Realizing topological surface states in a lower-dimensional flat band

Abstract

The anomalous surface states of symmetry protected topological (SPT) phases are usually thought to be only possible in conjunction with the higher dimensional topological bulk. However, it has recently been realized that a class of anomalous SPT surface states can be realized in the same dimension if symmetries are allowed to act in a nonlocal fashion. An example is the particle-hole symmetric half filled Landau level, which effectively realizes the anomalous surface state of a 3D chiral Topological Insulator (class AIII). A dual description in terms of Dirac composite fermions has also been discussed. Here we explore generalizations of these constructions to multicomponent quantum Hall states. Our results include a duality mapping of the bilayer case to composite bosons with Kramers degeneracy and the possibility of a particle hole symmetric integer quantum Hall state when the number of components is a multiple of eight. Next, we make a further extension by half filling other classes of topological bands and imposing particle hole symmetry. When applied to time-reversal invariant topological insulators we realize a different chiral class (CII) topological surface state. Notably, half-filling a 3D TI band allows for the realization of the surface of the otherwise inaccessible 4D topological insulator, which supports an anomalous 3D Dirac cone. Surface topological orders equivalent to the 3D Dirac cone (from the global anomaly standpoint) are constructed and connections to Witten's SU(2) anomaly are made. These observations may also be useful for numerical simulations of topological surface states and of Dirac fermions without fermion doubling.

22 pages, 2 Figures, 3 Tables; published version

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• Magnetic Topological Quantum Chemistry
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Universal Features of Higher-Form Symmetries at Phase Transitions
• From Bosonic Topological Transition to Symmetric Fermion Mass Generation
• Deconfined Quantum Critical Point on the Triangular Lattice
• Fractional Quantum Hall Effect in Weyl Semimetals
• Symmetry enriched U(1) quantum spin liquids
• Charge density waves in Weyl semimetals
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Multiplicative topological phases
• Topological Edge and Interface states at Bulk disorder-to-order Quantum Critical Points
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands
• Localized surfaces of three dimensional topological insulators
• Composite helical edges from Abelian fractional topological insulators
• Partial filled Landau Level at even denominator, a vortex metal with Berry phase
• Fermionic dualities with axial gauge fields
• Fractionalization as an alternate to charge ordering in electronic insulators
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
• Marginally localized edges of time-reversal symmetric topological superconductors
• Deconfined Quantum Critical Point with Non-locality
• Non-Landau Quantum Phase Transitions and nearly-Marginal non-Fermi Liquid
• Fermionic skyrmions and bosonization for a Gross-Neveu transition