Semiclassical electron transport at the edge of a twodimensional topological insulator: Interplay of protected and unprotected modes
Abstract
We study electron transport at the edge of a generic disordered twodimensional topological insulator, where some channels are topologically protected from backscattering. Assuming the total number of channels is large, we consider the edge as a quasionedimensional quantum wire and describe it in terms of a nonlinear sigma model with a topological term. Neglecting localization effects, we calculate the average distribution function of transmission probabilities as a function of the sample length. We mainly focus on the two experimentally relevant cases: a junction between two quantum Hall (QH) states with different filling factors (unitary class) and a relatively thick quantum well exhibiting quantum spin Hall (QSH) effect (symplectic class). In a QH sample, the presence of topologically protected modes leads to a strong suppression of diffusion in the other channels already at scales much shorter than the localization length. On the semiclassical level, this is accompanied by the formation of a gap in the spectrum of transmission probabilities close to unit transmission, thereby suppressing shot noise and conductance fluctuations. In the case of a QSH system, there is at most one topologically protected edge channel leading to weaker transport effects. In order to describe `topological' suppression of nearly perfect transparencies, we develop an exact mapping of the semiclassical limit of the onedimensional sigma model onto a zerodimensional sigma model of a different symmetry class, allowing us to identify the distribution of transmission probabilities with the average spectral density of a certain randommatrix ensemble. We extend our results to other symmetry classes with topologically protected edges in two dimensions.
 Publication:

Physical Review B
 Pub Date:
 March 2016
 DOI:
 10.1103/PhysRevB.93.125405
 arXiv:
 arXiv:1511.02227
 Bibcode:
 2016PhRvB..93l5405K
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 20 pages, 14 figures