Hall conductance in a weakly time-reversal invariant open system

TL;DR

This paper demonstrates that non-equilibrium effects can induce Hall conductance in systems weakly breaking time-reversal symmetry, even without magnetic fields, through fermionic self-energy modifications caused by interactions.

Contribution

It introduces a model showing how non-equilibrium interactions can generate Hall conductance in weakly time-reversal invariant open systems, highlighting the role of fermionic self-energy effects.

Findings

Non-equilibrium effects induce Hall conductance without magnetic fields.

Fermionic self-energy from interactions breaks time-reversal invariance.

Wave-function renormalization is essential for Hall conductance emergence.

Abstract

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.