High frequency conductance of a quantum Hall insulator

Insulators do not carry DC current but can conduct electricity at high frequencies. In a quantum Hall insulator, this capacitive current is enabled by the time-dependent polarization of Landau orbits and is expected to carry information about the quantum geometry of the underlying Hilbert space. To measure this conductance, we embed a graphene quantum Hall insulator in a resonator where a dispersive shift of the resonator frequency sensitively tracks the capacitive response of these insulating states. Finite temperature and disorder broadening creates a conventional quantum capacitive response that competes with the quantum geometric contribution. We discuss ways to disentangle these contributions and show preliminary experiments.