Abstract: Solid-state materials including bismuth, MoTe2, and BiBr have been predicted to be higher-order topological insulators (HOTIs). In theoretical HOTI models, the 3D bulk and 2D surfaces are gapped, and odd numbers of 1D gapless topological modes appear bound to the hinges of finite-sized 3D 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. In HOTIs
with chiral hinge states, the bulk topology has been shown to be characterized by a nontrivial axion angle, and hence chiral HOTIs can in principle be characterized experimentally through the framework of axion electrodynamics, rather than higher-order topology. For helical HOTIs, however, the bulk axion angle is trivial, and the only experimental signatures proposed to date rely on global symmetry arguments and hinge-state measurements. It is hence desirable to identify unambiguous bulk and surface signatures of helical HOTI phases analogous to - but distinct from - the axionic magnetoelectric effects present in 3D topological insulators (TIs) and chiral HOTIs. In this talk, I will present numerical and theoretical analysis of helical HOTIs demonstrating the existence of quantized bulk topological signatures beyond the axion angle, placing helical HOTIs on the same physical footing as well-understood 3D TIs and magnetic axion insulators.