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Title: 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 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 andmore » 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.« less

Authors:
 [1]
  1. 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: S0003-4916(10)00225-3; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 0003-4916
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; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY; TWO-DIMENSIONAL CALCULATIONS; ANGULAR MOMENTUM; ENERGY-LEVEL TRANSITIONS; INVARIANCE PRINCIPLES; MAGNETISM; MATHEMATICS; PARTICLE PROPERTIES

Citation Formats

Cho, Gil Young, Moore, Joel E., E-mail: 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., E-mail: 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., E-mail: 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., E-mail: 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 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.},
doi = {10.1016/j.aop.2010.12.011},
url = {https://www.osti.gov/biblio/21579900}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 6,
volume = 326,
place = {United States},
year = {2011},
month = {6}
}