Non-symmorphic topological metals and insulators

Barry Bradlyn (Princeton)

Spatial symmetries allow for the stabilization of topological phases more exotic than those that can be found with time-reversal symmetry alone. Unlike in the continuum, in non-symmorphic crystals rotation and reflection symmetries are intimately bound to fractional lattice translations. I will first show how these non-symmorphic symmetries can stabilize gapless free-fermion excitations unlike any found in high-energy physics. This includes the first natural generalization of the Weyl fermion, described by a k⋅S Hamiltonian. For each new class of fermion that arises, I will analyze its topological properties and comment on possible experimental realizations. Next, I will show how non-symmorphic symmetries stabilize exotic states on the surface of topological crystalline insulators. For crystals invariant under one and two glide symmetries, I will catalog all possible bulk topological phases by considering symmetry constraints on the non-Abelian Berry matrix. In particular, I will show that these crystals allow for a new topological phase whose surface spectrum consists of only a single four-fold degenerate Dirac fermion. To conclude, I will show how these results can be understood via a new approach to band theory which puts symmetry and topology at center stage.