Longitudinal and transverse magnetoresistance of SrTiO$_3$ with a single closed Fermi surface

TL;DR

This paper provides a theoretical analysis of magnetoresistance in SrTiO$_3$, revealing that a single closed Fermi surface can produce both transverse and longitudinal MR, challenging traditional views and matching experimental data.

Contribution

It extends the MR formula to arbitrary Fermi surface shapes and explains the angular dependence of MR in SrTiO$_3$ based on detailed band structure considerations.

Findings

Calculated MR of 300% at 10 T matches experimental data.

Angular dependence of mass tensor components explains MR types.

Negative Gaussian curvature of Fermi surface influences MR behavior.

Abstract

The magnetoresistance (MR) of SrTiO$_3$ is theoretically investigated based on the Boltzmann equation by considering its detailed band structure. The formula for MR proposed by Mackey and Sybert is extended to be applicable to a system with an arbitrarily shaped Fermi surface. It is shown that the angular dependence of the diagonal component of the mass tensor causes transverse MR, whereas that of the off-diagonal component causes longitudinal MR with only a single closed Fermi surface, which overturns the textbook understanding of MR. The calculated MR (300% at 10 T) quantitatively agrees with the experimental results for SrTiO$_3$ including the behavior of the linear MR. The negative Gaussian curvature of the Fermi surface of SrTiO$_3$ and its resulting negative longitudinal and transverse MR are also discussed.