Non-equilibrium transport properties of helical Tomonaga-Luttinger liquids

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Topological insulators are gapped in the bulk but form gapless edge states at the boundaries. These edge states preserve the bulk symmetries [Qi06] and have therefore rather specific properties. In twodimensional (2D) topological insulators, the edge states are one-dimensional (1D). This 1D system (in the presence of electron-electron interactions) has been coined helical Tomonaga-Luttinger liquid (hTLL) [Wu06,Xu06] because the spin and the direction of motion are strongly bound. The proposed projects deal with non-equilibrium transport properties of hTLLs. Using the Keldysh formalism and bosonization, we intend to calculate the non-linear current as well as the current noise in multiterminal setups based on hTLLs coupled to normal metal as well as superconducting electron reservoirs. Due to the helicity of the 1D system, we expect exciting appearances of fractional charges which should be observable in shot noise measurements. The most interesting question we would like to address is under which circumstances one can expect to see the above mentioned fractional excitations in a realistic experimental scenario.