Current Noise of Hydrodynamic Electrons

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.

9 pages, 4 figures with appendix; typo corrected in Eq. 5 and Eq. 8

References in corpus (10)

• Hydrodynamics of electrons in graphene
• Slow imbalance relaxation and thermoelectric transport in graphene
• Quantum-critical relativistic magnetotransport in graphene
• Hydrodynamic approach to two-dimensional electron systems
• Stokes flow around an obstacle in viscous two-dimensional electron liquid
• Freely flowing currents and electric field expulsion in viscous electronics
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• Large Violation of the Wiedemann Franz Law in Heusler, Ferromagnetic, Weyl Semimetal Co${}_2$MnAl
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Cited by in corpus (4)

• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
• Two-dimensional hydrodynamic electron flow through periodic and random potentials
• Resolving the Corbino Shockley-Ramo Paradox for Hydrodynamic Current Noise
• Non-local origin and correlations in the Johnson noise at nonuniform temperatures