Interaction-induced charge transfer in a mesoscopic electron spectrometer

In this paper, we theoretically investigate a mesoscopic electron spectrometer that allows for the probing of relaxation processes in quantum Hall edge channels, which has recently been experimentally realized. The device is composed of an emitter quantum dot that injects energy-resolved electrons into the channel closest to the sample edge, to be subsequently probed downstream by a detector quantum dot of the same type. In addition to inelastic processes in the sample that stem from interactions inside the region between the quantum dot energy filters (inner region), anomalous signals are measured when the detector energy exceeds the emitter energy. Considering finite-range Coulomb interactions in the sample, we find that energy exchange between electrons in the current-inducing source channel and the inner region, similar to Auger recombination processes, is responsible for such anomalous currents. In addition, our perturbative treatment of interactions shows that electrons emitted from the source, which dissipate energy to the inner region before entering the detector, contribute to the current most strongly when emitter-detector energies are comparable. Charge transfer in which the emitted electron is exchanged for a charge carrier from the Fermi sea, on the other hand, preferentially occurs close to the Fermi level.