Topological obstructions to band insulating behavior in nonsymmorphic crystalline systems

TYPECondensed Matter Seminar
Speaker:Dan Arovas
Affiliation:UC San Diego
Location:Lidow Nathan Rosen (300)
Abstract:Band insulators appear in a crystalline system only when the filling—the number of electrons per unit cell and spin
projection—is an integer. At fractional filling, an insulating phase that preserves all symmetries is a Mott insulator; that is,
it is either gapless or, if gapped, exhibits fractionalized excitations and topological order. We raise the inverse question—at
an integer filling is a band insulator always possible? Here we show that lattice symmetries may forbid a band insulator even
at certain integer fillings, if the crystal is non-symmorphic—a property shared by most three-dimensional crystal structures.
In these cases, one may infer the existence of topological order if the ground state is gapped and fully symmetric. This is
demonstrated using a non-perturbative flux-threading argument, which has immediate applications to quantum spin systems
and bosonic insulators in addition to electronic band structures in the absence of spin–orbit interactions.