strictly in the absence of a lattice and other orientational symmetry breaking couplings. | cond-mat.str-el |
Indeed, as far as we know, the analytical models are limited to time dependent nucleation rates. 16,36 In particular, Jun et al. 36 have derived an analytical solution for the one-dimensional case. Particularly relevant to the present work are the results of Pineda et al. 16 who have obtained an accurate analytical description for the two-and three-dimensional cases. In the present work we will consider those transformations that fulfill the Kolmogorov-Johnson-Mehl-Avrami (KJMA) premises. | cond-mat.mtrl-sci |
This is particularly evident in the dependence of the MAE on the capping film thickness: while thickening the Cu and Ag caps lowers the MAE, high PMA can be obtained for Co films buried under > 6 ML of Au, the largest anisotropy corresponding to coverages of 2 ML. Our results point to the wealth of possibilities to engineer the particular easy-axis in nanometer sized structures that comes about when a precise control of the thickness and structure of magnetic films is available. As a rule, the ingredients to obtain a large PMA in Co films are an expanded 2D lattice, and a thin capping with a metal of high spin-orbit interaction. This can be best achieved with ultrathin films. Acknowledgments This research was partly supported by the Office of Basic Energy Sciences, Division of Materials Sciences, U. S. Department of Energy under Contracts No. DE-AC04-94AL85000 and No. | cond-mat.mtrl-sci |
The results of the calculation of average values of x and y for this polarization arex(t) = V 0x t + x ZB (t),(21) where the constant velocity is defined by the expression V 0x = hk 0 m -γ 1 + γ 2 √ 3 1 - 1 a 2 + 1 a 4 - e -a 2 a 4 ,(22) and x ZB (t) describes the oscillatory motion (Zittebewegung)xZB (t) = √ 3 2k 0 a 2 exp(- a 2 t 2 /t 2 0 1 + t 2 /t 2 0 ) sin( a 2 t/t 0 1 + t 2 /t 2 0 )- t t 0 × × cos( a 2 t/t 0 1 + t 2 /t 2 0 ) + √ 3 2k 0 a 2 e -a 2 t t 0 ,(23) ȳ(t) = √ 3 4k 0 1- 1 a 2 -(1- 1 a 2 ) exp(- a 2 t 2 /t 2 0 1 + t 2 /t 2 0 ) cos( a 2 t/t 0 1 + t 2 /t 2 0 )+ + t a 2 t 0 exp(- a 2 t 2 /t 2 0 1 + t 2 /t 2 0 ) sin( a 2 t/t 0 1 + t 2 /t 2 0 ) . (24) The space-time diagram of this solution, shown in Fig. 4 again shows the Zitterbewegung of the position's mean values. It is interesting to stress that for the packet polarization determined by Eq. ( 17) the oscillatory behavior occurs in both x and y directions. The amplitude of oscillations in x direction is much less than that in y direction. | cond-mat.mes-hall |