Dimensional Crossover in 2D Crossbars

TL;DR

This paper investigates quantum crossbars, revealing a dimensional crossover from 1D to 2D behavior in their spectral and correlation properties, with potential for experimental observation and applications in plasmon propagation.

Contribution

It demonstrates the validity of bosonization in QCBs and uncovers the 1D to 2D crossover in spectral characteristics depending on wave vector direction.

Findings

System behaves as a sliding Luttinger liquid in the infrared limit

High frequency spectral features are either 1D or 2D depending on wave vector direction

Periodic energy transfer ('Rabi oscillations') between arrays is predicted

Abstract

Spectrum of boson fields and two-point correlators are analyzed in quantum crossbars (QCB, a superlattice formed by two crossed interacting arrays of quantum wires), with short range inter-wire interaction. 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 Brillouin zone. As a result, the crossover from 1D to 2D regime may be experimentally observed. Plasmon propagation in arbitrary direction is possible. Periodic energy transfer between arrays ("Rabi oscillations") is predicted.