Orbital magnetic susceptibility involves rich physics such as interband effects despite of its conceptual simplicity. In order to appreciate the rich physics related to the orbital magnetic susceptibility, it is essential to derive a formula to decom
pose the susceptibility into the contributions from each band. Here, we propose a scheme to perform this decomposition using the modified Wannier functions. The derived formula nicely decomposes the susceptibility into intraband and interband contributions, and from the other aspect, into itinerant and local contributions. The validity of the formula is tested in a couple of simple models. Interestingly, it is revealed that the quality of the decomposition depends on the degree of localization of the used Wannier functions. The formula here complements another formula using Bloch functions, or the formula derived in the semiclassical theory, which deepens our understanding of the orbital magnetic susceptibility and may serve as a foundation of a better computational method. The relationship to the Berry curvature in the present scheme is also clarified.
We theoretically investigate possible photoinduced topological phase transitions in the organic salt $alpha$-(BEDT-TTF)$_2$I$_3$, which possesses a pair of inclined massless Dirac-cone bands between the conduction and valence bands under uniaxial pre
ssure. The Floquet analyses of a driven tight-binding model for this material reveal rich photoinduced variations of band structures, Chern numbers, and Hall conductivities under irradiation with elliptically polarized light. The obtained phase diagrams contain a variety of nonequilibrium steady phases, e.g., the Floquet Chern insulator, Floquet semimetal, and Floquet normal insulator phases. This work widens a scope of target materials for research on photoinduced topological phase transitions and contributes to development of research on the optical manipulations of electronic states in matters.
To understand the unexpectedly high thermoelectric performance observed in the thin-film Heusler alloy Fe$_2$V$_{0.8}$W$_{0.2}$Al, we study the magnon drag effect, generated by the tungsten based impurity band, as a possible source of this enhancemen
t, in analogy to the phonon drag observed in FeSb$_2$. Assuming that the thin-film Heusler alloy has a conduction band integrating with the impurity band, originated by the tungsten substitution, we derive the electrical conductivity $L_{11}$ based on the self-consistent t-matrix approximation and the thermoelectric conductivity $L_{12}$ due to magnon drag, based on the linear response theory, and estimate the temperature dependent electrical resistivity, Seebeck coefficient and power factor. Finally, we compare the theoretical results with the experimental results of the thin-film Heusler alloy to show that the origin of the exceptional thermoelectric properties is likely to be due to the magnon drag related with the tungsten-based impurity band.
We study longitudinal electric and thermoelectric transport coefficients of Dirac fermions on a simple lattice model where tuning of a single parameter enables us to change the type of Dirac cones from type-I to type-II. We pay particular attention t
o the behavior of the critical situation, i.e., the type-III Dirac cone. We find that the transport coefficients of the type-III Dirac fermions behave neither the limiting case of the type-I nor type-II. On one hand, the qualitative behaviors of the type-III case are similar to those of the type-I. On the other hand, the transport coefficients do not change monotonically upon increasing the tilting, namely, the largest thermoelectric response is obtained not for the type-III case but for the optically tilted type-I case. For the optimal case, the sizable transport coefficients are obtained, e.g., the dimensionless figure of merit being 0.18.
We study the Seebeck effect in the three-dimensional Dirac electron system based on the linear response theory with Luttingers gravitational potential. The Seebeck coefficient $S$ is defined by $S = L_{12} / L_{11} T$, where $T$ is the temperature, a
nd $L_{11}$ and $L_{12}$ are the longitudinal response coefficients of the charge current to the electric field and to the temperature gradient, respectively; $L_{11}$ is the electric conductivity and $L_{12}$ is the thermo-electric conductivity. It is confirmed that $L_{11}$ and $L_{12}$ are related through Motts formula in low temperatures. The dependences of the Seebeck coefficient on the chemical potential $mu$ and the temperature $T$ when the chemical potential lies in the band gap ($|mu| < Delta$) are partially captured by $S propto (Delta - mu) / k_{mathrm{B}} T$ for $mu > 0$ as in semiconductors. The Seebeck coefficient takes the relatively large value $|S| simeq 1.7 ,mathrm{m V/K}$ at $T simeq 8.7,mathrm{K}$ for $Delta = 15 ,mathrm{m eV}$ by assuming doped bismuth.
It has been proposed that paramagnetic materials exhibit a unique thermoelectric effect near the ferromagnetic transition point due to spin fluctuations. This phenomenon is often referred to as paramagnon drag. We calculate the contribution of this p
aramagnon drag to the Seebeck coefficient microscopically on the basis of the linear response theory. This leed to a general formula for the contribution to the Seebeck coefficient due to the paramagnon drag, and we clarify the conditions in which the Seebeck coefficient enhances near the ferromagnetic transition point for a single-band and isotropic system. Moreover, we calculate the Seebeck coefficients for a band $varepsilon propto k^n$ and a mixture of free-electron-like and flat bands.
Lee, Rice and Anderson, in their monumental paper, have proved the existence of a collective mode describing the coupled motion of electron density and phonons in one-dimensional incommensurate charge density wave (CDW) in the Peierls state. This mod
e, which represents the coherent sliding motion of electrons and lattice distortions and affects low energy transport properties, is described by the phase of the complex order parameter of the Peierls condensate, leading to Frohlich superconductivity in pure systems. Once spatial disorder is present, however, phason is pinned and system is transformed into an insulating ground state: a dramatic change. Since phason can be considered as an ultimate of phonon drag effect, it is of interest to see its effects on thermoelectricity, which has been studied in the present paper based linear response theory of Kubo and Luttinger. The result indicates that a large absolute value of Seebeck coefficient proportional to the square root of resistivity is expected at low temperatures k_B T/Delta <<1 (Delta: Peierls gap) with opposite sign to the electronic contributions in the absence of Peierls gap.
We examine an effect of acoustic phonon scattering on an electric conductivity of single-component molecular conductor [Pd(dddt)$_2$] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) with a half-filled band by applying the previous calculation in a tw
o-dimensional model with Dirac cone [Phys. Rev. B {bf 98},161205 (2018)], where the electric transport by the impurity scattering exhibits the noticeable interplay of the Dirac cone and the phonon scattering,resulting in a maximum of the conductivity with increasing temperature. The conductor shows a nodal line semimetal where the band crossing of HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) provides a loop of Dirac points located close to the Fermi energy followed by the density of states (DOS) similar to that of two-dimensional Dirac cone. Using a tight-binding (TB) model [arXiv:2008.09277], which was obtained using the crystal structure observed from a recent X ray diffraction experiment under pressure, it is shown that the obtained conductivity explains reasonably the anomalous behavior in [Pd(dddt)$_2$] exhibiting almost temperature independent resistivity at finite temperatures. This paper demonstrates a crucial role of the acoustic phonon scattering at finite temperatures in the electric conductivity of Dirac electrons. The present theoretical results of conductivity are compared with those of experiments.
We study the nuclear magnetic relaxation rate and Knight shift in the presence of the orbital and quadrupole interactions for three-dimensional Dirac electron systems (e.g., bismuth-antimony alloys). By using recent results of the dynamic magnetic su
sceptibility and permittivity, we obtain rigorous results of the relaxation rates $(1/T_1)_{rm orb}$ and $(1/T_1)_{rm Q}$, which are due to the orbital and quadrupole interactions, respectively, and show that $(1/T_1)_{rm Q}$ gives a negligible contribution compared with $(1/T_1)_{rm orb}$. It is found that $(1/T_1)_{rm orb}$ exhibits anomalous dependences on temperature $T$ and chemical potential $mu$. When $mu$ is inside the band gap, $(1/T_1)_{rm orb} sim T ^3 log (2 T/omega_0)$ for temperatures above the band gap, where $omega_0$ is the nuclear Larmor frequency. When $mu$ lies in the conduction or valence bands, $(1/T_1)_{rm orb} propto T k_{rm F}^2 log (2 |v_{rm F}| k_{rm F}/omega_0)$ for low temperatures, where $k_{rm F}$ and $v_{rm F}$ are the Fermi momentum and Fermi velocity, respectively. The Knight shift $K_{rm orb}$ due to the orbital interaction also shows anomalous dependences on $T$ and $mu$. It is shown that $K_{rm orb}$ is negative and its magnitude significantly increases with decreasing temperature when $mu$ is located in the band gap. Because the anomalous dependences in $K_{rm orb}$ is caused by the interband particle-hole excitations across the small band gap while $left( 1/T_1 right)_{rm orb}$ is governed by the intraband excitations, the Korringa relation does not hold in the Dirac electron systems.
The orbital susceptibility for graphene is calculated exactly up to the first order with respect to the overlap integrals between neighboring atomic orbitals. The general and rigorous theory of orbital susceptibility developed in the preceding paper
is applied to a model for graphene as a typical two-band model. It is found that there are contributions from interband, Fermi surface, and occupied states in addition to the Landau--Peierls orbital susceptibility. The relative phase between the atomic orbitals on the two sublattices related to the chirality of Dirac cones plays an important role. It is shown that there are some additional contributions to the orbital susceptibility that are not included in the previous calculations using the Peierls phase in the tight-binding model for graphene. The physical origin of this difference is clarified in terms of the corrections to the Peierls phase.
