Cyclotron resonance of a two-dimensional Wigner crystal

Abstract

The scattering of two-dimensional electrons forming a Wigner crystal by vibrations of a medium (semiconductor or liquid helium) is considered. A method is developed that gives explicit expressions (including essential corrections to the Born approximation) for the cyclotron resonance (CR) peak shape. The halfwidth and shift of the peak are analysed in detail for the cases of relatively low and high electron densities (or, respectively, strong and weak magnetic fields). The results show that at low densities CR may be used to detect the short-range order in the electron system, while at high densities the transverse sound velocity may be determined for the Wigner crystal. The theory describes quantitatively the specific dependences of the CR parameters on the electron density observed experimentally for electrons above the liquid helium surface.