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

TL;DR

This paper introduces filling-enforced quantum band insulators (QBIs) in spin-orbit coupled crystals, which cannot be described by localized orbitals due to quantum entanglement, expanding understanding of topological phases in certain cubic non-symmorphic crystals.

Contribution

The paper theoretically discovers a new class of QBIs enforced by electron filling in specific cubic non-symmorphic crystals with spin-orbit coupling.

Findings

Filling-enforced QBIs occur at electron fillings below atomic limits.

These QBIs are characterized by quantum entanglement rather than protected surface states.

They are found in models of certain cubic crystals with non-symmorphic space groups.

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.