Engineering topics
Kane, C. L.
Publications and source records attributed to Kane, C. L..
Wallpaper fermions and the nonsymmorphic Dirac insulator
Materials whose gapless surface states are protected by crystal symmetries include mirror topological crystalline insulators and nonsymmorphic hourglass insulators. There exists only a very limited set of possible surface crystal symmetries, captured by the 17 “wallpaper groups.” Here we show that a consideration of symmetry-allowed band degeneracies in the wallpaper groups can be used to understand previously described topological crystalline insulators and to predict phenomenologically distinct examples. In particular, the two wallpaper groups with multiple glide lines, pgg and p 4 g , allow for a topological insulating phase whose surface spectrum consists of only a single, fourfold-degenerate, true Dirac fermion, representing an exception to a symmetry-enhanced fermion-doubling theorem. We theoretically predict the presence of this phase in Sr 2 Pb 3 in space group 127 ( P 4 /mbm) .
Bulk Dirac Points in Distorted Spinels
Here, we report on a Dirac-like Fermi surface in three-dimensional bulk materials in a distorted spinel structure on the basis of density functional theory as well as tight-binding theory. The four examples we provide in this Letter are BiZnSiO 4 , BiCaSiO 4 , BiAlInO 4 , and BiMgSiO 4 . A necessary characteristic of these structures is that they contain a Bi lattice which forms a hierarchy of chainlike substructures, with consequences for both fundamental understanding and materials design.