Nonuniversal Critical Conductance Fluctuations of Chiral Surface States in the Bulk Integral Quantum Hall Effect -- An Exact Calculation

摘要

The chiral surface electrons in the bulk quantum Hall effect probably formthe first extended system in which conductance fluctuations can be calculatednon-perturbatively in the presence of disorder. By use of the Kubo formula withappropriate boundary conditions, we calculate exactly the variance ofconductance with non-perturbative methods. We find that the conductancefluctuations of this system are ``nonuniversal'' and the variance of theconductance scales in a very peculiar way. This result can be checked withexact computation using the Landauer-Buttiker formula and both methods show thesame scaling behavior. We have also calculated the diffusion constantfluctuations exactly. We find that the diffusion constant fluctuations vanishand thus play no role in the conductance fluctuations.