Landau Damping in a 2D Electron Gas with Imposed Quantum Grid

Dielectric properties of semiconductor substrate with imposed two dimensional (2D) periodic grid of quantum wires or nanotubes (quantum crossbars, QCB) are studied. It is shown that a capacitive contact between QCB and semiconductor substrate does not destroy the Luttinger liquid character of the long wave QCB excitations. However, the dielectric losses of a substrate surface are drastically modified due to diffraction processes on the QCB superlattice. QCB-substrate interaction results in additional Landau damping regions of the substrate plasmons. Their existence, form and the density of losses are strongly sensitive to the QCB lattice constant.