No abstract

The electronic distribution functions of two Coulomb-coupled chiral edge states forming a quasi-onedimensional system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy exchange between the two edge states is determined by the shot noise of the edge states generated at a quantum point contact ͑QPC͒. In close vicinity to the QPC, we derive analytic expressions for the distribution functions. We further give an iterative procedure with which we can compute numerically the distribution functions arbitrarily far away from the QPC. Our results are compared with recent experiments.

We study current carrying helical edge states in a two-dimensional topological insulator coupled to an environment of localized spins, i.e. a spin bath. The localized spins mediate elastic spin-flip scattering between the helical edge states, and we show how this induces a spin-bath magnetization for a finite current through the edge states. The magnetization appears near the boundaries of the topological insulator, while the bulk remains unmagnetized, and it reaches its maximal value in the high bias regime. Furthermore, the helical edge states remain ballistic in steady state, if no additional spin-flip mechanisms for the localized spins are present. However, we demonstrate that if such mechanisms are allowed, then these will induce a finite current decrease from the ballistic value.

Abstract. We calculate the linear response thermopower S of a quantum point contact using the Landauer formula and therefore assume non-interacting electrons. The purpose of the paper, is to compare analytically and numerically the linear thermopower S of non-interacting electrons to the low temperature approximation,, and the so-called Mott expression,, where G(µ, T ) is the (temperature dependent) conductance. This comparison is important, since the Mott formula is often used to detect deviations from single-particle behavior in the thermopower of a point contact.