Higher Order Topological Phases: A General Principle of Construction

ORAL

Abstract

In this talk, we discuss a general principle for constructing higher-order topological (HOT) phases [1]. We argue that if a D-dimensional first-order or regular topological phase involves m Hermitian matrices that anti-commute with additional p-1 mutually anti-commuting matrices, it is conceivable to realize an nth-order HOT phase, where n=1,..., p, with appropriate combinations of discrete symmetry-breaking Wilsonian masses. An nth-order HOT phase accommodates zero modes on a surface with co-dimension n. We exemplify these scenarios for prototypical three-dimensional gapless systems, such as a nodal-loop semimetal possessing SU(2) spin rotational symmetry, and Dirac semimetals, transforming under (pseudo-)spin-1/2 or 1 representation. The former system permits an unprecedented realization of a 4th-order phase, without any surface zero modes. Our construction can be generalized to HOT insulators and superconductors in any dimension and symmetry class.

[1] D. Călugăru, V. Juričić, and B. Roy, arXiv:1808.08965.

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Presenters

  • Dumitru Calugaru

    Max-Planck-Institut fur Physik komplexer Systeme, Dresden, Germany, Cavendish Laboratory, University of Cambridge

Authors

  • Dumitru Calugaru

    Max-Planck-Institut fur Physik komplexer Systeme, Dresden, Germany, Cavendish Laboratory, University of Cambridge

  • Vladimir Juricic

    NORDITA, Nordic Institute for Theoretical Physics, Stockholm University and KTH, Stockholm, Sweden, NORDITA, the Nordic Institute for Theoretical Physics, Stockholm University and KTH, Stockholm, Sweden, Nordic Institute for Theoretical Physics, Stockholm

  • Bitan Roy

    Max Planck Institute for the Physics of Complex Systems, Dresden, Germany, Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany, Max Planck Institute for the Physics of Complex Systems, Max-Planck-Institut fur Physik komplexer Systeme, Dresden, Germany, Max Planck Institute for the Physics of Complex System