Beyond Axion Electrodynamics in Helical Higher-Order Topological Insulators*

Solid-state materials including bismuth, MoTe₂, and BiBr have been predicted to be higher-order topological insulators (HOTIs). In theoretical HOTI models, odd numbers of helical hinge modes encircle finite-sized samples, providing an indicator of the bulk HOTI phase in the presence of global crystal symmetries. However, the boundaries of real material samples lack the global symmetries of HOTI models, and there exist topologically trivial models with extrinsic hinge states. Furthermore, unlike chiral HOTIs (magnetic axion insulators), the bulk axion angle θ of helical HOTIs is trivial (modulo 2π). It is hence desirable to identify unambiguous bulk and surface experimental signatures of helical HOTI phases analogous to – but distinct from – the axionic magnetoelectric effects present in 3D TIs and chiral HOTIs with θ = π. In this talk, we use dimensional reduction, non-Abelian Berry phase, magnetic flux insertion, and field theory to demonstrate the existence of quantized bulk topological signatures of helical HOTI phases beyond θ, placing helical HOTIs on the same physical footing as well-understood axionic insulators. We conclude by discussing the experimental implications of our findings.