Quantum spin Hall insulators are characterized by topologically protected counterpropagating edge states. Here we study the dynamical response of these helical edge states under a time-dependent flux biasing, in the presence of a heat bath. It is sho
wn that the relaxation time of the edge carriers can be determined from a measurement of the dissipative response of topological insulator disks. The effects of various perturbations, including Zeeman coupling and disorder, are also discussed.
We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in proximity of a superconductor. Using both analytical and numerical technique
s we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local Majorana polarization and Majorana density and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.
