Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$ topological invariants, which characterize the ground state. In two dimensions, there is a single ${Z}_{2}$ invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four ${Z}_{2}$ invariants that distinguish the ordinary insulator from ``weak'' and ``strong'' topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ as well as $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.

/pdf/topological-insulators-with-inversion-symmetry-1vaykhe1u1.pdf

Topological insulators with inversion symmetry

Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on topological insulator materials with an emphasis on basic theory and materials properties. After presenting a historical perspective and basic theories of topological insulators, it discusses all the topological insulator materials discovered as of May 2013, with some illustrative descriptions of the developments in materials discoveries in which the author was involved. A summary is given for possible ways to confirm the topological nature in a candidate material. Various synthesis techniques as well as the defect chemistry that are important for realizing bulk-insulating samples are discussed. Characteristic properties of topological insulators are discussed with an emphasis on transport properties. In particular, the Dirac fermion physics and the resulting peculiar qu...

http://inspirehep.net/record/1229385/files/arXiv:1304.5693.pdf

Topological Insulator Materials

Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on topological insulator materials with an emphasis on basic theory and materials properties. After presenting a historical perspective and basic theories of topological insulators, it discusses all the topological insulator materials discovered as of May 2013, with some illustrative descriptions of the developments in materials discoveries in which the author was involved. A summary is given for possible ways to confirm the topological nature in a candidate material. Various synthesis techniques as well as the defect chemistry that are important for realizing bulk-insulating samples are discussed. Characteristic properties of topological insulators are discussed with an emphasis on transport properties. In particular, the Dirac fermion physics and the resulting peculiar quantum oscillation patterns are discussed in detail. It is emphasized that proper analyses of quantum oscillations make it possible to unambiguously identify surface Dirac fermions through transport measurements. The prospects of topological insulator materials for elucidating novel quantum phenomena that await discovery conclude the review.

The past two decades have witnessed the rapid growth of thermoelectric (TE) research. Novel concepts and paradigms are described here that have emerged, targeting superior TE materials and higher TE performance. These superior aspects include band convergence, "phonon-glass electron-crystal", multiscale phonon scattering, resonant states, anharmonicity, etc. Based on these concepts, some new TE materials with distinct features have been identified, including solids with high band degeneracy, with cages in which atoms rattle, with nanostructures at various length scales, etc. In addition, the performance of classical materials has been improved remarkably. However, the figure of merit zT of most TE materials is still lower than 2.0, generally around 1.0, due to interrelated TE properties. In order to realize an "overall zT > 2.0," it is imperative that the interrelated properties are decoupled more thoroughly, or new degrees of freedom are added to the overall optimization problem. The electrical and thermal transport must be synergistically optimized. Here, a detailed discussion about the commonly adopted strategies to optimize individual TE properties is presented. Then, four main compromises between the TE properties are elaborated from the point of view of the underlying mechanisms and decoupling strategies. Finally, some representative systems of synergistic optimization are also presented, which can serve as references for other TE materials. In conclusion, some of the newest ideas for the future are discussed.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/adma.201702816

Compromise and Synergy in High-Efficiency Thermoelectric Materials.

We show that the strongly spin-orbit coupled materials Bi_2Te_3 and Sb_2Te_3 and their derivatives belong to the Z_2 topological-insulator class. Using a combination of first-principles theoretical calculations and photoemission spectroscopy, we directly show that Bi_2Te_3 is a large spin-orbit-induced indirect bulk band gap (δ∼150  meV) semiconductor whose surface is characterized by a single topological spin-Dirac cone. The electronic structure of self-doped Sb_2Te_3 exhibits similar Z_2 topological properties. We demonstrate that the dynamics of spin-Dirac fermions can be controlled through systematic Mn doping, making these materials classes potentially suitable for topological device applications.

/pdf/observation-of-time-reversal-protected-single-dirac-cone-1j060nlgsj.pdf

S. Scherrer

Papers

Thermal properties of high quality single crystals of bismuth telluride—Part I: Experimental characterization

Transport properties of Bi-rich Bi-Sb alloys

Growth of Bi1 − xSbx alloys by the traveling heater method

Thermal properties of high quality single crystals of bismuth telluride—Part II: Mixed-scattering model

Heterodiffusion of selenium in Bi2Te3