Resistance of helical edges formed in a semiconductor heterostructure

Abstract

Time-reversal symmetry prohibits elastic backscattering of electrons\npropagating within a helical edge of a two-dimensional topological insulator.\nHowever, small band gaps in these systems make them sensitive to doping\ndisorder, which may lead to the formation of electron and hole puddles. Such a\npuddle -- a quantum dot -- tunnel-coupled to the edge may significantly enhance\nthe inelastic backscattering rate, due to the long dwelling time of an electron\nin the dot. The added resistance is especially strong for dots carrying an odd\nnumber of electrons, due to the Kondo effect. For the same reason, the\ntemperature dependence of the added resistance becomes rather weak. We present\na detailed theory of the quantum dot effect on the helical edge resistance. It\nallows us to make specific predictions for possible future experiments with\nartificially prepared dots in topological insulators. It also provides a\nqualitative explanation of the resistance fluctuations observed in short HgTe\nquantum wells. In addition to the single-dot theory, we develop a statistical\ndescription of the helical edge resistivity introduced by random charge puddles\nin a long heterostructure carrying helical edge states. The presence of charge\npuddles in long samples may explain the observed coexistence of a high sample\nresistance with the propagation of electrons along the sample edges.\n