Flux Response of Higher-Order Topological Insulators

One of the highlights of the past few years of topological condensed matter physics has been the discovery of new forms of 3D topological crystalline insulators that are characterized by gapped bulks and surfaces and gapless hinges. Incipient experimental signatures of the gapless hinge states of these “higher-order” topological insulators (HOTIs) have been observed in bismuth, MoTe₂, and WTe₂. However, these signatures have also attracted other explanations. Therefore, it is of intense interest to establish additional indicators of higher-order topology beyond anomalous hinge states. In this work, we use threaded π-flux to probe HOTIs with and without time-reversal symmetry. We establish a general framework that captures the 0D and 1D bound states, charge, and spin that accumulate on the flux cores and tubes. Our framework captures all previous results, such as the fractional charges bound to flux cores in Chern insulators. However, we also discover new examples. Specifically, we demonstrate that π-flux tubes in inversion- and time-reversal-symmetric HOTIs bind Kramers pairs of end states, which represent observable signatures of the anomalous “half” quantum spin Hall effect present on the surfaces of weak topological insulators and HOTIs.