Dissipative Callan-Harvey mechanism in 2+1 D Dirac system: The fate of edge states along a domain wall

The Callan-Harvey mechanism in 2+1 D Jackiw-Rebbi model is revisited. We analyzed Callan-Harvey anomaly inflow in the massive Chern insulator (quantum anomalous Hall system) subject to external electric field. In addition to the conventional current flowing from the bulk to edge due to parity anomaly, we considered the dissipation of the edge charge due to interaction with external bosonic bath in 2+1 D and due to external bath of photons in 3+1 D. In the case of 2+1 D bosonic bath, we found the new stationary state, which is defined by the balance between Callan-Harvey current and the outgoing flow caused by the dissipation processes. In the case of 3+1 D photon bath, we found a critical electric field, below which this balance state can be achieved, but above which there is no such a balance. Furthermore, we estimated the photon-mediated transition rate between 2+1 D bulk and 1+1 D topological edge state of the order of one ns$^{-1}$ (nanosecond) at the room temperature.