Surface and Edge States in Topological Semi-metals

We study the topologically non-trivial semi-metals by means of the 6-band Kane model. Existence of surface states is explicitly demonstrated by calculating the LDOS on the material surface. In the strain free condition, surface states are divided into two parts in the energy spectrum, one part is in the direct gap, the other part including the crossing point of surface state Dirac cone is submerged in the valence band. We also show how uni-axial strain induces an insulating band gap and raises the crossing point from the valence band into the band gap, making the system a true topological insulator. We predict existence of helical edge states and spin Hall effect in the thin film topological semi-metals, which could be tested with future experiment. Disorder is found to significantly enhance the spin Hall effect in the valence band of the thin films

Spin-Helical Dirac Fermions in 3D Topological Insulator Quantum Wires

The next generation of electronic devices based on 3D topological insulators will be developed from advanced functional nanostructures and heterostructures. Toward this goal, single-crystalline nanowires offer interesting opportunities for new developments due to the strong quantum confinement of spin-helical surface Dirac fermions and to the possibility to realize core-shell lateral nanostructures adapted to the control of the electro-chemical potential at the interface with a topological insulator. Here, we review the specific transport properties of 3D topological insulator quantum wires and the influence of disorder. Having a large energy quantization, weakly-coupled Dirac surface modes are prone to quasi-ballistic transport, with some analogies to carbon nanotubes but with spin-textured quantum states weakly coupled by non-magnetic disorder. Due to a small interaction with their environment, these surface modes are good candidates to realize novel quantum spintronic devices, spanning from ballistic spin conductors to localized spin filters. A specific topological mode also holds promises to control chiral edge states and Majorana bound states in truly 1D quantum wires, being tunable with a magnetic field or an electrical gate. Challenges toward these goals are briefly discussed, as well as the need for novel functional heterostructures