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

By M. Metlitski, Ashvin Vishwanath. 2015

154 citations recorded by the source corpus.

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 a dual Dirac fermion coupled to a gauge field. This duality is established by considering two alternate descriptions of the 3d topological insulator (TI) surface. The first description is the usual Dirac cone surface state. The second description is accessed via an electric-magnetic duality of the bulk TI coupled to a gauge field, which maps it to a gauged topological superconductor. This alternate description ultimately leads to a new surface theory - dual QED3. The dual theory provides an explicit derivation of the T-Pfaffian state, a proposed surface topological order of the TI, which is simply the paired superfluid state of the dual fermions. The roles of time reversal and particle-hole symmetry are exchanged by the duality, which connects some of our results to a recent conjecture by Son on particle-hole symmetric quantum Hall states.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/ee00554ad9a37404c5e7ec384391e4afff0c1f3b

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In Atomic and Molecular Physics, and Optics

1. Chong Wang
2. Cenke Xu
3. T. Senthil
4. H. Nastase
5. Jeff Murugan
6. A. Nahum
7. M. Metlitski
8. E. Witten

Citations in the corpus

• Particle-vortex duality in topological insulators and superconductors (2016, background): “ understood as the boundarymode of a topological insulator, and the composite fermion of an effective low-energy theory for the half-filled Landau level of a Fermi liquid [13]. It was argued already in [14] that this conjecture should be derivable from a (fermionic) particle-vortex duality, but the ar”
• Deconfined quantum critical points: symmetries and dualities (2017, methodology): “The self-duality is obtained by applying the fermionic particle-vortex duality [30,31,38,40] to both flavors of fermions: ψ1 → χ2, ψ2 → χ1.”