Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect
PHYSICAL REVIEW X 3, 011016 (2013) Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect Ashvin Vishwanath Department of Physics, University of California, Berkeley, California 94720, USA Materials Science Division, Lawrence Berkeley National Laboratories, Berkeley, California 94720, USA T. Senthil Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 4 October 2012; revised manuscript received 31 December 2012; published 28 February 2013) We discuss physical properties of ‘‘integer’’ topological phases of bosons in D ¼ 3 þ 1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order; they are bosonic analogs of free- fermion topological insulators and superconductors. While a formal cohomology-based classification of such states was recently discovered, their physical properties remain mysterious. Here, we develop a field-theoretic description of several of these states and show that they possess unusual surface states, which, if gapped, must either break the underlying symmetry or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two-dimensional theory. While these phases are the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, to a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by a quantized magnetoelectric response , which, somewhat surprisingly, is an odd multiple of 2.Two different surface theories are shown to capture these phenomena: The first is a nonlinear sigma model with a topological term.
[Show full text]