Effect of interplane coupling on the quantized Hall effect in multilayer structures.

Abstract

The effect of electron-electron interaction on the particle-hole excitations for a fully filled band of coupled layers is studied. For coupled layers, there exists a continuum of particle-hole excitations with a plasmonlike collective excitation which lies at the bottom of the continuum for small transverse momentum transfer q. As q is increased, this excitation rises and is split off the top of the continuum. Eventually it comes down and merges with the continuum again when q reaches 2.2${l}^{\mathrm{\ensuremath{-}}1}$. This collective excitation has similarities to the so-called magnetoexciton (plasmon) studied in two-dimensional (2D) systems. Due to the long-range nature of the Coulomb interaction, in addition to the cyclotron energy, the excitation energies depend on the angle of propagation \ensuremath{\vartheta} with respect to the xy plane as ${\mathrm{cos}}^{2}$\ensuremath{\vartheta}. The response function is also investigated. Over a substantial region of phase space, it can be very well reproduced by a single-mode approximation. The instability toward the formation of a Wigner solid in multilayer structures is investigated by treating the interlayer coupling in the mean-field approximation. It is found that this tendency is much stronger in the fractional case than in the integral case, chiefly because the density-response function is much larger in the latter situation. The effect of the interplane hopping and charge transfer between layers is discussed.