Nonlocal thermoelectric detection of interaction and correlations in edge states

Nonlocal thermoelectricity is proposed as a direct probe of interactions, nonthermal states, and the effect of correlations in the nonequilibrium heat transport between 1D quantum channels. In copropagating quantum Hall edge states contacted at different temperatures, the nonlocal thermoelectrical response is only expected if the electron-electron interaction mediates the heat exchange directly measuring the interaction strength. Considering the low-energy limit of zero-range interactions, we analytically solve the charge and energy currents of a nonequilibrium interacting system, determining the universal scaling law in terms of an interaction-dependent energy-relaxation length. Further, a setup with two controllable quantum point contacts allows thermoelectricity to monitor the thermalization of an interacting system as well as the fundamental role of cross-correlations in the heat exchange at intermediate length scales.