Intrinsic Magnetoresistance in Three-Dimensional Dirac Materials

TL;DR

This paper develops a quantum theory explaining intrinsic anisotropic magnetoresistance in 3D Dirac materials, revealing how it depends on carrier density, mobility, and magnetic field, with implications for experimental measurements.

Contribution

It introduces a novel quantum framework for intrinsic magnetoresistance in 3D Dirac fermions, linking it to fundamental material properties and providing formulas for experimental analysis.

Findings

Longitudinal magnetoresistance is negative and quadratic in B.

In-plane transverse magnetoresistance is positive and quadratic in B.

Relative magnetoresistance depends inversely on the fourth power of the Fermi wave vector.

Abstract

Recently, negative longitudinal and positive in-plane transverse magnetoresistance have been observed in most topological Dirac/Weyl semimetals, and some other topological materials. Here we present a quantum theory of intrinsic magnetoresistance for three-dimensional Dirac fermions at a finite and uniform magnetic field B. In a semiclassical regime, it is shown that the longitudinal magnetoresistance is negative and quadratic of a weak field B while the in-plane transverse magnetoresistance is positive and quadratic of B. The relative magnetoresistance is inversely quartic of the Fermi wave vector and only determined by the density of charge carriers, irrelevant to the external scatterings in the weak scattering limit. This intrinsic anisotropic magnetoresistance is measurable in systems with lower carrier density and high mobility. In the quantum oscillation regime a formula for the phase shift in Shubnikov-de Hass oscillation is present as a function of the mobility and the magnetic field, which is useful for experimental data analysis.