Vibrational excitations in the paired phases of a two-dimensional electron crystal in a perpendicular magnetic field

We evaluate the elementary excitations of both spin-singlet and spin-triplet paired crystalline phases of a two-dimensional system of electrons in a perpendicular magnetic field. We use the harmonic Hamiltonian derived from a truncation of the intercell interactions at dipolar terms and treat it within a circular-cell approximation. At this level the excitations are of two types, i.e. a discrete spectrum of localized vibrorotational modes and a continuum of dispersive magneto-oscillations. The eigenfunctions and eigenfrequencies of the intracell dynamics depend on a single parameter, which contains the electron density and the magnetic length, and are exhibited as functions of this parameter for various sets of values of the radial and angular-momentum quantum numbers. The propagating excitations describe collective oscillations of the centre of mass of the electron pairs and derive, as in the usual unpaired crystal phase, from the magnetic-field-induced shifts of plasmons and transverse phonons of the crystal in zero field. Several illustrations of their dispersion curves are given. Possible extensions of the theory to include anharmonicity and higher intercell couplings are briefly discussed.