Quantum dot to disordered wire crossover: A complete solution in all length scales for systems with unitary symmetry

TL;DR

This paper provides an exact, nonperturbative solution for the crossover between quantum dots and disordered wires with unitary symmetry, covering all length scales and regimes, and deriving key transport properties.

Contribution

It offers a complete analytical solution of a supersymmetric nonlinear sigma model for the quantum dot to wire crossover, valid across all regimes and length scales, including new expressions for conductance moments and shot noise.

Findings

Closed-form expressions for conductance moments

Analytical results for shot-noise power

Density of transmission eigenvalues derived

Abstract

We present an exact solution of a supersymmetric nonlinear sigma model describing the crossover between a quantum dot and a disordered quantum wire with unitary symmetry. The system is coupled ideally to two electron reservoirs via perfectly conducting leads sustaining an arbitrary number of propagating channels. We obtain closed expressions for the first three moments of the conductance, the average shot-noise power and the average density of transmission eigenvalues. The results are complete in the sense that they are nonperturbative and are valid in all regimes and length scales. We recover several known results of the recent literature by taking particular limits.