Imaging impurities at quantum Hall edges in graphene: Dissipation rings induced by forward scattering

Motivated by the recent experiment by Marguerite et al. on imaging in graphene samples, we investigate theoretically the dissipation induced by resonant impurities in the quantum Hall regime. Briefly, the impurity induced forward scattering of quantum Hall particles leads to an enhanced phonon emission, which reaches its maximum when the impurity state is fine tuned to its resonance by an applied tip voltage. Our analysis of the effect of a tip potential on the dissipation thus reveals peculiar thermal rings near the impurity, in consistency with experimental observations. This thermal ring behavior, while appearing similar as that in two dimensional materials, turns out to be physically novel and contains features that are unique in quantum Hall systems.