Topological insulators are insulating in the bulk, while there are topologically protected edge/surface states. These edge/surface states are different from conventional edge/surface states, and show various novel properties. We briefly outline basic properties of topological insulators, both in 2D and 3D.
The present article systematically describes surface electronic structure of the topological insulator through a comparison with various types of surface states. Followed by explanations of the state-of-the-art spin- and momentum-resolved photoemission experiments, recent reports of spin-polarized band dispersion of the edge-state (surface state) of the three-dimensional topological insulators are presented.
From a viewpoint of transport properties, topological insulators are the materials that are insulating in the bulk but are metallic at their edge. After briefly introducing the basic phenomena such as Dirac fermions and quantum spin Hall effect for topological insulators, we describe the details of the quantum oscillations originating from the surface state of a three-dimensional topological insulator Bi1-xSbx, which was observed for the first time by our group. Intriguingly, this material was found to exhibit a novel angular-dependent magnetoresistance oscillation phenomenon, whose origin is still unknown but probably reflects a new physics in the surface transport properties of the topological insulator.
We introduce the topological aspects of Dirac electrons in graphene, and relation between topology and Hall effect is briefly overviewed for the models introduced by Haldane and by Kane-Mele. We then describe recent proposals for how to control the topological Hall effect by lasers applied to graphene. Namely, nonlinear optical properties of Dirac electrons are discussed where one can generate a dynamical mass at the Dirac point, which is predicted to induce a “photovoltaic Hall effect”. This effect can be measured by electric transport or nonlinear optical methods.
We study charge transport on the surface state of topological insulator where two-dimensional Dirac electron is generated. We put ferromagnetic insulator or superconductor on the topological insulator and reveal anomalous charge transport on the surface. We first consider the charge transport through a ferromagnetic insulator/ferromagnetic insulator (FI/FI) junction on a topological insulator. The resulting conductance across the interface depends sensitively on the directions of the magnetizations of the two FI, showing anomalous behaviors compared with the conventional spin valve. It is found that the conductance depends strongly on the in-plane direction of the magnetization. Moreover, in sharp contrast to the conventional magnetoresistance effect, the conductance at the parallel configuration can be much smaller than that at the antiparallel configuration. We also study the transport properties of a normal metal (N)/FI/superconductor (S) junction formed on the surface of a three-dimensional topological insulator, where chiral Majorana edge mode exists at the FI/S interface. We find that the chiral Majorana edge mode generated in N/FI/S junction strongly influences the charge conductance.
A brief review is given on the symmetry-based classification of topological insulators and topological superconductors for spatial dimensions 1, 2, and 3. Several representative examples are discussed.
By comparing topologically trivial materials (Au, Bi, graphene) and topological insulators (Bi1-xSbx, Bi2Se3), we discuss what the features unique to topological surface states are. The properties reported so far for topological insulators are all explained by Rashba effect due to strong spin-orbit interaction and break down of space-inversion symmetry at surfaces. Topological arguments are not needed. Spin-split surface states with spin-texture Fermi surfaces, however, are very attractive play grounds for exploring spin-flow physics.