Plasmon excitations and one- to two-dimensional crossover in quantum crossbars

The spectrum of boson fields and two-point correlators are analyzed in quantum crossbars (QCB, a superlattice formed by m crossed interacting arrays of quantum wires), with short-range interarray capacitive interaction. Spectral and correlation properties of double $\mathrm{}(m=2\mathrm{})\mathrm{}$ and triple $\left(m-3\right)$ QCB are studied. It is shown that the standard bosonization procedure is valid, and the system behaves as a sliding Luttinger liquid in the infrared limit, but the high-frequency spectral and correlation characteristics have either one-dimensional (1D) or 2D nature depending on the direction of the wave vector in the 2D elementary cell of the reciprocal lattice. As a result, the crossover from the 1D to 2D regime may be experimentally observed. It manifests itself as the appearance of additional peaks of optical absorption, nonzero transverse space correlators, and periodic energy transfer between arrays (“Rabi oscillations”).