Evidence for a magnetic-field-induced Wigner glass in the two-dimensional electron system in Si inversion layers

Abstract

Cyclotron resonance experiments on the two-dimensional electron system in Si inversion layers are described that probe the dynamical response in the extreme quantum limit. A remarkable narrowing and shifting of the absorption line is observed as the electron density ${n}_{s}$ is reduced to the point that only the lowest spin-valley-Landau level is occupied. This anomalous behavior has been studied as a function of magnetic field ($B\ensuremath{\le}7.5$ T), electron density (${n}_{s}\ensuremath{\ge}\frac{{10}^{10}}{{\mathrm{cm}}^{2}}$), temperature (1.2-30 K), and substrate bias (surface electric field). The spectroscopy is performed with a Michelson interferometer which determines conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ from 5 to 60 ${\mathrm{cm}}^{\ensuremath{-}1}$ with all the external parameters of the system, in particular the magnetic field, held fixed. The results are compared with a variety of models including single-electron trapping, electron-phonon coupling, and a pinned charge-density wave (CDW). Although all suffer some shortcomings, the most satisfactory account of the experimental results is obtained by assuming that the electrons form some sort of short-range-ordered structure at low temperatures in the extreme quantum limit. A quantitative comparison is made with the pinned-CDW model of Fukuyama and Lee. Fitting this model to the experimental data results in a pinning parameter that depends inversely on wave-function thickness normal to the interface. The modulation depth of the CDW and the correlation length of the short-range order are also extracted. The picture that emerges in the extreme quantum limit is that of a highly disordered Wigner glass.