Hall conductance in a weakly time-reversal invariant open system

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.

Figures (4)

• Figure 1: The diagrams that give chirality-mixing contributions to the self-energy component $\Sigma^{A}$, to one-loop order. The external legs have been included to clarify which propagator type is ingoing or outgoing, even though we only compute the amputated diagram. We use a convention with dashed (solid) lines for quantum (classical) fields to more clearly show the propagators that we are using.
• Figure 2: Feynman diagrams for the polarization tensor component $\Pi^R_{\mu\nu}$, to one-loop order.
• Figure 3: The chirality-mixing diagrams for the self-energy component $\Sigma^{R}$, to one-loop order.
• Figure 4: The chirality-mixing diagrams for the self-energy component $\Sigma^{K}$, to one-loop order.