Effective field theories for topological insulators by functional bosonization

Atma Chan, Taylor L. Hughes, Shinsei Ryu, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


Effective field theories that describe the dynamics of a conserved U(1) current in terms of "hydrodynamic" degrees of freedom of topological phases in condensed matter are discussed in general dimension D=d+1 using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII), and in the "primary series" of topological insulators, in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ (when D is even) terms. For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative "fractional" topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.

Original languageEnglish (US)
Article number085132
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number8
StatePublished - Feb 25 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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