Transport properties of bilayer topological insulators

在二维空间中，时间反转对称的拓扑绝缘体被称为量子自旋霍尔绝缘体。它们的特点是在QSH系统的物理边界处的体能带结构和特殊的螺旋边缘状态的差距。在Hg（Cd）Te和InAs/GaSb量子威尔斯阱的基础上实现了这些系统。实际上，在这些量子阱结构中，二维电子气（2DEG）可以处于三种不同的状态：（i）TI状态;（ii）正常带绝缘体状态;（iii）导带和价带相互接触的Dirac半金属状态。然后，（两个层的）两个2DEG可以以不同的方式彼此相互作用，例如，通过隧穿过程或库仑相互作用。研究双层拓扑相的命运是有趣的。事实上，双层结构提供了产生拓扑绝缘相的全新可能性，例如通过激子凝聚体的形成。在这个项目中，我们想研究双层拓扑绝缘体的输运性质。该分析应在物理条件下进行，其中两个层仅通过库仑相互作用相互作用。其中一个关键问题，我们要解决的是，在每一层的层间输运性质的拓扑相位的印记。为此，我们将计算这些双层结构中的库仑阻力问题，即如果电压施加到层1，则层2中的电流响应。有趣的是，根据组分的拓扑相位，这个问题需要我们考虑两个1D螺旋边缘状态之间的耦合，两个2DEG，甚至1D螺旋边缘状态（在一层）和2DEG（在另一层）之间的耦合。显然，丰富的输运物理可以出现在这些双层系统中，我们希望它有助于我们更好地理解库仑相互作用和拓扑绝缘相的物质的相互作用。特别是，我们要作出可观察到的预测，表征双层系统中的相互作用效应和拓扑秩序的共存。

In two spatial dimensions (2D), time-reversal symmetric topological insulators (TI) are called quantum spin Hall (QSH) insulators. They are characterized by a gap in the bulk band structure and peculiar helical edge states at the physical boundaries of QSH systems. Realizations of these systems have been achieved on the basis of Hg(Cd)Te and InAs/GaSb quantum wells. In fact, the 2D electron gas (2DEG), in these quantum well structures, can be in three distinct regimes: (i) TI regime; (ii) normal band insulator regime; and (iii) Dirac semimetal regime where conduction and valence band touch each other.Novel physics arises if two QSH systems are combined in a bilayer structure. Then, the two 2DEGs (of the two layers) can interact with each other in different ways, for instance, via tunneling processes or Coulomb interaction. It is interesting to study the fate of the bilayer topological phases. In fact, the bilayer scenario offers totally new possibilities of generating topological insulating phases, e.g. through the formation of an exciton condensate.In this project, we want to study transport properties of bilayer topological insulators. This analysis should be done, under physical conditions, where the two layers interact with each other solely via Coulomb interaction. One of the key issues, we would like to address, is the imprint of the topological phases within each layer on the interlayer transport properties. To do so, we will calculate the Coulomb drag problem in these bilayer structures, i.e. the current response in layer 2 if a voltage is applied to layer 1. Interestingly, depending on the topological phases of the constituents, this problem requires us to consider a coupling between two 1D helical edge states, two 2DEGs, or even a coupling between a 1D helical edge state (in one layer) and a 2DEG (in the other layer). Evidently, rich transport physics can emerge in these bilayer systems and we expect that it helps us to better understand the interplay of Coulomb interaction and topological insulating phases of matter. Particularly, we want to make observable predictions that characterize the co-existence of interaction effects and topological order in bilayer systems.