Conductance Fluctuations in Mesoscopic Quantum Wires

Abstract

The conductance fluctuations in mesoscopic quantum wires at zero temperature are studied by using the tight binding model and the transfer matrix formalism with the Landauer formula. The numerical calculations for the conductance g (scaled by e²/h) are carried out for the overall range from the ballistic to the localized regime, and it is found numerically that a relation between the averaged conductance ‹ g› and the conductance fluctuation δ g is described by the single parameter near the ballistic regime and also near the localized regime. In the ballistic regime, we find analytically that δ g/M is proportional to (1-‹ g› /2M), which agrees well with the result of the numerical calculations (M being the channel number). By using the conductance formula due to the resonant tunneling, we discuss the behavior of the conductance near the localized regime, and find analytically that the ratio (δ g)²/‹ g› tends to the value 0.5 as ‹ g› → 0, which is consistent with the numerical result.