title: Local currents in a 2D topological insulator.
abstract: Symmetry protected edge states in 2D topological insulators are interesting both from the fundamental point of view as well as from the point of view of potential applications in nanoelectronics as perfectly conducting 1D channels and functional elements of circuits. Here using a simple tight-binding model and the Landauer-Büttiker formalism we explore local current distributions in a 2D topological insulator focusing on effects of non-magnetic impurities and vacancies as well as finite size effects. For an isolated edge state, we show that the local conductance decays into the bulk in an oscillatory fashion as explained by the complex band structure of the bulk topological insulator. We demonstrate that although the net conductance of the edge state is topologically protected, impurity scattering leads to intricate local current patterns. In the case of vacancies we observe vortex currents of certain chirality, originating from the scattering of current-carrying electrons into states localized at the edges of hollow regions. For finite size strips of a topological insulator we predict the formation of an oscillatory band gap in the spectrum of the edge states, the emergence of Friedel oscillations caused by an open channel for backscattering from an impurity and antiresonances in conductance when the Fermi energy matches the energy of the localized state created by an impurity.
authors.affiliation: Department of Physics and Astronomy & Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588-0299, USA.
authors.forename: Xiaoqian
authors.initials: X
authors.lastname: Dang
authors.forename: J D
authors.initials: JD
authors.lastname: Burton
authors.forename: Evgeny Y
authors.initials: EY
authors.lastname: Tsymbal