Characterization of the Local Density of States Fluctuations near the Integer Quantum Hall Transition in a Quantum Dot Array

TL;DR

This paper analytically investigates the fluctuations of the local density of states near the quantum Hall transition in a quantum dot array, revealing non-perturbative fluctuation behavior and potential experimental implications.

Contribution

It provides one of the first analytic characterizations of local density of states fluctuations in a 2D mesoscopic structure near the quantum Hall transition.

Findings

Non-perturbative results for moments of local density of states

Identification of fluctuation behavior near transition

Connection to experimental measurement techniques

Abstract

We present a calculation for the second moment of the local density of states in a model of a two-dimensional quantum dot array near the quantum Hall transition. The quantum dot array model is a realistic adaptation of the lattice model for the quantum Hall transition in the two-dimensional electron gas in an external magnetic field proposed by Ludwig, Fisher, Shankar and Grinstein. We make use of a Dirac fermion representation for the Green functions in the presence of fluctuations for the quantum dot energy levels. A saddle-point approximation yields non-perturbative results for the first and second moments of the local density of states, showing interesting fluctuation behaviour near the quantum Hall transition. To our knowledge we discuss here one of the first analytic characterizations of chaotic behaviour for a two-dimensional mesoscopic structure. The connection with possible experimental investigations of the local density of states in the quantum dot array structures (by means of NMR Knight-shift or single-electron-tunneling techniques) and our work is also established.