Chiral anomaly in real space from stable fractional charges at the edge of a quantum spin Hall insulator

The chiral anomaly is based on a nonconserved 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. Here we 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 edges of a quantum spin Hall insulator by means of magnetic barriers. Such a setup gives rise to fractional charges which we show to be sharp quantum numbers for large barrier strengths. 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 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, which is connected to the presence of fractional charges in the very same system.