Theory of collective magnetophonon resonance and melting of a field-induced Wigner solid

Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data. Firstly, violation of the Fukuyama-Lee sum rule as the transition is approached is shown to be a consequence of the non-Lorentzian form taken by the resonance. Secondly, this non-Lorentzian shape is shown to be caused by dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers.