Non-equilibrium transport properties of helical Tomonaga-Luttinger liquids

拓扑绝缘体在整体上是间隙的，但在边界处形成无间隙的边缘状态。这些边缘状态保持了体对称性[Qi06]，因此具有相当特定的性质。在二维拓扑绝缘子中，边缘态是一维的。这种一维系统（存在电子-电子相互作用）被称为螺旋Tomonaga-Luttinger液体（hTLL） [Wu06,Xu06]，因为自旋和运动方向是强束缚的。建议的项目处理htls的非平衡输运性质。利用Keldysh形式和玻色子化，我们打算计算基于htls耦合到正常金属和超导电子库的多端装置中的非线性电流和电流噪声。由于一维体系的螺旋性，我们期望在散粒噪声测量中可以观察到令人兴奋的分数电荷。我们想要解决的最有趣的问题是，在什么情况下，人们可以期望在现实的实验场景中看到上述分数激励。

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.