## Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator    [PDF]

Xie Chen, Lukasz Fidkowski, Ashvin Vishwanath
The surfaces of three dimensional topological insulators (3D TIs) are generally described as Dirac metals, with a single Dirac cone. It was previously believed that a gapped surface implied breaking of either time reversal T or U(1) charge conservation symmetry. Here we discuss a novel possibility in the presence of interactions, a surface phase that preserves all symmetries but is nevertheless gapped and insulating. A requirement is that the surface develops topological order of a kind that cannot be realized in a purely 2D system with the same symmetries. We discuss two candidate surface states - both of which are non-Abelian Fractional Quantum Hall states which, when realized in 2D, have \sigma_{xy}=1/2 and hence break T symmetry. However, by constructing an exactly soluble 3D lattice model, we show they can be realized as T symmetric surface states. Both the corresponding 3D phases are confined, have \theta=\pi magnetoelectric response, and require electrons that are Kramers doublets. The first, the T-Pfaffian state, is the (Read-Moore) Pfaffian state with the neutral sector reversed, while the second, the Pfaffian-antisemion state is a product of the Pfaffian state with antisemion topological order. The latter can be connected to the superconducting TI surface state on breaking charge U(1) symmetry, while for the T-Pfaffian there is no simple way to do so. We discuss two physical scenarios for the T-Pfaffian, either (i) it is equivalent to the Pfaffian-antisemion theory and also describes the 3D TI surface OR (ii) it represents a new, interacting 3D TI.
View original: http://arxiv.org/abs/1306.3250