Abstract
We review the recently proposed Dirac composite fermion theory of the half-filled Landau level. This paper is based on a talk given at the Nambu Symposium at University of Chicago, March 11-13, 2016.
Highlights
The fractional quantum Hall effect (FQHE) was discovered in 1982 [1], only a couple of years following the discovery of the integer quantum Hall effect (IQHE)
The values of ν for which there is a gap are either integers, in which case we have an IQHE, or rational numbers, which correspond to the FQHE
We have a problem: We want to map the FQHE in the Jain sequences to the IQHE of the CFs, but is it possible to have an IQH state with half-integer filling factor? it is, if the composite fermion is a massless Dirac fermion
Summary
The fractional quantum Hall effect (FQHE) was discovered in 1982 [1], only a couple of years following the discovery of the integer quantum Hall effect (IQHE). The quantum Hall problem is attractive for theorists partly because of its very simple starting point: a Hamiltonian describing particles moving on a two-dimensional plane, in a constant magnetic field, and interacting with each other through a two-body potential, H=. The values of ν for which there is a gap are either integers, in which case we have an IQHE, or rational numbers, which correspond to the FQHE. When 0 < ν < 1, the lowest Landau level (LLL; n = 0) is partially filled, so the noninteracting Hamiltonian has an exponentially large (in the number of electrons) ground-state degeneracy. The miracle of the FQHE is that for certain rational values of ν, interactions between electrons lead to a gap. There are two energy scales in the fractional quantum Hall (FQH) problem.
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