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arXiv:1706.00429 · Bulletin of the American Physical Society

Symmetric-Gapped Surface States of Fractional Topological Insulators

Gil Young Cho, Jeffrey C. Y. Teo, Eduardo Fradkin

Published Jun 1, 2017• 0 citations
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Abstract

We construct the symmetric-gapped surface states of a fractional topological insulator with electromagnetic $θ$-angle $θ_{em} = \fracπ{3}$ and a discrete $\mathbb{Z}_3$ gauge field. They are the proper generalizations of the T-pfaffian state and pfaffian/anti-semion state and feature an extended periodicity compared with their of "integer" topological band insulators counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.

DOI
10.48550/arxiv.1706.00429

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We construct the symmetric-gapped surface states of a fractional topological insulator with electromagnetic θθθ-angle θem=π3θ_{em} = \fracπ{3}θem​=3π​ and a discrete Z3\mathbb{Z}_3Z3​ gauge field. They are the proper generalizations of the T-pfaffian state and pfaffian/anti-semion state and feature an extended periodicity compared with their of "integer" topological band insulators counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.
We construct the symmetric-gapped surface states of a fractional topological insulator with an electromagnetic $\ensuremath{\theta}$ angle ${\ensuremath{\theta}}_{\text{em}}=\frac{\ensuremath{\pi}}{3}$ and a discrete Z3{\mathbb{Z}}_{3}Z3​ gauge field. They are the proper generalizations of the T-Pfaffian state and Pfaffian/antisemion state and feature an extended periodicity compared with their ``integer'' topological band insulator counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.
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Time-reversal invariant three-dimensional topological insulators can be defined fundamentally by a topological field theory with a quantized axion angle $\ensuremath{\theta}$ of 0 or $\ensuremath{\pi}$. It was recently shown that fractional quantized values of $\ensuremath{\theta}$ are consistent with time-reversal invariance if deconfined, gapped, fractionally charged bulk excitations appear in the low-energy spectrum due to strong correlation effects, leading to the concept of a fractional topological insulator. These fractionally charged excitations are coupled to emergent gauge fields, which ensure that the microscopic degrees of freedom, the original electrons, are gauge-invariant objects. A first step towards the construction of microscopic models of fractional topological insulators is to understand the nature of these emergent gauge theories and their corresponding phases. In this work, we show that low-energy effective gauge theories of both Abelian or non-Abelian type are consistent with a fractional quantized axion angle if they admit a Coulomb phase or a Higgs phase with gauge group broken down to a discrete subgroup. The Coulomb phases support gapless but electrically neutral bulk excitations while the Higgs phases are fully gapped. The Higgs and non-Abelian Coulomb phases exhibit multiple ground states on boundaryless spatial three-manifolds with nontrivial first homology, while the Abelian Coulomb phase has a unique ground state. The ground-state degeneracy receives an additional contribution on manifolds with boundary due to the induced boundary Chern-Simons term.
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