Electronic Properties of Quantum Wire Networks

TL;DR

This thesis develops a theory for plasmon excitations in quantum wire networks, revealing a crossover from one-dimensional to two-dimensional behavior observable via optical spectroscopy techniques.

Contribution

It introduces a comprehensive bosonization-based model for QCBs, analyzing spectral and correlation properties, and predicts experimental signatures of dimensional crossover.

Findings

QCB behaves as a crossed sliding Luttinger liquid at low energies

High-frequency spectral features exhibit 1D or 2D characteristics depending on wave vector direction

Optical spectroscopy can detect the 1D to 2D crossover through line splitting

Abstract

Quantum wire networks (``quantum crossbars'', QCB) represent a 2D grid formed by superimposed crossing arrays of parallel conducting quantum wires, molecular chains or metallic single-wall carbon nanotubes. QCB coupled only by capacitive interaction in the crosses have similar low-energy, long-wave properties characterized as a crossed sliding Luttinger liquid (CSLL) phase. In this Thesis we develop a theory of interacting Bose excitations (plasmons) in QCB. We analyze spectrum of boson fields and two-point correlators in QCB. We show that the standard bosonization procedure is valid, and the system behaves as a CSLL 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 BZ of reciprocal lattice. As a result, the crossover from 1D to 2D regime may be experimentally observed. An effective tool for probing QCB spectral properties is the optical spectroscopy. The characteristic values of QCB frequencies and wave vectors determine two possible directions of such an experimental observation. The first of them is IR spectroscopy of QCB where the frequency of an external ac field lies at the same region as the QCB frequency. The second one is an UV scattering on QCB where the wave vector of a scattered field lies in the same region as that of the QCB wave vectors. In both cases, 1D to 2D crossover manifests itself as a splitting of single lines into multiplets.