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

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. In different regimes, f'(pk) vs n(s) can be fit to f(pk)proportional to n(s)(-1/2) or to f(pk)proportional to n(s)(-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(pk) is consistent with a weakly pinned Wigner crystal in which domain size increases with n(s), due to larger carrier-carrier interaction.