Symmetry-Protected Topological Phases of Quantum Matter

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators (TBIs) to interacting many-particle systems known as symmetry-protected topological (SPT) phases. As with the TBIs, these states have a bulk gap and no exotic excitations but have nontrivial surface states that are protected by symmetry. We describe the various possible phases and their properties in three-dimensional systems with realistic symmetries. We develop many key ideas for the theory of these states using simple examples. The emphasis is on physical rather than mathematical…

• NS
  National Science Foundation

  Award: DMR-1305741
• IP
  Institut Périmètre de physique théorique
• DO
  Division of Materials Research