Landau damping in a two-dimensional electron gas with imposed quantum grid

Dielectric properties of a semiconductor substrate with an imposed two-dimensional (2D) periodic grid of quantum wires or nanotubes (quantum crossbars, QCBs) are studied. It is shown that a capacitive contact between the 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 and form and the density of losses are strongly sensitive to the QCB lattice constant.