Kinetic theory of electronic transport in random magnetic fields

TL;DR

This paper develops a kinetic theory for electronic transport in inhomogeneous magnetic fields, revealing how viscous effects and electron-electron collisions influence resistivity, especially in the context of Fermi liquids like SrTiO3.

Contribution

It introduces a theoretical framework for quasiparticle transport in small inhomogeneous magnetic fields, bridging ballistic and hydrodynamic regimes, and explains a new resistivity mechanism in Fermi liquids.

Findings

Resistivity grows with electron-electron collision rate at high temperatures.

Viscous effects can suppress conductance below ballistic levels.

The theory may explain T^2 resistivity in SrTiO3.

Abstract

We present the theory of quasiparticle transport in perturbatively small inhomogeneous magnetic fields across the ballistic-to-hydrodynamic crossover. In the hydrodynamic limit, the resistivity $\rho$ generically grows proportionally to the rate of momentum-conserving electron-electron collisions at large enough temperatures $T$. In particular, the resulting flow of electrons provides a simple scenario where viscous effects suppress conductance below the ballistic value. This new mechanism for $\rho\propto T^2$ resistivity in a Fermi liquid may describe low $T$ transport in single-band $\mathrm{SrTiO}_3$.