Topological BF field theory description of topological insulators
Abstract
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The nongaugeinvariance 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 symmetrybreaking phases of matter are described by LandauGinzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the twodimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of ChernSimons 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 threedimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when timereversalsymmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when timereversal symmetry is broken andmore »
 Authors:

 Department of Physics, University of California, Berkeley, CA 94720 (United States)
 Publication Date:
 OSTI Identifier:
 21579900
 Resource Type:
 Journal Article
 Journal Name:
 Annals of Physics (New York)
 Additional Journal Information:
 Journal Volume: 326; Journal Issue: 6; Other Information: DOI: 10.1016/j.aop.2010.12.011; PII: S00034916(10)002253; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 00034916
 Country of Publication:
 United States
 Language:
 English
 Subject:
 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; THREEDIMENSIONAL CALCULATIONS; TOPOLOGY; TWODIMENSIONAL CALCULATIONS; ANGULAR MOMENTUM; ENERGYLEVEL TRANSITIONS; INVARIANCE PRINCIPLES; MAGNETISM; MATHEMATICS; PARTICLE PROPERTIES
Citation Formats
Cho, Gil Young, Moore, Joel E., Email: jemoore@berkeley.edu, and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720. Topological BF field theory description of topological insulators. United States: N. p., 2011.
Web. doi:10.1016/j.aop.2010.12.011.
Cho, Gil Young, Moore, Joel E., Email: jemoore@berkeley.edu, & Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720. Topological BF field theory description of topological insulators. United States. https://doi.org/10.1016/j.aop.2010.12.011
Cho, Gil Young, Moore, Joel E., Email: jemoore@berkeley.edu, and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720. Wed .
"Topological BF field theory description of topological insulators". United States. https://doi.org/10.1016/j.aop.2010.12.011.
@article{osti_21579900,
title = {Topological BF field theory description of topological insulators},
author = {Cho, Gil Young and Moore, Joel E., Email: jemoore@berkeley.edu and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720},
abstractNote = {Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The nongaugeinvariance 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 symmetrybreaking phases of matter are described by LandauGinzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the twodimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of ChernSimons 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 threedimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when timereversalsymmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when timereversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D ChernSimons 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 pointlike and linelike objects.},
doi = {10.1016/j.aop.2010.12.011},
url = {https://www.osti.gov/biblio/21579900},
journal = {Annals of Physics (New York)},
issn = {00034916},
number = 6,
volume = 326,
place = {United States},
year = {2011},
month = {6}
}