Saved in:
Bibliographic Details
Main Authors: Takahashi, Keigo, Matsuura, Hiroyasu, Maebashi, Hideaki, Ogata, Masao
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.07229
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916997379391488
author Takahashi, Keigo
Matsuura, Hiroyasu
Maebashi, Hideaki
Ogata, Masao
author_facet Takahashi, Keigo
Matsuura, Hiroyasu
Maebashi, Hideaki
Ogata, Masao
contents We study the electrical and thermal transport properties and the violation of the Wiedemann-Franz (WF) law of two-carrier semimetals using exact treatments of the Boltzmann equation with the impurity and electron-electron scatterings in a magnetic field. For comparison, we also study those in the case of Baber scattering: a single-carrier system with an impurity scattering and phenomenological momentum-dissipative electron-electron scattering. In both systems, the longitudinal and transverse WF laws, $L = L_{\text{H}} = L_{0}= π^2k_B^2/3e^2$, hold at zero temperature, where the Lorenz ratio $L$ and the Hall Lorenz ratio $L_{\text{H}}$ are ratios of thermal conductivity $κ_{μν}$ to electrical conductivity $σ_{μν}$ divided by temperature. However, the electron-electron scattering makes Lorenz ratios deviate from $L_{0}$ with increasing temperature. To describe the WF law in a magnetic field, we introduce another set of Lorenz ratios, $\widetilde{L}$ and $\widetilde{L}_{\text{H}}$, defined as the ratios of the resistivity and the Hall coefficient to their thermal counterparts. The WF laws for them, $\widetilde{L} = \widetilde{L}_{\text{H}} = L_{0}$, and their violation are helpful for the discussion of $L$ and $L_{\text{H}}$. For Baber scattering, our exact result shows $L_{\text{H}}/L_{0} \sim (L/L_{0})^2$ in a weak magnetic field. In semimetals, the violations of the WF laws are significant, reflecting the different temperature dependence between the electrical and thermal resistivities in a magnetic field. This is because the momentum conservation of the electron-electron scattering has a completely different effect on electrical and thermal magnetotransport. We sort out these behaviors using $\widetilde{L}$ and $\widetilde{L}_{\text{H}}$. We also provide a relaxation time approximation, which is useful for comparing theory and experiment.
format Preprint
id arxiv_https___arxiv_org_abs_2510_07229
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Electrical and thermal magnetotransport and the Wiedemann-Franz law in semimetals with electron-electron scattering
Takahashi, Keigo
Matsuura, Hiroyasu
Maebashi, Hideaki
Ogata, Masao
Strongly Correlated Electrons
Materials Science
We study the electrical and thermal transport properties and the violation of the Wiedemann-Franz (WF) law of two-carrier semimetals using exact treatments of the Boltzmann equation with the impurity and electron-electron scatterings in a magnetic field. For comparison, we also study those in the case of Baber scattering: a single-carrier system with an impurity scattering and phenomenological momentum-dissipative electron-electron scattering. In both systems, the longitudinal and transverse WF laws, $L = L_{\text{H}} = L_{0}= π^2k_B^2/3e^2$, hold at zero temperature, where the Lorenz ratio $L$ and the Hall Lorenz ratio $L_{\text{H}}$ are ratios of thermal conductivity $κ_{μν}$ to electrical conductivity $σ_{μν}$ divided by temperature. However, the electron-electron scattering makes Lorenz ratios deviate from $L_{0}$ with increasing temperature. To describe the WF law in a magnetic field, we introduce another set of Lorenz ratios, $\widetilde{L}$ and $\widetilde{L}_{\text{H}}$, defined as the ratios of the resistivity and the Hall coefficient to their thermal counterparts. The WF laws for them, $\widetilde{L} = \widetilde{L}_{\text{H}} = L_{0}$, and their violation are helpful for the discussion of $L$ and $L_{\text{H}}$. For Baber scattering, our exact result shows $L_{\text{H}}/L_{0} \sim (L/L_{0})^2$ in a weak magnetic field. In semimetals, the violations of the WF laws are significant, reflecting the different temperature dependence between the electrical and thermal resistivities in a magnetic field. This is because the momentum conservation of the electron-electron scattering has a completely different effect on electrical and thermal magnetotransport. We sort out these behaviors using $\widetilde{L}$ and $\widetilde{L}_{\text{H}}$. We also provide a relaxation time approximation, which is useful for comparing theory and experiment.
title Electrical and thermal magnetotransport and the Wiedemann-Franz law in semimetals with electron-electron scattering
topic Strongly Correlated Electrons
Materials Science
url https://arxiv.org/abs/2510.07229