symmetry kitaev 2009 ensions if and only if the

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Unformatted text preview: etry ¯ Kitaev, 2009; ensions if and only if the target space of the NLσ M on the d -dimensional boundary allows classes Ludwig, Ryu, Schnyder, Furusaki, Z2 , or ither (i) a Z2 topological term, which is the case when πd¯ (G / H ) = πd −1 (G / H ) = 2009. a WZW term, which is the case when πd (G / H ) = πd¯+1 (G / H ) = Z. By using this rule in Thursday, January 6, 2011 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 IQHE 0 1 2 3 4 5 d space dimensionality 6 7 8 9 10 Complex case: A AIII Z 0 0 Z Z 0 0 Z Z 0 0 Z Z 0 0 Z Z 0 0 Z Z 0 0 Z ... ... Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 2Z 0 0 0 Z Z2 Z2 0 0 2Z 0 0 0 Z Z2 Z2 Z2 0 2Z 0 0 0 Z Z2 Z2 Z2 0 2Z 0 0 0 Z Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z ... ... ... ... ... ... ... ... Su, Real case: Schrieffer, Heeger AI BDI D D p-wave DIII supercond AII uctor CII C CI 11 ... symmetry ¯ Kitaev, 2009; ensions if and only if the target space of the NLσ M on the d -dimensional boundary allows classes Ludwig, Ryu, Schnyder, Furusaki, Z2 , or ither (i) a Z2 topological term, which is the case when πd¯ (G / H ) = πd −1 (G / H ) = 2009. a WZW term, which is the case when πd (G / H ) = πd¯+1 (G / H ) = Z. By using this rule in Thursday, January 6, 2011 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 IQHE 0 1 2 3 4 5 d space dimensionality 6 7 8 9 10 Complex case: A AIII Z 0 0 Z Z 0 0 Z Z 0 0 Z Z 0 0 Z Z 0 0 Z Z 0 0 Z ... ... Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 2Z 0 0 0 Z Z2 Z2 0 0 2Z 0 0 0 Z Z2 Z2 Z2 0 2Z 0 0 0 Z Z2 Z2 Z2 0 2Z 0 0 0 Z Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z 0 0 0 0 Z Z2 Z2 0 2Z ... ... ... ... ... ... ... ... Su, Real case: Schrieffer, Heeger AI BDI D D p-wave DIII supercond AII uctor CII C CI 11 ... symmetry 3 ¯ Kitaev, 2009; ensions if and only if the target He, phasethe NLσ M on the d -dimensional boundary allows space of B classes Ludwig, Ryu, Schnyder, Furusaki, Z2 , or ither (i) a Z2 topological term, which is the case when πd¯ (G / H ) = πd −1 (G / H ) = 2009. a WZW term, which is t...
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This document was uploaded on 03/12/2014 for the course PHYSICS 240C at UC Davis.

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