磁性和超导电性的拓扑绝缘体中的量子输运

Topological insulators (TIs) are popular objects for the research in condensed matter physics and material science in the past several years. In contrast to traditional semiconductors and insulators, TIs have a full insulating gap in the bulk and conductive gapless edge or surface states. TIs have drawn intensively interest both in theories and experiments for their fundamental physics and potential applications. In this work plan, following the recent experimental and theoretical progress, we will study the quantum transport properties and topological quantum transitions in the magnetic and superconducting TIs. By means of the analytically solving the Hamiltonian and the numerical Green’s function method, we aim to find how the physical properties of the topological insulators vary as changing their magnetism and superconductivity, explain some experimental observations, predict probable novel physical phenomena, and design various functional devices by using of their distinguished characteristics. We expect that the spin-selected transport of the edge and surface states and the topological quantum phase transitions in the TIs are realized by controlling the magnetic, electrical field and Rashba spin-orbital coupling. We hope to derive the existence conditions of the Majorana Fermion in the heterostructures composed of the ferromagnetic TIs and superconductors, describe its laws of motion, and propose quantum computation devices based on its characteristics.

拓扑绝缘体是最近几年凝聚态物理和材料学科研究的热点。它不同于传统的半导体和绝缘体，拓扑绝缘体同时具有绝缘的体态和导电的表面态或边态。由于它的基础物理意义和潜在的应用价值，拓扑绝缘体在实验和理论上都获得了广泛的关注。本项目将根据近几年来报道的实验和理论的研究进展，研究有磁性或超导电性下拓扑绝缘体的量子输运性质和拓扑量子相变。主要研究目标是，利用解析求解和数值Green函数两种方法，研究弄清拓扑绝缘体在磁性和超导电性的调控下物理性质的变化规律，解释部分实验现象，预言可能的新奇物理现象，以及利用拓扑绝缘体的特性设计各种功能器件。我们预期通过外加磁场、电场和Rashba自旋轨道耦合等的调控，实现磁性拓扑绝缘体的边态和表面态自旋的选择性输运和控制拓扑量子相变；预期提出铁磁性拓扑绝缘体和超导体异质结中Majorana Fermi的存在条件，给出其运动规律，并根据其特性设计功能器件。

按照本项目的研究计划，在刚过去的2014年度我们主要做了磁性拓扑绝缘体和超导性拓扑绝缘体两个方面的研究工作，都取得了部分有意义的研究结果。首先，我们研究了在交换场、外电场和Rashba自旋轨道耦合调控下硅烯材料的拓扑性质。通过三种调控的合理选择，我们实现了丰富的拓扑量子态，其中包括量子自旋Hall态、量子反常Hall态、谷极化的金属态。我们还在继续研究这些量子态在量子输运性质上的特征表现。其次，我们研究了在一个具有自旋轨道耦合的半导体量子肼中产生拓扑超导的问题。我们发现可以利用改变外加磁场大小或方向的方法实现了同自旋配对的拓扑超导，并利用数值求解Bogoliubov-de Gennes超导方程的方法计算了超导能隙和相图，所得结果还在分析和整理中。我们正在加快推进研究计划，预计在2015年完成论文的发表工作。