Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries notably multiferroics and, remarkably, of “topological insulators” in which… (More)

Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different… (More)

We introduce exotic gapless states—‘composite Dirac liquids’—that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit… (More)

We consider gapped Z2 spin liquids, where spinon quasiparticles may carry fractional quantum numbers of space-group symmetry. In particular, spinons can carry fractional crystal momentum. We show… (More)

We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature… (More)

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling theta, a fact we derive for the single-particle case using a recent theory of… (More)

Ling Wang,1,2 Andrew Essin,1,2 Michael Hermele,3 and Olexei Motrunich2 1Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA 2Department… (More)

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling θ, a fact we derive for the single-particle case using a recent theory of… (More)

We use the method of bulk-boundary correspondence of topological invariants to show that disordered topological insulators have at least one delocalized state at their boundary at zero energy. Those… (More)