Topological BF field theory description of topological insulators

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.12.011· OSTI ID:21579900

Cho, Gil Young ^[1]

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1. Department of Physics, University of California, Berkeley, CA 94720 (United States)

Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.

• OSTI ID: 21579900
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 6; Other Information: DOI: 10.1016/j.aop.2010.12.011; PII: S0003-4916(10)00225-3; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON EXPANSION
ELECTRODYNAMICS
ELECTROMAGNETISM
EXCITATION
FERMIONS
FIELD THEORIES
GAUGE INVARIANCE
HALL EFFECT
MATTER
SPIN
STATISTICS
SURFACES
SYMMETRY
SYMMETRY BREAKING
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGY
TWO-DIMENSIONAL CALCULATIONS
ANGULAR MOMENTUM
ENERGY-LEVEL TRANSITIONS
INVARIANCE PRINCIPLES
MAGNETISM
MATHEMATICS
PARTICLE PROPERTIES