Abstract
We introduce exotic gapless states---`composite Dirac liquids'---that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but nevertheless feature a single massless Dirac cone built from emergent electrically neutral fermions. These states thus comprise electrical insulators that, interestingly, retain thermal properties similar to those of the non-interacting topological insulator surface. A variety of novel fully gapped phases naturally descend from composite Dirac liquids. Most remarkably, we show that gapping the neutral fermions via Cooper pairing---which crucially does not violate charge conservation---yields symmetric non-Abelian topologically ordered surface phases captured in several recent works. Other (Abelian) topological orders emerge upon alternatively gapping the neutral Dirac cone with magnetism. We establish a hierarchical relationship between these descendant phases and expose an appealing connection to paired states of composite Fermi liquids arising in the half-filled Landau level of two-dimensional electron gases. To controllably access these states we exploit a quasi-1D deformation of the original electronic Dirac cone that enables us to analytically address the fate of the strongly interacting surface. The algorithm we develop applies quite broadly and further allows the construction of symmetric surface topological orders for recently introduced bosonic topological insulators.
Highlights
Three-dimensional topological insulators (3D TIs) [1,2,3,4,5] possess an electrically inert interior yet harbor a wealth of physics at their surfaces that could not exist without the accompanying bulk
Pairing the neutral fermions generates the Pfaffian-antisemion state captured by vortex-condensation arguments, while magnetically gapping the second-generation neutral Dirac cone again yields an Abelian topological order
Consider a TI material whose surface supports three charged Dirac cones. (Some remarks on the singlecone case appear below.) Each magnetic domain wall from Fig. 2(a) correspondingly carries three copropagating chiral electrons that we describe with operators ψ y ∼ eiφy ; ψ Æ;y ∼ eiφÆ;y : ð30Þ
Summary
Three-dimensional topological insulators (3D TIs) [1,2,3,4,5] possess an electrically inert interior yet harbor a wealth of physics at their surfaces that could not exist without the accompanying bulk. With perturbatively weak electron-electron interactions the above discussion summarizes the essence of 3D TI boundary physics: Massless Dirac cones imply preservation of both time reversal and charge conservation, while a gapped surface necessitates breaking at least one of these symmetries. We show that magnetically gapping the neutral Dirac cone instead yields a time-reversal-breaking Abelian topological order corresponding to the 113 state. These CDL descendants are very similar in spirit to the weak- and strongpairing phases [12] that derive from 2D composite Fermi liquids. Pairing the neutral fermions generates the Pfaffian-antisemion state captured by vortex-condensation arguments, while magnetically gapping the second-generation neutral Dirac cone again yields an Abelian topological order.
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