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

Microwave frequency conductivity Re(sigma(xx)) of high quality two-dimensio nal hole systems (2DHS) in a large perpendicular magnetic field (B) is meas ured with the carrier density (n(s)) of the 2DHS controlled by a backgate b ias. 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)pr oportional to n(s)(-1/2) or to f(pk)proportional to n(s)(-3/2). The data cl early indicate that both carrier-carrier interactions and disorder are indi spensable 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.