Microwave Dynamical Conductivity in the Quantum Hall Regime

Dynamical conductivity contains information of dissipative and nondissipative processes induced by ac-electric fields. In the integer quantum Hall (QH) effect where the nondissipative Hall current is the most prominent feature, its robustness is assured by localized states within the Landau levels. We establish a noncontact method with a circular cavity resonator and detect the real and imaginary parts of the longitudinal and Hall conductivities at a microwave frequency in magnetic fields. The conventional Shubnikov-de Haas oscillations and QH plateaus are observed in the real parts of longitudinal and Hall conductivities, respectively, while periodic structures can be seen in the imaginary parts which are scaled by the QH filling factor. The latter originates from intra-Landau level transitions between different orbital angular momenta. The results demonstrate that the dynamical conductivity measurement provides microscopic information which is not accessible by conventional static methods. The present noncontact method would pave the way to reveal the electron dynamics in other two-dimensional systems such as twisted bilayer graphene.