Genus-protected higher-order topological phases

Abstract

Higher-order topological phases (HOTPs) feature protected gapless modes on boundaries of higher codimension, such as the corners or hinges of a crystal. They are understood as being protected by lattice symmetries: If the latter are broken, it becomes possible to remove the boundary modes without closing the bulk gap. In this work, we present construction schemes for HOTPs protected solely by the bulk gap, by fundamental symmetries, and by the global topology of the system shape (its genus, or number of holes), independent of any crystalline symmetries. As long as the fundamental local symmetries are preserved, the resulting boundary states cannot be removed by any purely-surface perturbation.