Longitudinal conductivity of massless fermions with tilted Dirac cone in magnetic field

TL;DR

This paper studies how tilting of Dirac cones in a 2D relativistic electron gas affects longitudinal conductivity under magnetic fields, revealing anisotropic behavior and implications for experimental detection.

Contribution

It provides a detailed analysis of anisotropic conductivity due to tilted Dirac cones in magnetic fields, including numerical studies and experimental implications.

Findings

Conductivity behaves differently parallel and perpendicular to the tilt.

Tilting induces anisotropy that varies with magnetic field.

The effect of tilting on conductivity is mainly a change in prefactor.

Abstract

We investigate a longitudinal conductivity of a two-dimensional relativistic electron gas with a tilted Dirac cone in magnetic field. It is demonstrated that the conductivity behaves differently in the directions parallel and perpendicular to the tilting of the cone. At high magnetic fields the conductivity at non-zero Landau levels in the direction perpendicular to the tilting modifies non-trivially, in contrast to the parallel case. At zero temperature the crossover of the conductivity at the Dirac point from high to low magnetic field is studied numerically. It is found that that the tilting produces anisotropy of the conductivity which changes with the magnetic field which is different from the anisotropy coming from the Fermi velocity. We also discuss the conductivity at finite temperatures and finite magnetic fields which can be directly compared with the experiments in $\alpha$-(BEDT-TTF)$_2$I$_3$ organic conductor. We find that the tilting does not affect so much the magnetic-filed dependence of the conductivity except for the prefactor. We discuss the interpretation of recent experimental data and make some proposals to detect the effect of the tilting in future experiments.