Numerical Study of the Higher Order Moments of Conductance Fluctuations in Mesoscopic Structures

Abstract

It is well-known that the conductance of a disordered mesoscopic structure exhibits sample-specific fluctuations in a magnetic field due to quantum interference effects [1]. The magnetic field changes the phase-relationships between the various Feynman trajectories in the structure thereby causing the conductance to fluctuate. In this paper, we have performed a numerical study of conductance fluctuations. Instead of using a magnetic field, we have induced the fluctuations by randomly altering the impurity configuration within the structure. Changing the impurity configuration has the same effect as applying a magnetic field since both alter the phase-relationships between the various Feynman paths which causes the conductance to fluctuate¹. In addition to studying the fluctuations, we have also examined the probability distribution of the 2-probe Landauer conductances and calculated various moments of the distribution. As expected, we find that the second moment of the distribution (the standard deviation or the rms value of the fluctuations) is close to the claimed universal value of e ² /h [2], but its exact magnitude is somewhat affected by the presence of evanescent states.