Classification of interacting electronic topological insulators in three dimensions

Abstract

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 6 new electronic topological insulators that have no non-interacting counterpart. Combined with the previously known band-insulators, these produce a total of 8 topologically distinct phases. Two of the new topological insulators have a simple physical description as Mott insulators in which the electron spins form spin analogs of the familiar topological band-insulator. The remaining are obtained as combinations of these two `topological paramagnets' and the topological band insulator. We prove that these 8 phases form a complete list of all possible interacting topological insulators, and are classified by a Z_2^3 group-structure. Experimental signatures are also discussed for these phases.

New version contains more results on experimental signatures and a more rigorous proof of a key statement (see Appendix D,E), with references reorganized

References in corpus (9)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Symmetry protected Spin Quantum Hall phases in 2-Dimensions
• Interaction effects on 1D fermionic symmetry protected topological phases

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