Recent experiments and theories have suggested that strong spin–orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic quantum-entanglement effects. Such systems feature two-dimensional surface states whose electrodynamic properties are described not by the conventional Maxwell equations but rather by an attached axion field, originally proposed to describe interacting quarks. It has been proposed that a topological insulator with a single Dirac cone interfaced with a superconductor can form the most elementary unit for performing fault-tolerant quantum computation. Here we present an angle-resolved photoemission spectroscopy study that reveals the first observation of such a topological state of matter featuring a single surface Dirac cone realized in the naturally occurring Bi_2Se_3 class of materials. Our results, supported by our theoretical calculations, demonstrate that undoped Bi_2Se_3 can serve as the parent matrix compound for the long-sought topological device where in-plane carrier transport would have a purely quantum topological origin. Our study further suggests that the undoped compound reached via n-to-p doping should show topological transport phenomena even at room temperature.

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Observation of a large-gap topological-insulator class with a single Dirac cone on the surface

Three-dimensional topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. By investigating the surface state of Bi2Te3 with angle-resolved photoemission spectroscopy, we demonstrate that the surface state consists of a single nondegenerate Dirac cone. Furthermore, with appropriate hole doping, the Fermi level can be tuned to intersect only the surface states, indicating a full energy gap for the bulk states. Our results establish that Bi2Te3 is a simple model system for the three-dimensional topological insulator with a single Dirac cone on the surface. The large bulk gap of Bi2Te3 also points to promising potential for high-temperature spintronics applications.

http://science.sciencemag.org/content/sci/325/5937/178.full.pdf

Experimental realization of a three-dimensional topological insulator, Bi2Te3

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

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Experimental Realization of a Three-Dimensional Topological Insulator

In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

New perspectives for Rashba spin–orbit coupling

High momentum resolution angle resolved photoemission spectra from the Au(111) $\mathrm{sp}$-derived surface state exhibit a doublet. The separation between the peaks increases linearly with ${k}_{\ensuremath{\Vert}}$, and reaches a maximum of 110 meV at $0.153{\AA{}}^{\ensuremath{-}1}$, when one of the bands crosses the Fermi level. These results are interpreted as spin-split surface state bands, with the spins aligned in the plane of the surface perpendicular to the electronic momentum. The origin of the splitting is spin-orbit coupling, which can break spin degeneracy in systems which lack inversion symmetry.

Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy.

Low-energy excitations in solids are fundamental to life as we know it. They determine quantities such as conduction and specific heat, which are important properties for things as common as how high the electric bill is. One type of low-energy excitation is the electron-phonon interaction. Understanding the electron-phonon interaction helped unlock the door to the description of traditional superconductivity and may be fundamental to understanding the mechanism of the more technologically exciting high-Tc superconductors. As electromechanical miniaturization progresses and the number of surface atoms becomes comparable to the number of bulk atoms for a given sample or device, surface properties are becoming more and more important. The combination of the increasing importance of surface properties and an interest in the electron-phonon interaction has led to a significant increase in research in this area. See the reviews by Plummer et al.1 and Kevan and Rotenberg2 and references therein. In 1995 McDougall et al.3 published a seminal paper on the use of photoemission spectroscopy to measure , the electron-phonon mass enhancement parameter. The relevant theory is as follows. The contributions to the hole lifetime and therefore to the total photoemission linewidth, are electron-electron, electron-phonon, and electron-impurity scattering. Electron-impurity scattering is not temperature dependent and the temperature dependence of electronelectron scattering is negligible. For temperatures T with kbT greater than phonon energies the temperature dependence of the photoemission linewidth W should be almost entirely due to the electron-phonon interaction which has the temperature-dependent linewidth

B. A. McDougall

Papers

Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy.

Electron-phonon mass enhancement parameter of the Γ̄ surface state on Au(111) measured by photoemission spectroscopy