Topological invariants of a filling-enforced quantum band insulator

Journal Article · 15 August 2021 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.104.085128 · OSTI ID:1827106

Krishnan, Abijith ^[1]; Vishwanath, Ashvin ^[2]; Po, Hoi Chun ^[1]

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1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2. Harvard Univ., Cambridge, MA (United States)

Traditional ionic and covalent compound insulators arise from a commensuration between electron count and system volume. On the other hand, conventional topological insulators, outside of quantum Hall effect systems, do not typically display such a commensuration. Instead, they can undergo a phase transition to a trivial insulator that preserves the electron filling. Nevertheless, in some crystalline insulators, termed filling-enforced quantum band insulators (feQBIs), electron filling can dictate nontrivial topology in the insulating ground state. Currently, little is known about the relation between feQBIs and conventional topological invariants. In this work, we study such relations for a particularly interesting example of a half-filling feQBI that is realized in space group 106 with spinless electrons. In this work, we prove that any four-band feQBI in space group 106 with filling 2 must have a nontrivial topological invariant, namely, the $$\mathbb{Z}$$₂ glide invariant, and thus must have a quantized magnetoelectric polarizability θ = π. We thus have found a three-dimensional example where electron filling and band topology are tied. Such a locking raises intriguing questions about the generality of the band-inversion paradigm in describing the transition between trivial and topological phases.

• Research Organization: Ames Laboratory (AMES), Ames, IA (United States)
• Sponsoring Organization: National Science Foundation (NSF); U.S. Department of Energy; USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: AC02-07CH11358
• OSTI ID: 1827106
• Report Number(s): IS-J--10,597; 1745302
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 8 Vol. 104; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English