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Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators

Max A. Metlitski and Ashvin Vishwanath
Phys. Rev. B 93, 245151 – Published 27 June 2016
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Abstract

Particle-vortex duality is a powerful theoretical tool that has been used to study bosonic systems. Here, we propose an analogous duality for Dirac fermions in 2+1 dimensions. The physics of a single Dirac cone is proposed to be described by a dual theory, QED3, with again a single Dirac fermion but coupled to a gauge field. This duality is established by considering two alternate descriptions of the three-dimensional topological insulator (TI) surface. The first description is the usual Dirac fermion surface state. The dual description is accessed via an electric-magnetic duality of the bulk TI coupled to a gauge field, which maps it to a gauged chiral topological insulator. This alternate description ultimately leads to a new surface theory, QED3, which provides a simple description of otherwise intractable interacting electronic states. For example, an explicit derivation of the T-Pfaffian state, a proposed surface topological order of the TI, is obtained by simply pair condensing the dual fermions. The roles of time-reversal and particle-hole symmetries are exchanged by the duality, which connects some of our results to a recent conjecture by Son on particle-hole symmetric quantum Hall states.

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  • Received 15 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.245151

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

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Fermionic Vortices Find their Dual

Published 27 June 2016

Theoretical work reveals a surprising relationship between the physics of fermionic vortices and quantum electrodynamics.

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Authors & Affiliations

Max A. Metlitski1,2 and Ashvin Vishwanath3,4

  • 1Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
  • 2Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
  • 3Department of Physics, University of California, Berkeley, California 94720, USA
  • 4Materials Science Division, Lawrence Berkeley National Laboratories, Berkeley, California 94720, USA

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Issue

Vol. 93, Iss. 24 — 15 June 2016

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