Conductance through quantum wires with Lévy-type disorder: Universal statistics in anomalous quantum transport

Departamento de Física Teórica, Facultad de Ciencias, and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza - Pedro Cerbuna 12, E-50009, Zaragoza, Spain, EU

^a gopar@unizar.es

Received: 1 October 2010
Accepted: 26 November 2010

Abstract

In this letter we study the conductance G through one-dimensional quantum wires with disorder configurations characterized by long-tailed distributions (Lévy-type disorder). We calculate analytically the conductance distribution which reveals a universal statistics: the distribution of conductances is fully determined by the exponent α of the power-law decay of the disorder distribution and the average ⟨ln G⟩, i.e., all other details of the disorder configurations are irrelevant. For 0<α<1 we found that the fluctuations of ln G are not self-averaging and ⟨ln G⟩ scales with the length of the system as L^α, in contrast to the predictions of the standard scaling theory of localization where ln G is a self-averaging quantity and ⟨ln G⟩ scales linearly with L. Our theoretical results are verified by comparing with numerical simulations of one-dimensional disordered wires.