Theory of minigap plasmons in a two-dimensional electron gas subjected to a one-dimensional periodic potential

We investigate the plasmon excitations in a two-dimensional (2D) electron gas subjected to a one-dimensional (1D) weak periodic potential. We derive and discuss the dispersion relations for both intrasubband and intersubband excitations within the framework of Bohm-Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe a splitting of the 2D plasmon dispersion. The splitting is caused by the superlattice effect of the charge-density modulation on the collective excitation spectrum. Several illustrative examples are presented on the computed plasmon excitation energy as a function of the propagation vector as well as the Bloch vector. We also discuss how the tunneling and the potential amplitude influence the minigaps and the plasmon excitations.