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), Journal Name: Annals of Physics (New York) Journal Issue: 6 Vol. 326; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BOSON EXPANSION
ELECTRODYNAMICS
ELECTROMAGNETISM
ENERGY-LEVEL TRANSITIONS
EXCITATION
FERMIONS
FIELD THEORIES
GAUGE INVARIANCE
HALL EFFECT
INVARIANCE PRINCIPLES
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PARTICLE PROPERTIES
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THREE-DIMENSIONAL CALCULATIONS
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