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      Topological insulators and superconductors

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          Abstract

          Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi\(_2\)Te\(_3\) and Bi\(_2\)Se\(_3\) crystals. We review theoretical models, materials properties and experimental results on two-dimensional and three-dimensional topological insulators, and discuss both the topological band theory and the topological field theory. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. We review the theory of topological superconductors in close analogy to the theory of topological insulators.

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          The electronic properties of graphene

          This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. We show that the Dirac electrons behave in unusual ways in tunneling, confinement, and integer quantum Hall effect. We discuss the electronic properties of graphene stacks and show that they vary with stacking order and number of layers. Edge (surface) states in graphene are strongly dependent on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. We also discuss how different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.
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            Quantized Hall Conductance in a Two-Dimensional Periodic Potential

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              CPConservation in the Presence of Pseudoparticles

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                Author and article information

                Journal
                11 August 2010
                10.1103/RevModPhys.83.1057
                1008.2026

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Rev. Mod. Phys. 83, 1057-1110 (2011)
                55 pages, 44 figures, Review article commissioned by the Review of Modern Physics. Please help us to improve the article by emailing us your comments and missing references
                cond-mat.mes-hall cond-mat.supr-con

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