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Classification of topological insulators and superconductors in three spatial dimensions
 Phys. Rev. B
"... Abstract. An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a topologically trivial and a topologically nontri ..."
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Abstract. An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a topologically trivial and a topologically nontrivial state. Our approach consists in reducing the problem of classifying topological insulators (superconductors) in d spatial dimensions to the problem of Anderson localization at a (d − 1) dimensional boundary of the system. We find that in each spatial dimension there are precisely five distinct classes of topological insulators (superconductors). The different topological sectors within a given topological insulator (superconductor) can be labeled by an integer winding number or a Z2 quantity. One of the five topological insulators is the “quantum spin Hall ” (or: Z2 topological) insulator in d = 2, and its generalization in d = 3 dimensions. For each dimension d, the five topological insulators correspond to a certain subset of five of the ten generic symmetry classes of Hamiltonians introduced more than a decade ago by Altland and Zirnbauer in the context of disordered systems (which generalizes the three well known “WignerDyson ” symmetry classes).
et INSTITUT DE PHYSIQUE THÉORIQUE CEA/SACLAY Thèse de doctorat
, 2013
"... Sujet de la thèse: Edge states and supersymmetric sigma models présentée par Roberto BONDESAN pour obtenir le grade de Docteur de l’Université Paris 6 Soutenue le 14 Septembre 2012 devant le jury composé de: ..."
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Sujet de la thèse: Edge states and supersymmetric sigma models présentée par Roberto BONDESAN pour obtenir le grade de Docteur de l’Université Paris 6 Soutenue le 14 Septembre 2012 devant le jury composé de:
Topology, Crystallized (Experiments): P. Dziawa et al., arXiv:1206.1705; S.Y. Xu et al., arXiv:1206.2088
"... A key difference between quantum Hall phases induced by a magnetic field and topological insulator phases induced by spinorbit coupling is that the latter depend crucially on a symmetry, time reversal. The action of timereversal symmetry on electrons leads to a new kind of topological invariant in ..."
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A key difference between quantum Hall phases induced by a magnetic field and topological insulator phases induced by spinorbit coupling is that the latter depend crucially on a symmetry, time reversal. The action of timereversal symmetry on electrons leads to a new kind of topological invariant in twodimensional systems [1] that takes only two possible values: if this “Z2 invariant” is even, the system is an ordinary insulator and generically has no edge state, while if it is odd, the system has a protected conducting edge state. Breaking timereversal symmetry allows these two phases to be connected adiabatically (i.e., without closing the energy gap). The interplay of symmetry and topology is more complicated in three dimensions, particularly when crystalline point or space group symmetries are considered, and a large number of phases have been conjectured theoretically. Recent experimental photemission work by two groups confirms the existence in Pb1−xSnxSe [2] and Pb1−xSnxTe [3] of one such phase, the “topological crystalline insulator”; this term was introduced by Liang Fu in a 2011 PRL [4].
Topological Insulators/Isolants Topologiques  An Introduction to Topological Order in Insulators
, 2013
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4. Geometry, Symmetry, and Physics 8
"... Abstract: These are some thoughts meant to accompany one of the summary talks at Strings2014, Princeton, June 27, 2014. This is a snapshot of a personal and perhaps heterodox view of the relation of Physics and Mathematics, together with some guesses about some of the directions forward in the field ..."
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Abstract: These are some thoughts meant to accompany one of the summary talks at Strings2014, Princeton, June 27, 2014. This is a snapshot of a personal and perhaps heterodox view of the relation of Physics and Mathematics, together with some guesses about some of the directions forward in the field of Physical Mathematics. At least, this is my view as of July 21, 2014.