Microwave resonance and weak pinning in two-dimensional hole systems at high magnetic fields

Abstract

Microwave frequency conductivity $\mathrm{Re}({\ensuremath{\sigma}}_{\mathrm{xx}})$ 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 ${(f}_{\mathrm{pk}})$ as ${n}_{s}$ is reduced. In different regimes, ${f}_{\mathrm{pk}}$ vs ${n}_{s}$ can be fit to ${f}_{\mathrm{pk}}\ensuremath{\propto}{n}_{s}^{\ensuremath{-}1/2}$ or to ${f}_{\mathrm{pk}}\ensuremath{\propto}{n}_{s}^{\ensuremath{-}3/2}.$ 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 ${f}_{\mathrm{pk}}$ is consistent with a weakly pinned Wigner crystal in which domain size increases with ${n}_{s},$ due to larger carrier-carrier interaction.