The chiral anomaly in real space

TL;DR

This paper introduces a novel real-space approach to the chiral anomaly using a quantum dot system at the edge of a quantum spin Hall insulator, linking spectral flow to observable charge transfer.

Contribution

It proposes a new real-space realization of the chiral anomaly in a quantum dot setup, mapping it onto a flux in a quantum spin Hall ring, and predicts measurable effects.

Findings

Fractional charges are sharp quantum numbers at large barrier strength.

The system can be mapped onto a quantum spin Hall ring with flux.

Observable consequences of the chiral anomaly are predicted.

Abstract

The chiral anomaly is based on a non-conserved chiral charge and can happen in Dirac fermion systems under the influence of external electromagnetic fields. In this case, the spectral flow leads to a transfer of right- to left-moving excitations or vice versa. The corresponding transfer of chiral particles happens in momentum space. We here describe an intriguing way to introduce the chiral anomaly into real space. Our system consists of two quantum dots that are formed at the helical edge of a quantum spin Hall insulator on the basis of three magnetic impurities. Such a setup gives rise to fractional charges which we show to be sharp quantum numbers for large barrier strength. Interestingly, it is possible to map the system onto a quantum spin Hall ring in the presence of a flux pierced through the ring where the relative angle between the magnetization directions of the impurities takes the role of the flux. The chiral anomaly in this system is then directly related to the excess occupation of particles in the two quantum dots. This analogy allows us to predict an observable consequence of the chiral anomaly in real space.