Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology

Abstract

We perform a systematic study of the signatures of fragile topology in over 50 nonmagnetic two-dimensional materials with formula AB$_2$, belonging to space group $P$-$3m1$. Using group theory analysis in the framework of topological quantum chemistry, we find fragile bands near the Fermi level for all the materials studied. Since stable topological bands are also present in these systems, the interplay of both phases is discussed, showing that corner charges appear in over 80% of the materials and are linked to fragile topology. Using first-principles calculations, we predict fractionally-charged corner charges protected by $C_3$ symmetry. Our work aims to broaden the scope of materials with experimentally accessible fragile bands.