Application of Random-Matrix Theory to Quantum Electron Transport

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We have studied conductance of disordered wires with symplectic symmetry at zero temperature. In the symplectic universality class, the parity of conducting channel number N plays an essential role in electron transport. In contrast to the ordinary case of an even N, a perfectly conducting channel without backscattering is stabilized in the odd-N case. The purpose of this study is to clarify the even-odd difference arising in the behavior of conductance. To accomplish this purpose, we have adapted the random-matrix theory to our problem, and formulated the scaling theory by which we can consider both the even-and odd-channel cases within a unified manner. Based on the scaling theory, we have shown that in the ordinary even-channel case, the averaged dimensionless conductance vanishes in the long-wire limit, while it approaches to unity in the odd-channel case. We have also shown that the localization length for the odd channel case is much shorter than that for the even-channel case. We observe that these even-odd differences are attributed to the perfectly conducting channel that exists only in the odd-channel case. To confirm the validity of the scaling theory, we have performed large-scale numerical simulations. We have presented a simple tight-binding model on the square lattice for disordered wires with symplectic symmetry, and studied the behavior of the conductance focusing on the even-odd difference. We have obtained numerical results that strongly support our theory.