Microwave Resonance and Carrier-Carrier Interaction in Two-Dimensional Hole Systems at High Magnetic Field

Microwave frequency conductivity, Re($\sigma_{xx}$), of high quality two-dimensional hole systems (2DHS) in a large perpendicular magnetic field (B) is measured with the carrier density ($n_s$) of the 2DHS controlled by a backgate bias. The high B insulating phase of the 2DHS exhibits a microwave resonance that remains well-defined, but shifts to higher peak frequency ($f_{pk}$) as $n_s$ is reduced. Over a wide range of $n_s, f_{pk} \propto n_s^{-1/2}$ is observed for the two samples we measured. The data clearly indicate that both carrier-carrier interactions and disorder are indispensable in determining the dynamics of the insulator. The $n_s$ dependence of $f_{pk}$ is consistent with a weakly pinned Wigner crystal in which domain size increases with $n_s$, due to larger carrier-carrier interaction.