Long-range perturbation of helical edge states by nonmagnetic defects in two-dimensional topological insulators

Abstract

We study the electronic states that are formed due to the tunnel coupling between helical edge states (HESs) and bound states of nonmagnetic point defects in two-dimensional topological insulators in the general case of broken axial spin symmetry. It is found that the coupling of HESs and a single defect leads to the formation of composite HESs composed of the bound states and a set of the conventional HESs. Their spectral density near the defect has a resonance shifted relative to the energy level of the bound state. But of most importance is a long-range perturbation of the HESs around the defect, which is a cloud consisting of both Kramers partners of conventional edge states. Therefore each of the composite HESs contains both the right- and left-moving conventional HESs. The amplitude of this perturbation decreases inversely with the distance from the defect. In a system of many defects, this perturbation leads to a long-range coupling between bound states of different defects mediated by the HESs and causes amazing effects. We study these effects for a two-defect system where the proposed mechanism of indirect coupling leads to a splitting of the resonances of isolated defects even if the distance between them is very large. As a result an asymmetric structure of two-peak resonance arises that very unusually changes with the distance between the defects.

11 pages, 7 figures; typos are corrected in Eqs. (28) and (A3)

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• The Quantum Spin Hall Effect: Theory and Experiment
• Spatially resolved study of backscattering in the quantum spin Hall state
• Mesoscopic transport in two-dimensional topological insulators
• Electronic states induced by nonmagnetic defects in two-dimensional topological insulators
• Non-magnetic defects in the bulk of two-dimensional topological insulators
• Optical transitions in two-dimensional topological insulators with point defects

Cited by in corpus (3)

• Conductance suppression by nonmagnetic point defects in helical edge channels of two-dimensional topological insulators
• Electron pairs bound by the spin-orbit interaction in 2D gated Rashba materials with two-band spectrum
• A non-magnetic mechanism of backscattering in helical edge states