Fingerprint of surface and bulk states in transport of 3D topological insulators

3D拓扑绝缘体（TI）由金属类Dirac表面态组成，而材料的主体是绝缘的。虽然在角分辨光电发射实验中观察到了狄拉克色散，但这些材料的输运性质仍然存在问题。这主要是由于对于典型的3D TI如Bi 2Se 3和Bi 2 Te 3，体电导率是不可忽略的，并且必须考虑表面和体状态之间的共存或耦合。此外，每个表面在3D TI中互连，并且表面具有球体的拓扑结构而不是无限的2D系统。由于输运实验可以直接获得这些系统中的拓扑不变量，在单个严格二维无质量狄拉克费米子的情况下，拓扑不变量应该是半整数量子霍尔平台，在这一方案中提出的基本问题是，这两种机制如何改变这些材料的输运性质和拓扑不变量。我们将使用分析和数值方法来逐步了解它们是如何改变的表面和体状态的共存和耦合改变了这些材料中的传输、电流-磁和磁光效应。特别地，我们打算研究磁场中表面态之间的简单结，不同的表面-体耦合模型，最后在非平衡绿色函数方法内的晶格上离散的全三维狄拉克模型。实验相关的目标，这一建议是调和的争议，如果霍尔电导率可以量化，以及如何的电流磁和磁光效应的影响，散装和无序效应。这个建议的基本理论问题是理解量子霍尔效应在三维和三维TI的拓扑不变量在现实系统中的普适性找到的条件。非相互作用图像是否足以描述三维TI的输运特性？

3D topological insulators (TIs) consist of the metallic Dirac–like surface states while the bulk of the material is insulating. Although the Dirac dispersion was observed in angle resolved photoemission experiments, the transport properties of these materials are still in question. This is mainly due to the fact that for the typical 3D TI as Bi2Se3 and Bi2Te3, the bulk conductivity is not negligible and coexistence or coupling between surface and bulk states has to be taken into account. Additionally, each of the surfaces is interconnected in 3D TIs, and the surface has rather the topology of the sphere than an infinite 2D system. Since transport experiments give direct access to the topological invariant in these systems, which in the case of a single strictly 2D massless Dirac fermion should be the half integer quantum Hall plateaus, the fundamental question asked in this proposal is how both of these mechanisms alter the transport properties and the topological invariant in these materials.We will use both analytical and numerical approaches to understand step by step how the coexistence and coupling of the surface and bulk states modify the transport, galvano-magnetic, and magneto-optical effects in these materials. In particular we intend to study simple junctions between surface states in magnetic fields, different models of surface-bulk coupling and finally full three-dimensional Dirac model discretized on the lattice within non-equilibrium Green function method. The experimentally relevant goal of this proposal is to reconcile the controversy if and when Hall conductivity can be quantized and how the galvano-magnetic and magneto-optical effects are affected by bulk and disorder effects. The fundamental theoretical questions of this proposal are to understand the quantum Hall effect in three-dimensions and to find the conditions for the universality of the topological invariant of 3D TIs in the realistic systems. Is the non-interacting picture sufficient to describe transport properties of 3D TIs?