Composite Dirac liquids: parent states for symmetric surface topological order

TL;DR

This paper introduces composite Dirac liquids as exotic gapless states on 3D topological insulator surfaces, revealing new gapped phases and topological orders through interactions and pairing mechanisms, with broad applicability.

Contribution

It presents a novel class of gapless states called composite Dirac liquids and explores their descendant phases and topological orders via analytical methods.

Findings

Composite Dirac liquids are electrically insulating but have a gapless Dirac cone from neutral fermions.

Gapping neutral fermions via Cooper pairing yields non-Abelian topological surface phases.

Alternative gapping with magnetism produces Abelian topological orders.

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.