Hui, Aaron - The Ohio State University

Noise thermometry in electron hydrodynamics

Johnson noise thermometry, based on the Johnson-Nyquist theorem, offers a powerful primary thermometry technique to access the electron temperature at the nanoscale. In practical situations, one needs to generalize the Johnson-Nyquist theorem to handle spatially inhomogenous temperature profiles. This was previously done for Wiedemann-Franz-obeying ohmic devices, where it was found that Joule heating leads to a geometry-independent increase in Johnson noise. However, there has been great recent interest in strongly-interacting electron hydrodynamic systems which do not admit a local conductivity nor obey the Wiedemann-Franz law, signatures of which have even been observed in previous thermometry experiments. In this paper, we study low-frequency Johnson noise in the hydrodynamic setting for a rectangular geometry. As opposed to the ohmic setting, we find that the Johnson noise is no longer geometry-independent due to non-local viscous gradients. Despite this, ignoring the geometric correction only leads to an error of at most 40% as compared to naively using the ohmic result.