# Sign of viscous magnetoresistance in electron fluids

## TL;DR

This paper demonstrates that in clean metals, viscous electron flow leads to always positive bulk magnetoresistance, providing a clear experimental signature of hydrodynamic electron behavior.

## Contribution

It establishes that bulk magnetoresistance is always positive in the hydrodynamic regime, regardless of inhomogeneity strength, and analyzes the transition from ballistic to hydrodynamic transport.

## Key findings

- Bulk magnetoresistance is always positive in the hydrodynamic regime.
- Weak inhomogeneity does not change the sign of magnetoresistance.
- Magnetotransport can serve as a test for viscous effects in bulk electron flow.

## Abstract

In sufficiently clean metals, it is possible for electrons to collectively flow as a viscous fluid at finite temperature. These viscous effects have been predicted to give a notable magnetoresistance, but whether the magnetoresistance is positive or negative has been debated. We argue that regardless of the strength of inhomogeneity, bulk magnetoresistance is always positive in the hydrodynamic regime. We also compute transport in weakly inhomogeneous metals across the ballistic-to-hydrodynamic crossover, where we also find positive magnetoresistance. The non-monotonic temperature dependence of resistivity in this regime (a bulk Gurzhi effect) rapidly disappears upon turning on any finite magnetic field, suggesting that magnetotransport is a simple test for viscous effects in bulk transport, including at the onset of the hydrodynamic regime.