Composite Dirac liquids: parent states for symmetric surface topological order

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.

23 Pages, 5 figures

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Cited by in corpus (17)

• Symmetric Mass Generation
• Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Fractional chiral superconductors
• Interacting surface states of three-dimensional topological insulators
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Generalized parafermions and non-local Josephson effect in multi-layer systems
• Symmetry Transmutation and Anomaly Matching
• Topological order in interacting semimetals
• Dihedral twist liquid models from emergent Majorana fermions
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays