Spectroscopy of Heat Transport and Violation of the Wiedemann--Franz Law in a GaAs Hydrodynamic Mesoscopic Channel

Abstract

The Wiedemann--Franz law, which determines the universality of the ratio of thermal conductivity to electrical conductivity, is studied in the hydrodynamic electron transport regime, where electron--electron scattering predominates over scattering by disorder. In this case, the different relaxation of electric and thermal currents can lead to a violation of the Wiedemann--Franz law, which is expected to be even more pronounced in mesoscopic electron systems. This paper reports the propagation of hot electrons in a GaAs hydrodynamic narrow channel, studied using micrometer-resolution photoluminescence thermometry. A temperature dependence of the Lorenz number was obtained, indicating a violation of the Wiedemann--Franz law. The important role of narrow constrictions in this violation was also demonstrated, and theoretical arguments are presented.