Plasmon excitations and 1D - 2D dimensional crossover in quantum crossbars

TL;DR

This paper analyzes the spectral and correlation properties of quantum crossbars, revealing a dimensional crossover from 1D to 2D behavior that can be observed experimentally through optical and energy transfer phenomena.

Contribution

It demonstrates the validity of bosonization in quantum crossbars and characterizes the 1D to 2D crossover in spectral and correlation features.

Findings

System behaves as a sliding Luttinger liquid at low frequencies.

High frequency properties exhibit 1D or 2D nature depending on wave vector direction.

Experimental signatures include additional optical absorption peaks and Rabi oscillations.

Abstract

Spectrum of boson fields and two-point correlators are analyzed in quantum crossbars (QCBs, a superlattice formed by m crossed interacting arrays of quantum wires), with short range inter-wire capacitive interaction. Spectral and correlation properties of double (m=2) and triple (m-3) QCBs 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 1D or 2D nature depending on the direction of the wave vector in the 2D elementary cell of reciprocal lattice. As a result, the crossover from 1D to 2D regime may be experimentally observed. It manifests itself as appearance of additional peaks of optical absorption, non-zero transverse space correlators and periodic energy transfer between arrays ("Rabi oscillations").