狄拉克费米子-超导体结中的非局域输运研究

In superconducting metals, a Cooper pair can be formed from two electrons separated in space. The nonlocal transport measurement is an effective method to investigate such nonlocal correlations and entanglements in a normal metal-superconductor junction. The low energy electronic properties for bulk states in graphene and surface states in three-dimensional topological insulators (3DTIs) can be described by two-dimensional Dirac equation. Their transport properties attract extensive interests due to their novelties. However, the nonlocal transport properties of Dirac fermion-superconductor systems have not attracted much attentions yet. In this project, we intend to investigate the nonlocal transport properties of Dirac fermion-superconductor junctions, which originate from quantum effects including Dirac fermions, topological states and correlations. By using theoretical calculations and numerical simulations, we will predict and explain new phenomena in these systems. Moreover, since the Dirac spinors in graphene and 3DTI are pseudo-spin and physical spin respectively, which have different physical origins, we will focus on the similarities and differences of nonlocal properties between them when they are connected with superconductors. The results will offer understandings for new physical effects, and guidelines for experimental probes.

金属超导体中，两个电子可以在空间距离很大的范围内配对形成库柏对。正常金属-超导体结的非局域输运测量是研究电子的这种非局域关联与纠缠的有效方法。石墨烯体电子态和三维拓扑绝缘体表面电子态在低能区可以用二维狄拉克方程描述，因此它们具有与传统半导体和金属不同的独特电子性质。其输运性质成为近年来的研究热点。然而，狄拉克费米子-超导系统中的非局域输运的问题却尚未引起人们的关注。本项目拟针对狄拉克费米子-超导结中的狄拉克费米子、拓扑量子态和电子关联等量子力学效应导致的非局域输运展开理论探讨和数值模拟，预言和解释新的物理现象。同时我们还强调，表征石墨烯和三维拓扑绝缘体表面态的旋量分别是赝自旋和物理自旋，具有不同的物理意义，我们将进一步研究这两者在超导非局域效应方面的相同与不同之处。研究结果将预言和解释新的物理效应，并为实验观测提供理论依据。

我们研究了无序、外场和界面对一系列狄拉克费米子（重点是拓扑绝缘体和硅烯）非局域输运的影响。重要结果体现在四个方面。第一、自旋极化的非局域输运。第二、无序对非局域输运的影响，包括无序诱导的非局域边缘态和体态对非局域输运的影响。第三、狄拉克费米子异质结的非局域输运及谷极化。第四、硅烯-超导异质结中的交叉Andreev反射，预言了处于拓扑绝缘态的硅烯条带器件中，产生交叉Andreev反射（可接近100%）的几种方法，并分析了其成因。