Conductance scaling at the band center of wide wires with pure nondiagonal disorder

The Kubo formula is used to get the scaling behavior of the static conductance distribution of wide wires showing pure nondiagonal disorder. Following recent works that point to unusual phenomena in some circumstances, scaling at the band center of wires of odd widths has been numerically investigated. While the mean conductance shows a decrease that is only proportional to the inverse square root of the wire length, the median of the distribution exponentially decreases as a function of the square root of the length. Actually, the whole distribution decays as the inverse square root of the length except close to G=0 where the distribution accumulates the weight lost at larger conductances. It accurately follows the theoretical prediction once the free parameter is correctly fitted. Moreover, when the number of channels equals the wire length, but contacts are kept finite, the conductance distribution is still described by the previous model. It is shown that the common origin of this behavior is a simple Gaussian statistics followed by the logarithm of the E=0 wave function weight ratio of a system showing chiral symmetry, A finite value of the two-dimensional mean conductance is obtained in the infinite-size limit. Both conductance and wave function statistics distributions are given in this limit. These results are consistent with the critical character of the E = 0 wave function predicted in the literature.