real case ai bdi d diii aii cii c ci z z2 z2 0 2z 0

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 0 Z Z 0 0 Z Z 0 0 Z Z 0 0 Z Z 0 0 Z ... ... Real case: AI BDI D DIII AII CII C CI 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 ... ... ... ... ... ... ... ... 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 1 2 3 4 5 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 ... ... Real case: AI BDI D DIII AII CII C CI IQHE 0 d space dimensionality 6 7 8 9 10 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 ... ... ... ... ... ... ... ... 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 DIII AII CII C CI 11 ... symm...
View Full Document

This document was uploaded on 03/12/2014 for the course PHYSICS 240C at UC Davis.

Ask a homework question - tutors are online