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Bulletin of the American Physical Society

Non-equilibrium bosonization and its applications to quantum Hall systems

Ivan Levkivksyi, Eugene V. Sukhorukov

Published Mar 1, 2012• 0 citations
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One of the manifestations of the integrability of electron dynamics in one dimension is the existence of non-equilibrium stationary states. Such states emerge near a quantum point contact coupling two quantum Hall edges with different chemical potentials. We use a non-equilibrium bosonization technique to show that the effective temperature in such states at the fractional quantum Hall edge has a universal linear dependence on the current through the contact. In contrast, the temperature of one-dimensional equilibrium systems scales as the square root of the corresponding dissipating power. This striking difference from the equilibrium behavior can be used to experimentally detect these unique non-equilibrium states.
The quantum Hall effect and the quantum anomalous Hall effect both require time-reversal invariance to be broken. We show that non-equilibrium effects can cause Hall physics to arise even when the system is weakly time-reversal symmetric and no magnetic field is applied. In our model, this occurs due to a fermionic subsystem breaking time-reversal invariance even if the system as a whole does not. The fermions receive a TRI-breaking self-energy, caused by interactions with bosonic degrees of freedom in the system and with an external reservoir. As a result, the fermions develop a non-quantized Hall conductance. We demonstrate that, unlike in the equilibrium case, the presence of a mass term is insufficient for the Hall conductance to appear, and wave-function renormalization effects have to be included.