symmetry kitaev 2009 ensions if and only if the

Info icon This 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: 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...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern