Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu=5/2$ Quantum Hall Effect

Recent thermal Hall experiment triggered renewed interest in the problem of $\nu=5/2$ quantum Hall effect, which motivated novel interpretations based on formation of mesoscopic puddles made of Pfaffian and anti-Pfaffian topological orders. Here, we study an interface between the Pfaffian and anti-Pfaffian states, which may play crucial roles in thermal transport, by means of state-of-the-art density-matrix renormalization group simulations. We demonstrate an intrinsic electric dipole moment emerges at the interface, similar to the ``p-n" junction sandwiched between N-type and P-type semiconductor. Importantly, we elucidate the topological origin of this dipole moment, whose formation is to counterbalance the mismatch of guiding-center Hall viscosity of bulk Pfaffian and anti-Pfaffian state. In addition, these results imply that the formation of dipole moment could be helpful to stabilize the puddles made of Pfaffian and anti-Pfaffian state in experimental conditions.