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We investigate the scattering and localization properties of edge and bulk states in a disordered two-dimensional topological insulator when they coexist at the same fermi energy. Due to edge-bulk backscattering (which is not prohibited emph{a priori} by topology or symmetry), Anderson disorder makes the edge and bulk states localized indistinguishably. Two methods are proposed to effectively decouple them and to restore robust transport. The first kind of decouple is from long range disorder, since edge and bulk states are well separated in $k$ space. The second one is from an edge gating, owing to the edge nature of edge states in real space. The latter can be used to electrically tune a system between an Anderson insulator and a topologically robust conductor, i.e., a realization of a topological transistor.
The edge states of a two-dimensional quantum spin Hall (QSH) insulator form a one-dimensional helical metal which is responsible for the transport property of the QSH insulator. Conceptually, such a one-dimensional helical metal can be attached to an
We investigate topological states of two-dimensional (2D) triangular lattices with multi-orbitals. Tight-binding model calculations of a 2D triangular lattice based on $emph{p}_{x}$ and emph{p}_{y} orbitals exhibit very interesting doubly degenerate
We investigate the emergence of anti-ferromagnetic ordering and its effect on the helical edge states in a quantum spin Hall insulator, in the presence of strong Coulomb interaction. Using dynamical mean-field theory, we show that the breakdown of la
Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge states with
The surface states in three-dimensional (3D) topological insulators (TIs) can be described by a two-dimensional (2D) continuous Dirac Hamiltonian. However, there exists the Fermion doubling problem when putting the continuous 2D Dirac equation into a