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arXiv · 1808.08965

Higher Order Topological Phases: A General Principle of Construction

Dumitru Calugaru·Vladimir Juricic·Bitan Roy
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Abstract

We propose a general principle for constructing higher-order topological (HOT) phases. 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 $n$th-order HOT phase, where $n=1, \cdots, p$, with appropriate combinations of discrete symmetry-breaking Wilsonian masses. An $n$th-order HOT phase accommodates zero modes on a surface with codimension $n$. 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-$\frac{1}{2}$ or 1 representations. The former system permits an unprecedented realization of a fourth-order phase, without any surface zero modes. Our construction can be generalized to HOT insulators and superconductors in any dimension and symmetry class.

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Dumitru Calugaru, Vladimir Juricic, Bitan Roy. 2019-02-13. Higher Order Topological Phases: A General Principle of Construction. https://doi.org/10.1103/physrevb.99.041301

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