Abstract
We reconsider the composite fermion theory of general Jain's sequences with filling factor $\nu=N/(4N\pm1)$. We show that Goldman and Fradkin's proposal of a Dirac composite fermion leads to a violation of the Haldane bound on the coefficient of the static structure factor. To resolve this apparent contradiction, we add to the effective theory a gapped chiral mode (or modes) which already exists in the Fermi liquid state at $\nu=1/4$. We interpret the additional mode as an internal degree of freedom of the composite fermion, related to area-preserving deformations of the elementary droplet built up from electrons and correlation holes. In addition to providing a suitable static structure factor, our model also gives the expected Wen-Zee shift and a Hall conductivity that manifests Galilean invariance. We show that the charge density in the model satisfies the long-wavelength version of the Girvin-MacDonald-Platzman algebra.
Highlights
Since the discovery of the fractional quantum Hall effect (FQHE) in 1982 [1,2], many theoretical models have been invented to explain different aspects of this fascinating phenomenon
One breakthrough idea was proposed by Jain [3], who suggested that the low-energy degree of freedom of the FQHE is the composite fermion (CF), which can be thought of as an electron moving together with an even number of magnetic flux quanta, a picture inspired by previous ideas [4,5,6]
This paper aims to construct an effective theory that adequately describes the physics of the ν = N/(4N ± 1) Jain sequences in the lowest
Summary
Since the discovery of the fractional quantum Hall effect (FQHE) in 1982 [1,2], many theoretical models have been invented to explain different aspects of this fascinating phenomenon. The Dirac composite fermion theory [11] has been proposed as an effective field theory for FQH states near half-filling, which explicitly incorporates PH symmetry by assigning a Berry phase of π for the CF around the Fermi surface. Our model is a hybrid model that includes a Dirac composite fermion sector and an additional spin-2 mode with the effective action of the form of the bimetric theory In this model, in addition to the low-energy GMP mode at the energy scale of the effective cyclotron energy, which tends to zero as N → ∞, there is an extra high-energy mode with energy that remains finite in the limit N → ∞, and must already exist in the ν = 1/2n Fermi-liquid state. Some technical details of the calculations are left to the Appendixes
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