Classification of Interacting Electronic Topological Insulators in Three Dimensions

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Science  07 Feb 2014:
Vol. 343, Issue 6171, pp. 629-631
DOI: 10.1126/science.1243326

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Interacting and Topological

Topological insulators (TIs), which have a bandgap and a robust conducting surface state protected by time-reversal symmetry, are typically materials with weak electron-electron interaction and are well-described by band theory. A major experimental goal has been to observe such symmetry-protected topological (SPT) phases in interacting systems. Wang et al. (p. 629) used a theoretical approach to classify SPT phases of interacting fermions in three dimensions and found six other phases in addition to the noninteracting ones. The results lay the groundwork for future microscopic models and inform the experimental search for such materials.


A fundamental open problem in condensed-matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are six interacting electronic topological insulators that have no noninteracting counterpart. Combined with the previously known band insulators, these produce a total of eight topologically distinct phases. Two of the six interacting topological insulators can be described as Mott insulators in which the electron spins form spin analogs of the topological band insulator. The remaining phases are obtained as combinations of these two “topological paramagnets” and the topological band insulator. We prove that these eight phases form a complete list of all possible interacting topological insulators and discuss their experimental signatures.

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