Kopnin salomaa 1991 read and green 2000 2 4d quantum

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Unformatted text preview: n the spectrum). Kopnin, Salomaa, 1991. Read and Green, 2000. 2. 4D quantum Hall effect. Zhang, Hu, 2001 3. Solitons in 1D chains. Su, Schrieffer, Heeger (1978) Thursday, January 6, 2011 10 Other topological insulators? 1. 2D px+ipy superconductor (“insulator” since its Bogoliubov quasiparticles have a gap in the spectrum). Kopnin, Salomaa, 1991. Read and Green, 2000. 2. 4D quantum Hall effect. Zhang, Hu, 2001 3. Solitons in 1D chains. Su, Schrieffer, Heeger (1978) 4. Modern 2D and 3D topological insulators. Kane and Mele (2005); Zhang, Hughes, Bernevig, (2006); Moore, Balents, (2007); Fu, Kane, Mele (2007) Thursday, January 6, 2011 10 Altland-Zirnbauer’s tenfold way Thursday, January 6, 2011 11 Altland-Zirnbauer’s tenfold way Symmetries: 1. Time-reversal Thursday, January 6, 2011 11 Altland-Zirnbauer’s tenfold way Symmetries: 1. Time-reversal 2. Particle-hole Thursday, January 6, 2011 11 Altland-Zirnbauer’s tenfold way Symmetries: 1. Time-reversal 2. Particle-hole 3. Chiral (sublattice) Thursday, January 6, 2011 11 Altland-Zirnbauer’s tenfold Symmetries: 1. Time-reversal 3. Chiral (sublattice) Cartan label A (unitary) AI (orthogonal) AII (symplectic) AIII (ch. unit.) BDI (ch. orth.) CII (ch. sympl.) D (BdG) C (BdG) DIII (BdG) CI (BdG) Thursday, January 6, 2011 T C S 0 +1 −1 0 +1 −1 0 0 −1 +1 0 0 0 0 +1 −1 +1 −1 +1 −1 0 0 0 1 1 1 0 0 1 1 From: Ryu, Schnyder, Furusaki, Ludwig, 2010 2. Particle-hole respectively, as well as the 11 ty way ‘Hamiltonian’ lists, for each of t which the quantum mechanical The column ‘Cartan label’ is t space listed in the column ‘Ham (dating back to the year 1926). lists the (compact sectors of the localization physics at long wav U U U U O S S S S S Altland-Zirnbauer’s tenfold Symmetries: 1. Time-reversal 3. Chiral (sublattice) IQHE spin-orbit coupling coupling: modern top. ins. Su-Schrieffer-Heeger solitons p-wave spin-polarized superconductors 3He, phase B s-wave superconductors Thursday, January 6, 2011 Cartan label A (unitary) AI (orthogonal) AII (symplectic) AIII (ch. unit.) BDI (ch. orth.) CII (ch. sympl.) D (BdG) C (BdG) DIII (BdG) CI (BdG) T C S 0 +1 −1 0 +1 −1 0 0 −1 +1 0 0 0 0 +1 −1 +1 −1 +1 −1 0 0 0 1 1 1 0 0 1 1 From: Ryu, Schnyder, Furusaki, Ludwig, 2010 2. Particle-hole respectively, as well as the 11 ty way ‘Hamiltonian’ lists, for each of t which the quantum mechanical The column ‘Cartan label’ is t space listed in the column ‘Ham (dating back to the year 1926). lists the (compact sectors of the localization physics at long wav U U U U O S S S S S 12 the topologically distinct phases within a given symmetry class of topological insulators (superconductors) are characterized by an integer invariant (Z) or a Z2 quantity, respectively. The symbol ‘0’ denotes the case when there exists no topological insulator (superconductor), i.e. when all quantum ground states are Table from Ryu, Schnyder, Furusaki, Ludwig, 2010 topologically equivalent to the trivial state. Classification table of topological insulators and superconductors Cartan 0 1 2 3 4 5 d space dimensionality 6 7 8 9 10 Complex case: A AIII Z 0 0 Z Z 0...
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This document was uploaded on 03/12/2014 for the course PHYSICS 240C at UC Davis.

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