A 3d electron topological insulator (ETI) is a phase of matter
protected by particle-number conservation and time-reversal symmetry.
It was previously believed that the surface of an ETI must be gapless
unless one of these symmetries is broken. A well-known
symmetry-preserving, gapless surface termination of an ETI supports an
odd number of Dirac cones. In this talk, I will show that in the
presence of strong interactions, an ETI surface can actually be gapped
and symmetry preserving, at the cost of carrying an intrinsic
two-dimensional topological order. I will argue that such a
topologically ordered phase can be obtained by depositing an s-wave
superconductor on the ETI surface and then proliferating the flux 2hc/e vortex.
The resulting topological order consists of two sectors: a Moore-Read
sector, which supports non-Abelian charge e/4 anyons, and an Abelian anti-semion
sector, which is electrically neutral. The time-reversal and particle
number symmetries are realized in this surface phase in an "anomalous"
way: one which is impossible in a strictly 2d system. If time permits,
I will discuss related results on topologically ordered surface phases
of 3d topological superconductors.
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