An analytical treatment of in-plane magnetotransport in the Falicov-Sievert model

TL;DR

This paper presents an analytical method to efficiently compute in-plane magnetotransport properties considering complex Fermi surface trajectories influenced by Bragg scattering and magnetic breakdown, improving upon previous numerical approaches.

Contribution

It introduces an analytical expression for the in-plane resistivity tensor in the Falicov-Sievert model, enabling straightforward evaluation of magnetic breakdown effects.

Findings

Derived a compact analytical expression for the resistivity tensor.

Separated contributions from magnetic breakdown and complex trajectories.

Facilitated efficient computation of in-plane magnetotransport properties.

Abstract

We derive an analytical expression which allows efficient computation of the effect of all the Fermi surface trajectories induced by a combination of Bragg scattering and magnetic breakdown on the in-plane components of the resistivity tensor. The particular network of coupled orbits which we consider was first formulated by Falicov and Sievert, who studied the problem numerically. Our approach, based upon a method used previously to derive an analytical solution for interlayer transport, allows us to show that the conductivity tensor can be written as a sum of a matrix representing the effect of total magnetic breakdown and one representing a combination of complex electronic trajectories, and we find a compact expression for the in-plane components of the resistivity tensor that can be evaluated straightforwardly.