Gapless hinge states from adiabatic pumping of axion coupling

This work studies the general features of electronic states at the boundary of an insulator undergoing a cyclic evolution with a nonzero second Chern number. The figure combines two maps of Fermi surfaces, extended to 3D by including the dependence on the cyclic parameter $\ensuremath{\phi}$, in the surface states of $z$ normal (blue) and $y$ normal (red) facets. The authors find that hinges connecting these facets necessarily carry chiral modes when $\ensuremath{\phi}$ lies in the gray region between tangent planes, where the surface facets are insulating.