Energy Relaxation at the Quantum Hall Edge

Abstract

We address the recent experiments where an electron distribution function at the quantum Hall edge has been measured with high precision. It has been reported that the energy of electrons injected into one of the two chiral edge channels with the help of a quantum point contact is equally distributed between them, in agreement with earlier predictions, one being based on the Fermi gas approach, and the other utilizing the Luttinger liquid theory. We argue that the physics of the energy relaxation process may in fact be more rich, providing the possibility for discriminating between two physical pictures in experiment. Namely, using the non-equilibrium bosonization technique we evaluate the electron distribution function and find that the initial “double-step” distribution evolves through several intermediate asymptotics, before reaching eventual equilibrium state. We suggest that the missing energy paradox may be explained by the nonlinear dispersion of the spectrum of edge states.KeywordsElectron Distribution FunctionTotal Heat FluxBoson FieldEdge ChannelQuantum Point ContactThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.