Transport properties of bilayer topological insulators

在二维空间中，时间反转对称拓扑绝缘子（TI）被称为量子自旋霍尔（QSH）绝缘子。它们的特征是体带结构的间隙和QSH系统物理边界的特殊螺旋边缘状态。这些系统已经在Hg(Cd)Te和InAs/GaSb量子阱的基础上实现。事实上，在这些量子阱结构中，二维电子气体（2DEG）可以处于三种不同的状态：(i) TI状态；（ii）正常带绝缘子状态；(3)导价带相互接触的狄拉克半金属态。如果两个QSH系统以双层结构组合，则会产生新的物理现象。然后，（两层中的）两个2deg可以以不同的方式相互作用，例如，通过隧道过程或库仑相互作用。研究双层拓扑相的命运是很有意义的。事实上，双层方案提供了产生拓扑绝缘相的全新可能性，例如通过形成激子凝聚体。在这个项目中，我们想研究双层拓扑绝缘子的输运性质。这种分析应在两层仅通过库仑相互作用相互作用的物理条件下进行。我们想要解决的关键问题之一是，每层内的拓扑相对层间传输特性的影响。为此，我们将计算这些双层结构中的库仑阻力问题，即，如果向第1层施加电压，第2层的电流响应。有趣的是，根据成分的拓扑相，这个问题要求我们考虑两个一维螺旋边缘状态之间的耦合，两个2DEG，甚至是一维螺旋边缘状态（在一层）和2DEG（在另一层）之间的耦合。显然，在这些双层体系中可以出现丰富的输运物理，我们期望它有助于我们更好地理解物质的库仑相互作用和拓扑绝缘相的相互作用。特别是，我们希望做出可观察到的预测，以表征双层系统中相互作用效应和拓扑顺序共存的特征。

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.