Resolving the Corbino Shockley-Ramo paradox for hydrodynamic current noise

Abstract

Johnson noise thermometry enables direct measurement of the electron temperature, a valuable probe of many-body systems. Practical use of this technique calls for nonequilibrium generalizations of the Johnson-Nyquist theorem. For a hydrodynamic Corbino device, however, a naive use of the Shockley-Ramo theorem alongside the “Corbino paradox” leads to yet another paradox: current noise through the contacts would seem to be completely insensitive to bulk fluctuations. In this work, we resolve the unphysical “Corbino Shockley-Ramo paradox” by correctly formulating the hydrodynamic Shockley-Ramo problem. This allows us to properly formulate the problem of current noise in a hydrodynamic multiterminal device of arbitrary geometry, as well as validate a previously unjustified assumption for rectangular geometry results. As an example, we compute the Johnson noise in a hydrodynamic Corbino device, where we find a suppression of Johnson noise with magnetic field. This unusual characteristic serves as a qualitative signature of viscous hydrodynamic behavior. Published by the American Physical Society 2024