Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model
By Lukasz Fidkowski, Xie Chen, Ashvin Vishwanath. 2013
200 citations recorded by the source corpus.
Three dimensional topological superconductors (TScs) protected by time reversal (T) symmetry are characterized by gapless Majorana cones on their surface. Free fermion phases with this symmetry (class DIII) are indexed by an integer n, of which n=1 is realized by the B-phase of superfluid Helium-3. Previously it was believed that the surface must be gapless unless time reversal symmetry is broken. Here we argue that a fully symmetric and gapped surface is possible in the presence of strong interactions, if a special type of topological order appears on the surface. The topological order realizes T symmetry in an anomalous way, one that is impossible to achieve in purely two dimensions. For odd n TScs, the surface topological order must be non-Abelian. We propose the simplest non-Abelian topological order that contains electron like excitations, SO(3)_6, with four quasiparticles, as a candidate surface state. Remarkably, this theory has a hidden T invariance which however is broken in any 2D realization. By explicitly constructing an exactly soluble Walker-Wang model we show that it can be realized at the surface of a short ranged entangled 3D fermionic phase protected by T symmetry, with bulk electrons trasforming as Kramers pairs, i.e. T^2=-1 under time reversal. We also propose an Abelian theory, the semion-fermion topological order, to realize an even n TSc surface, for which an explicit model is derived using a coupled layer construction. We argue that this is related to the n=2 TSc, and use this to build candidate surface topological orders for n=4 and n=8 TScs. The latter is equivalent to the three fermion state which is the surface topological order of a Z2 bosonic topological phase protected by T invariance. One particular consequence of this is that an n=16 TSc admits a trivially gapped T-symmetric surface.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/14a102c07e47bb7816295795e65ff0411f0e37fb
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Chern-Simons-matter dualities with SO and USp gauge groups (2016, methodology): “The special case U(1)2 is known as the “fermion/semion theory” [57] and was discussed recently in [35,28].”
- Particle-vortex duality in topological insulators and superconductors (2016, background): “For example, it is known that three dimensional topological superconductors manifest a fully time-reversal symmetric and gapped surface in the presence of strong interactions and a special kind of topological order [24].”
- Classification of Interacting Topological Floquet Phases in One Dimension (2016, background): “[34] Lukasz Fidkowski, Xie Chen, and Ashvin Vishwanath, “Non-abelian topological order on the surface of a”
- Topological Phases Protected by Point Group Symmetry (2016, unknown): “A. σ2 = 1: Z16 classification As in the cases analyzed above, the first step is to analyze the possible 2d states on the mirror plane.”
- Fermionic symmetry protected topological phases and cobordisms (2014, background): “In four space-time dimensions, the cobordism classification says that fermionic SPT phases are labeled by elements of Z16.”
- Gapped boundary phases of topological insulators via weak coupling (2016, background): “When interactions are taken into account [42, 33, 34, 43], νT is no longer a Z-valued invariant, but is an invariant mod 16.”
- Fermion Path Integrals And Topological Phases (2015, background): “At the free fermion level, ν is an integer-valued invariant, but it has been argued [17–20] that at the interacting level, ν is only an invariant mod 16.”
- A Duality Web in 2+1 Dimensions and Condensed Matter Physics (2016, unknown): “The known semion/fermion theory [65] can be made explicitly T -invariant with an anomaly by writing it as a U(1)2 × U(1)−1 theory [51] 2 4π bdb− 1 4π bdb − 1 2π Adb − 1 2π (A+ A)db , (4.”