Energy spectrum of a layered system in a strong magnetic field

Abstract

We investigate the excitation spectrum of two- and three-layer electron systems in a strong perpendicular magnetic field with \ensuremath{\nu}=(1/2 and (1/3, respectively, in each layer. For layer separation z=0 the dispersion relations \ensuremath{\omega}(k) vanish as ${k}^{2}$ for k\ensuremath{\rightarrow}0, as one expects for Goldstone modes. For z>0, \ensuremath{\omega}(k) behaves as an acoustic mode, vanishing linearly for small k. For large values of k one finds that the dispersion relations have the form \ensuremath{\Delta}(z)-${e}^{2}$/\ensuremath{\kappa}${\mathrm{kl}}_{0}^{2}$, where ${l}_{0}$ is the magnetic length and \ensuremath{\kappa} the dielectric constant of the medium. At ${\mathrm{kl}}_{0}$ of order unity, the dispersion relations develop a dip as z is increased. These become soft modes at certain critical values of z, indicating that the system undergoes a phase transition as the layer spacing is increased.