Materials Prediction And Properties Study For Topological Crystalline Insulators And Topological Insulators

Based on the first-principles calculations, tight-binding model and k· p theory, wepredicted some candidates of topological crystalline insulators (TCIs) and topologicalinsulators (TIs) and studied their response to the external electric field and strain.Firstly, we found that, depending on the surface orientation, there are two qualita-tively diferent types of surface states of SnTe-class TCIs. In particular, the (111) surfacestates consist of four Dirac cones centered at time-reversal-invariant momenta (TRIM),while Dirac cones on (001) and (110) surfaces are located at non-TRIM. The latter typeof surface states exhibit a Lifshitz transition as a function of the Fermi energy, which isaccompanied by a Van Hove singularity in the density of states arising from saddle pointsin the band structure. Both two types of surface states are protected by mirror symmetry.Our prediction has been further confirmed quickly in experiments by many independentgroups.Secondly, taking the z→z mirror symmetry of quasi-two-dimensional systems,we extended the concept of the mirror Chern number into thin films. Then we demon-strate that thin films of SnTe and Pb1xSnxSe(Te) grown along the (001) direction aretopologically non-trivial in a wide range of film thickness and carry conducting spin-filtered edge states that are protected by the (001) mirror symmetry through the mirrorChern number. Application of an electric field perpendicular to the film will break themirror symmetry and generate a band gap in these edge states. This functionality moti-vates us to propose a topological transistor device in which charge and spin transport aremaximally entangled and simultaneously controlled by an electric field. The high on/ofoperation speed and coupling of spin and charge in such a device may lead to electronicand spintronic applications for topological crystalline insulators.Then, we found the (111) thin films of SnTe and Pb1xSnxSe(Te) can hostelectrically-tunable quantum spin Hall states in wide range of thickness. Varying withthe thickness,(111) thin films can be a normal insulator or a quantum spin Hall insula-tor. Typically,14-layers SnTe thin films are quantum spin Hall insulator, while12-layersSnTe thin films are not. Moreover, the band structures of thin films are very sensitive tothe external electrical field, and therefore the topological phase transition can be realizedunder experimentally achievable the electric field, typically,4×107V/m for12-layers SnTe thin films.At last, by taking Bi2Se3-class TIs as examples, we studied the efect of strain onthe topological phase. We found strain-induced topological phase transition is a universalphenomenon in those narrow-gap semiconductors for which the valence band maximum(VBM) and conduction band minimum (CBM) have diferent parities. The transitionoriginates from the opposite responses of the VBM and CBM, whose magnitudes de-pend critically on the direction of the applied strain. Our work suggests that strain canplay a unique role in tuning the electronic properties of topological materials for deviceapplications, as well as in the achievement of new topological materials.