Models of three-dimensional fractional topological insulators

Details Models of three-dimensional fractional topological insulators Models of three-dimensional fractional topological insulators

2011-11-29

arxiv.org/abs/1111.6816v1

Physics

Condensed Matter

Strongly Correlated Electrons

19 pages, 1 figure

Scientific paper

Time-reversal invariant three-dimensional topological insulators can be defined fundamentally by a topological field theory with a quantized axion angle theta of zero or pi. It was recently shown that fractional quantized values of 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 statistical 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 statistical 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 deconfined phase or a Higgs phase with gauge group broken down to a discrete subgroup. The deconfined phases support gapless but electrically neutral bulk excitations while the Higgs phases are fully gapped. The Higgs and non-Abelian deconfined phases exhibit multiple ground states on boundaryless spatial 3-manifolds with nontrivial first homology, while the Abelian deconfined 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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