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arXiv · 2211.01366

Current Noise of Hydrodynamic Electrons

Aaron Hui·Brian Skinner
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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.

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Aaron Hui, Brian Skinner. 2022-11-02. Current Noise of Hydrodynamic Electrons. https://doi.org/10.1103/physrevlett.130.256301

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