Microwave Conductivity Resonance of Two-Dimensional Hole System

Abstract

We have measured microwave conductivity, $\mathrm{Re}({\ensuremath{\sigma}}_{\mathrm{xx}})$, of a high quality two-dimensional hole system (2DHS) in the high magnetic field (B) insulating phase for frequency ( f) between 0.2 and 9 GHz. For $\ensuremath{\nu}<0.3$, $\mathrm{Re}({\ensuremath{\sigma}}_{\mathrm{xx}})$ vs f shows a well-defined peak at frequency ${f}_{\mathrm{pk}}$. As B is increased, the maximal $\mathrm{Re}({\ensuremath{\sigma}}_{\mathrm{xx}})$ increases. The resonance $Q$ ( ${f}_{\mathrm{pk}}$ divided by full line width at half maximum) increases linearly with B. ${f}_{\mathrm{pk}}$ vs B increases, but is nearly flat, at 1.25 GHz, for $B\ensuremath{\ge}10\mathrm{T}$. Oscillator strength, S, measured by integrating the spectrum, is likewise flat for $B\ensuremath{\ge}10\mathrm{T}$. The simultaneously B-independent S and ${f}_{\mathrm{pk}}$ are inconsistent with the conventional (Fukuyama-Lee) interpretation of the resonance as a Wigner crystal pinning mode.