Abstract:
Topological insulators(TIs) constitute a novel state of quantum matter which possesses non-trivial topological properties. Although discovered only in the recent few years, TIs have attracted intensive interest among the community of condensed matter physics and material science. TIs are insulating in the bulk but have conductive gapless edge or surface states on the boundaries, which have their origin in the non-trivial bulk band topology that is induced by the strong spin-orbital interactions in the materials. Existing in all dimensions, TIs exhibit a variety of exotic physics such as quantum spin Hall effect, momentum-spin locked surface states, Dirac fermion transport, quantized anomalous Hall effect, Majorana fermions, etc.
Disorder is found be able to induce a non-trivial TI from an originally trivial band insulator, where the conductance of a two terminal device drops to nearly zero and then rises to form an anomalous plateau as disorder strength is increased, and finally all the states become localized. The real space Chern number calculation as well as the effective medium theory suggests that disorder is fundamentally responsible for the emerging of the extended helical edge states in this system.
The concept of topological semi-metals is proposed. By calculating the local density of states on the surfaces, the existence of surface states and the gapless Dirac cone in the system is demonstrated although the bulk is not gaped. The uni-axial strain is found able to induce an insulating band gap and turn the semi-metal into true TI.