Transport properties of bilayer topological insulators

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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.