Filling-Enforced Quantum Band Insulators in Spin-Orbit Coupled Crystals

Abstract

While band insulators are usually described in wavevector space in terms of fully filled bands, they are sometimes also described in terms of a complementary Wannier picture in which electrons occupy localized, atom-like orbitals. Under what conditions does the latter picture break down? The presence of irremovable quantum entanglement between different sites can obstruct a localized orbital description, which occurs in systems like Chern and topological insulators. We collectively refer to such states as Quantum Band Insulators (QBIs). Here we report the theoretical discovery of a filling-enforced QBI - that is, a free electron insulator in which the band filling is smaller than the minimum number dictated by the atomic picture. Consequently such insulators have no representation in terms of filling localized orbitals and must be QBIs. This is shown to occur in models of certain cubic crystals with non-symmorphic space groups. Like topological insulators, filling-enforced QBIs require spin-orbit coupling. However, in contrast, they do not typically exhibit protected surface states. Instead their nontrivial nature is revealed by studying the quantum entanglement of their ground state wavefunction.

4.5 pages + 7.5 page Appendices, 2+4 figures; v3: Corrected Fig. 5 in Appendix B; added discussion on surface states (Fig. 6)

References in corpus (12)

• Topological Crystalline Insulators
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Wannier representation of Z_2 topological insulators
• Exponential localization of Wannier functions in insulators
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Spin-orbit effects in Na${}_4$Ir${}_3$O${}_8$, a hyper-kagomé lattice antiferromagnet
• Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Position momentum Duality in the Entanglement Spectrum of Free Fermions

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• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
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• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
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• Selection rules for quasiparticle interference with internal nonsymmorphic symmetries
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• Crystalline finite-size topology
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