The transverse magnetoresistance of the two-dimensional chiral metal

TL;DR

This paper calculates the positive transverse magnetoresistance of a two-dimensional chiral metal at low temperatures, linking it to the elastic mean free path and providing a potential experimental measurement method.

Contribution

It presents a theoretical calculation of magnetoresistance in a 2D chiral metal, connecting it to fundamental parameters like the elastic mean free path.

Findings

Magnetoresistance follows a Drude form with a specific field scale.

Experimental measurement can determine the elastic mean free path.

Magnetoresistance is positive in the studied regime.

Abstract

We consider the two-dimensional chiral metal, which exists at the surface of a layered, three-dimensional sample exhibiting the integer quantum Hall effect. We calculate its magnetoresistance in response to a component of magnetic field perpendicular to the sample surface, in the low temperature, but macroscopic, regime where inelastic scattering may be neglected. The magnetoresistance is positive, following a Drude form with a field scale, $B_0=\Phi_0/al_{\text{el}}$, given by the transverse field strength at which one quantum of flux, $\Phi_0$, passes through a rectangle with sides set by the layer-spacing, $a$, and the elastic mean free path, $l_{\text{el}}$. Experimental measurement of this magnetoresistance may therefore provide a direct determination of the elastic mean free path in the chiral metal.