Thermoelectric Response in Strongly Disordered Systems
© The Physical Society of Japan
This article is on
Thermoelectric Effect in Mott VariableRange Hopping
J. Phys. Soc. Jpn. 91, 044704 (2022).
Based on the Kubo–Luttinger linear response theory, we discovered that the lowT Seebeck coefficient for Mott variablerange hopping in a ddimensional system varies as S ∝ T^{d}^{/(d+1)}, which is different from the conventional S ∝ T^{(}^{d}^{−1)/(}^{d}^{+1)}. In addition, the experimental data for S of CuCrTiS_{4} at low T are in excellent agreement with our prediction S ∝ T^{3/4} (d = 3).
In 1957, Kubo established the linear response theory to kinetic perturbation (e.g., electric or magnetic field). In the following years, based on the combination of the thermal Green's function technique with the Kubo formula, the linear response theory has emerged as a powerful practical tool for analyzing quantum transport and the magnetic response of materials. In contrast, the linear response theory to thermodynamic perturbation (e.g., temperature gradient) was advocated by Luttinger in 1964. Luttinger succeeded in treating the temperature gradient as a kinetic perturbation by introducing a fictitious gravitational field (scalar field). Since 2018, the authors and their coworkers have been developing the Luttinger formula together with the thermal Green's function technique to determine the thermal response (i.e., thermoelectric (TE) effect and thermal transport) of materials from a quantum mechanical perspective. The developed technique has been successfully applied to various materials exhibiting interesting TE effects that cannot be explained in terms of the Boltzmann transport theory (BTT).
In this study, as a typical thermal response beyond the BTT framework, the authors investigated the TE response in Mott variablerange hopping (VRH) using the abovementioned Kubo–Luttinger (KL) theory together with the thermal Green's function technique. By incorporating the energy dependence of the localization length near the mobility edge based on the scaling theory of Anderson localization, we clarified that the Seebeck coefficient S(T) varies according to S ∝ T^{d}^{/(d+1)} in a ddimensional system, which is different from the widely used Mott–Davis expression, S ∝ T^{(d−1)/(d+1)}, based on the energyindependent localization length. In addition, we demonstrated that the lowT behavior of S(T) for thiospinel CuCrTiS_{4}, which is known as a typical TE material exhibiting Mott VRH at low T, is in complete agreement with our theoretical prediction S ∝ T^{3/4} (d = 3).
This study enables precise prediction of the performance of disordered TE materials exhibiting Mott VRH. The development of such a complete quantum theory that precisely predicts TE properties will play a role in realizing a sustainable society.
(Written by T. Yamamoto on behalf of all the authors.)
Thermoelectric Effect in Mott VariableRange Hopping
J. Phys. Soc. Jpn. 91, 044704 (2022).
Share this topic
Fields
Related Articles

Strange Metal Behavior Potentially Associated to Hidden Electronic Nematicity
Superconductivity
Electronic transport in condensed matter
20221110
Ironbased superconductor, Ba_{1x}Rb_{x}Fe_{2}As_{2}, exhibits “strange metal” behavior—linear dependence of resistivity on temperature. It seems that hidden electronic nematic fluctuations play a greater role than the wellknown antiferromagnetic fluctuations.

Spin Transport in a TwoDimensional Tilted Dirac Electron System
Electronic transport in condensed matter
Electronic structure and electrical properties of surfaces and nanostructures
2022413
We propose that spin current in an organic conductor, α(BETS)_{2}I_{3}, is an appropriate physical quantity to detect the topological nature of the material whose electrons obey a quasitwodimensional Dirac equation.

Violation of FluctuationDissipation Theorem Results in Robustness of Fluctuation Against Localization
Statistical physics and thermodynamics
Electronic transport in condensed matter
Electronic structure and electrical properties of surfaces and nanostructures
2022323
We study equilibrium current fluctuations in systems without timereversal symmetry, violating the fluctuationdissipation theorem. Notably, the offdiagonal fluctuation is insensitive to system imperfections in contrast to other fluctuations and conductivity.

Topological Aspects of a Nonlinear System: The Dimerized Toda Lattice
Electronic structure and electrical properties of surfaces and nanostructures
Electronic transport in condensed matter
2022316
A nonlinear topological phase is shown to emerge in the dimerized Toda lattice. It is experimentally detectable by measuring the voltage propagation in electric circuits.

Unusual Nonlinear Conductivity in ChargeOrdered α(BEDTTTF)_{2}I_{3}
Electronic transport in condensed matter
202239
Unusual nonlinear conduction is detected in organic molecular salt α(BEDTTTF)_{2}I_{3}. The observed thirdorder nonlinear conductivity implies a quadrupole instability hidden in this chargeordered organic salt.