Is the Composite Fermion a Dirac Particle?

We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in the magnetic field at charge neutrality, as well as for the ν=12 quantum Hall ground state of nonrelativistic fermions in the limit of n...

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Bibliographic Details
Published in:Physical review. X 2015-09, Vol.5 (3), p.031027, Article 031027
Main Author: Son, Dam Thanh
Format: Article
Language:English
Subjects:
Angular momentum
Condensed matter physics
Conjugates
Electromagnetism
Elementary excitations
Fermi surfaces
Fermions
Field theory
Field theory (physics)
Ground state
Integers
Magnetic fields
Quantum Hall effect
Quantum mechanics
Quantum numbers
Quantum phenomena
Quantum theory
Symmetry
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Summary:We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in the magnetic field at charge neutrality, as well as for the ν=12 quantum Hall ground state of nonrelativistic fermions in the limit of negligible inter-Landau-level mixing. We argue that when particle-hole symmetry is exact, the composite fermion is a massless Dirac fermion, characterized by a Berry phase of π around the Fermi circle. We write down a tentative effective field theory of such a fermion and discuss the discrete symmetries, in particular, CP . The Dirac composite fermions interact through a gauge, but non-Chern-Simons, interaction. The particle-hole conjugate pair of Jain-sequence states at filling factors n/(2n+1) and (n+1)/(2n+1) , which in the conventional composite fermion picture corresponds to integer quantum Hall states with different filling factors, n and n+1 , is now mapped to the same half-integer filling factor n+12 of the Dirac composite fermion. The Pfaffian and anti-Pfaffian states are interpreted as d -wave Bardeen-Cooper-Schrieffer paired states of the Dirac fermion with orbital angular momentum of opposite signs, while s -wave pairing would give rise to a particle-hole symmetric non-Abelian gapped phase. When particle-hole symmetry is not exact, the Dirac fermion has a CP -breaking mass. The conventional fermionic Chern-Simons theory is shown to emerge in the nonrelativistic limit of the massive theory.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.5.031027