Gapless hinge states from adiabatic pumping of axion coupling

TL;DR

This paper shows that in certain insulators, cyclic changes in the axion angle induce gapless hinge states, with their emergence predicted by surface topology markers and modeled using layered Haldane systems.

Contribution

It introduces a mechanism for gapless hinge states via adiabatic pumping of axion coupling, linking surface topology changes to hinge modes in 3D insulators.

Findings

Chiral hinge modes emerge during cyclic axion angle changes.

Surface markers accurately predict hinge mode appearance.

Hinge modes form Fermi arcs in a 4D crystal interpretation.

Abstract

We demonstrate that chiral hinge modes naturally emerge in insulating crystals undergoing a slow cyclic evolution that changes the Chern-Simons axion angle $\theta$ by $2\pi$. This happens when the surface (not just the bulk) returns to its initial state at the end of the cycle, in which case it must pass through a metallic state to dispose of the excess quantum of surface anomalous Hall conductivity pumped from the bulk. If two adjacent surfaces become metallic at different points along the cycle, there is an interval in which they are in topologically distinct insulating states, with chiral modes propagating along the connecting hinge. We illustrate these ideas for a tight-binding model consisting of coupled layers of the Haldane model with alternating parameters. The surface topology is determined in a slab geometry using two different markers, surface anomalous Hall conductivity and surface-localized charge pumping (flow of surface-localized Wannier bands), and we find that both correctly predict the appearance of gapless hinge modes in a rod geometry. When viewing the axion pump as a four-dimensional (4D) crystal with one synthetic dimension, the hinge modes trace Fermi arcs in the Brillouin zone of the 2D hinge connecting a pair of 3D surfaces of the 4D crystal.