Parity Violation in Aharonov-Bohm Systems: The Spontaneous Hall Effect

TL;DR

This paper demonstrates that a gas of charged particles interacting with flux tubes via Aharonov-Bohm effects can spontaneously exhibit a Hall effect due to many-body symmetry breaking, linking it to quantum Hall phenomena.

Contribution

It introduces a model showing spontaneous parity violation and Hall effect emergence in Aharonov-Bohm systems, highlighting many-body effects and universal constant dependence.

Findings

Non-zero transverse conductivity observed

Spontaneous Hall effect due to many-body interactions

Conductivity dependence similar to Quantum Hall Effect

Abstract

We show how macroscopic manifestations of $P$ (and $T$) symmetry breaking can arise in a simple system subject to Aharonov-Bohm interactions. Specifically, we study the conductivity of a gas of charged particles moving through a dilute array of flux tubes. The interaction of the electrons with the flux tubes is taken to be of a purely Aharonov-Bohm type. We find that the system exhibits a non-zero transverse conductivity, i.e., a spontaneous Hall effect. This is in contrast with the fact that the cross sections for both scattering and bremsstrahlung (soft photon emission) of a single electron from a flux tube are invariant under reflections. We argue that the asymmetry in the conductivity coefficients arises from many-body effects. On the other hand, the transverse conductivity has the same dependence on universal constants that appears in the Quantum Hall Effect, a result that we relate to the validity of the Mean Field approximation.