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• W2742475931 abstract "In this paper, we propose a generalization of the $S$-duality of four-dimensional quantum electrodynamics (${text{QED}}_{4}$) to ${text{QED}}_{4}$ with fractionally charged excitations, the fractional $S$-duality. Such ${text{QED}}_{4}$ can be obtained by gauging the $text{U(1)}$ symmetry of a topologically ordered state with fractional charges. When time-reversal symmetry is imposed, the axion angle ($ensuremath{theta}$) can take a nontrivial but still time-reversal-invariant value $ensuremath{pi}/{t}^{2}$ ($tensuremath{in}mathbb{Z}$). Here, $1/t$ specifies the minimal electric charge carried by bulk excitations. Such states with time-reversal and $text{U(1)}$ global symmetry (fermion number conservation) are fractional topological insulators (FTIs). We propose a topological quantum field theory description, which microscopically justifies the fractional $S$-duality. Then, we consider stacking operations (i.e., a direct sum of Hamiltonians) among FTIs. We find that there are two topologically distinct classes of FTIs: type I and type II. Type I ($tensuremath{in}{mathbb{Z}}_{mathrm{odd}}$) can be obtained by directly stacking a noninteracting topological insulator and a fractionalized gapped fermionic state with minimal charge $1/t$ and vanishing $ensuremath{theta}$. But type II ($tensuremath{in}{mathbb{Z}}_{mathrm{even}}$) cannot be realized through any stacking. Finally, we study the surface topological order of fractional topological insulators." @default.
• W2742475931 created "2017-08-17" @default.
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• W2742475931 date "2017-08-18" @default.
• W2742475931 modified "2023-10-18" @default.
• W2742475931 title "Fractional <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>S</mml:mi></mml:math> -duality, classification of fractional topological insulators, and surface topological order" @default.
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• W2742475931 doi "https://doi.org/10.1103/physrevb.96.085125" @default.
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