Dirac fermions in semiconductors

二维(2D)拓扑绝缘体形成了一种新的物质状态，其中块体的绝缘性能伴随着边缘状态。这些螺旋边态是由Kramers伙伴在具有强烈的自旋-轨道相互作用的材料中形成的，其中时间反转对称性是守恒的。同样，三维(3D)拓扑绝缘体的特征是金属表面状态，而材料的大部分是有间隙的。典型的2D和3D拓扑绝缘体是各种窄禁带半导体，其中通常的能带有序是颠倒的。在这个项目中，我们将从理论上探索当费米能级探测螺旋边态(量子自旋-霍尔态)或表面态时，以及当费米能量位于导带或价带(掺杂的拓扑绝缘体)深处时，拓扑绝缘体的输运性质。特别是，我们将研究量子自旋霍尔态与掺杂的拓扑绝缘体之间的界面，以及量子自旋霍尔态对诸如磁性杂质和磁场等破坏时间逆对称的微扰的响应。此外，我们还将研究掺杂拓扑绝缘体中的弱反局域化和普遍电导起伏，以更好地理解这些材料。我们将在Landauer-Büttiker-Keldysh形式中使用图解技术和数值计算。对拓扑绝缘体中输运的完整表征应该使我们能够评估在这些材料中存在狄拉克费米子的重要性和后果。

Two dimensional (2D) topological insulators form a new state of matter where insulating properties of the bulk are accompanied by edge states. These helical edge states are formed by Kramers partners in materials with strong spin-orbit interactions where time reversal symmetry is conserved. Similarly, three dimensional (3D) topological insulators are characterized by metallic surface states while the bulk of the material is gapped. Typical 2D and 3D topological insulators are various narrow gap semiconductors in which the usual band ordering is inverted. In this project, we will explore theoretically transport properties of topological insulators when the Fermi level probes the helical edge states (quantum spin-Hall state) or surface states, and when the Fermi energy lies deep in the conduction band or valence band (doped topological insulators). In particular, we will investigate interfaces between quantum spin Hall state and doped topological insulator and the response of the quantum spin Hall state to perturbations breaking time-reversal symmetry like magnetic impurities and magnetic fields. Further we will study weak antilocalization and universal conductance fluctuations in doped topological insulators to better understand these materials. We will use diagrammatic techniques accompanied by numerical calculations within the Landauer-Büttiker-Keldysh formalism. The complete characterization of the transport in topological insulators should allow us to evaluate the importance and consequences of the existence of Dirac fermions in these materials.