Helical liquids are one-dimensional systems where the direction of motion and a (pseudo) spin degree of freedom are strongly coupled to each other. They appear, for instance, at the edges of a two-dimensional topological insulator, i.e. a quantum spin Hall system, or can be engineered in one-dimensional systems with strong spin-orbit coupling. The fact that these one-dimensional excitations are helical results in novel physics: (i) as far as transport is concerned, there is protection against elastic backscattering. (ii) Since there is strong coupling between the direction of motion and the (pseudo) spin degree of freedom, it is evident that this feature can be functionalized to learn more about spin physics by charge measurements.
In this project, we plan to investigate the role of inelastic backscattering on transport properties of helical liquids. This investigation will then be applied to simple two-terminal situations at the edge of a quantum spin Hall system but also to more complicated four-terminal cases where two helical liquids are coupled by a central scattering region. Our aim is to identify the most relevant scattering mechanisms for transport experiments on two-dimensional topological insulators. This identification will first be done on the basis of intuitive theoretical models, for instance, a random Rashba spin-orbit coupling, to better understand the essential physics. Once the most important scattering mechanisms are identified, we plan to work on concepts to reduce them in actual experiments.
Evidently, the four-terminal setup might serve as an efficient spin manipulator and detector. We intend to analyze non-equilibrium transport properties of four-terminal setups that exploit the spin-to-charge conversion of helical liquids. This is a unique property of helical liquids that gives rise to new manipulation and detection schemes of interacting spin systems, like coupled Kondo impurities. Thereby, we envision a tunable Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction between the Kondo impurities which can be manipulated and likewise detected by bare charge currents running through the helical liquid leads.
[A09.2] J. C. Budich, F. Dolcini, P. Recher, and B. Trauzettel, Phonon induced backscattering in helical edge states, Phys. Rev. Lett. 108, 086602 (2012).