Current Noise of Hydrodynamic Electrons

TL;DR

This paper extends Johnson-Nyquist noise analysis to hydrodynamic electron systems, revealing geometry-dependent effects and providing a more accurate thermometry method for inhomogeneous electron temperatures.

Contribution

It introduces a generalization of Johnson noise for hydrodynamic electrons, accounting for non-local viscous effects and geometry dependence, which was lacking in prior models.

Findings

Johnson noise in hydrodynamic electrons depends on device geometry.

Ignoring geometric effects leads to at most 40% error in temperature measurement.

Hydrodynamic effects introduce non-local viscous gradients affecting noise.

Abstract

A resistor at finite temperature produces white noise fluctuations of the current called Johnson-Nyquist noise. Measuring the amplitude of this noise provides a powerful primary thermometry technique to access the electron temperature. In practical situations, however, one needs to generalize the Johnson-Nyquist theorem to handle spatially inhomogeneous temperature profiles. Recent work provided such a generalization for ohmic devices obeying the Wiedemann-Franz law, but there is a need to provide a similar generalization for hydrodynamic electron systems, since hydrodynamic electrons provide unusual sensitivity for Johnson noise thermometry but they do not admit a local conductivity nor obey the Wiedemann-Franz law. Here we address this need by considering low-frequency Johnson noise in the hydrodynamic setting for a rectangular geometry. Unlike in the ohmic setting, we find that the Johnson noise is geometry-dependent due to non-local viscous gradients. Nonetheless, ignoring the geometric correction only leads to an error of at most 40% as compared to naively using the ohmic result.