I will describe an exotic, two-dimensional, gapless state of matter, the `composite Dirac liquid,' comprised of electrically neutral fermions with a Dirac spectrum coupled to gapped charges. This state can, in principle, appear at the surface of a three-dimensional electronic topological insulator, and displays the thermal response properties of the usual surface state but is electromagnetically inert. Cooper pairing of the neutral fermions---which crucially does not violate charge conservation---yields symmetric, non-Abelian, topologically ordered surface phases captured in several recent works. Other (Abelian) topological orders emerge upon instead gapping the neutral Dirac cone with magnetism. On a technical level, I will describe the quasi-1D deformation of the original electronic Dirac cone that facilitates an analytic treatment of the strongly interacting surface and which generalizes naturally to a variety of symmetry-protected phases.
Work with David Mross and Jason Alicea