Influence of topological excitations on Shapiro steps and microwave dynamical conductance in bilayer exciton condensates

The quantum Hall state at total filling factor ${\nu }_T=1$ in bilayer systems realizes an exciton condensate and exhibits a zero-bias tunneling anomaly, similar to the Josephson effect in the presence of fluctuations. In contrast to conventional Josephson junctions, no Fraunhofer diffraction pattern has been observed, due to disorder induced topological defects, so-called merons. We consider interlayer tunneling in the presence of microwave radiation, and find Shapiro steps in the tunneling current-voltage characteristic despite the presence of merons. Moreover, the Josephson oscillations can also be observed as resonant features in the microwave dynamical conductance.