Application of Random-Matrix Theory to Quantum Electron Transport

我们研究了零温下辛对称性无序导线的电导。在辛普适性类中，传导通道数N的奇偶性对电子输运起着至关重要的作用。与通常的偶数N情形不同，没有背向散射的理想导电信道在奇数N情形下是稳定的。这项研究的目的是澄清电导行为中出现的奇偶差异。为了实现这一目的，我们将随机矩阵理论应用到我们的问题中，并建立了标度理论，利用该理论，我们可以统一地考虑偶通道和奇通道的情况。基于标度理论，我们证明了在通常的偶通道情况下，平均无量纲电导在长线极限时为零，而在奇通道情况下则趋于1。我们还证明了奇道情况下的局域长度比偶道情况下的局域长度要短得多。我们观察到，这些奇偶差异归因于只存在于奇通道情况下的理想导电通道。为了验证标度理论的有效性，我们进行了大规模的数值模拟。我们在正方形晶格上给出了一个简单的辛对称无序线的紧束缚模型，并研究了奇偶差情况下的电导行为。我们得到的数值结果有力地支持了我们的理论。

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.