Lukasz Fidkowski, Xie Chen, Ashvin Vishwanath
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 apless 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 3D system with T symmetry. 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. Both phases require electrons to transform as Kramers pairs, i.e. T^2=-1 under time reversal.
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http://arxiv.org/abs/1305.5851
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