Microwave resonances of the bubble phases in 1/4 and 3/4 filled higher Landau levels

Abstract

We have measured the diagonal conductivity in the microwave regime of an ultrahigh mobility two dimensional electron system. We find a sharp resonance in Re[sigma_{xx}] versus frequency when nu > 4 and the partial filling of the highest Landau level, nu^*, is ~ 1/4 or 3/4 and temperatures < 0.1 K. The resonance appears for a range of nu^* from 0.20 to 0.37 and again from 0.62 to 0.82. the peak frequency, f_{pk} changes from ~ 500 to ~ 150 as nu^* = 1/2 is approached. This range of f_{pk} shows no dependence on nu where the resonance is observed. The quality factor, Q, of the resonance is maximum at ~ nu^* = 0.25 and 0.74. We interpret the resonance as due to a pinning mode of the bubble phase crystal.