Composite Fermions with Spin at $\nu =1/2$

TL;DR

This paper explores the behavior of composite fermions with spin at filling factor 1/2, revealing an attractive interaction in the spin-singlet channel that may lead to a paired ground state, relevant for understanding fractional quantum Hall phenomena.

Contribution

It introduces a detailed analysis of spin effects in composite fermions at ν=1/2, highlighting the potential for a paired ground state due to effective interactions.

Findings

Effective attraction in the spin-singlet channel

Possible formation of Cooper pairs of composite fermions

Explanation of spin polarization measurements in fractional quantum Hall systems

Abstract

The model of Composite Fermions for describing interacting electrons in two dimensions in the presence of a magnetic field is described. In this model, charged Fermions are combined with an even number of magnetic flux quanta in such a way that the external magnetic field is compensated on the average for half filling of Landau levels and the interaction is incorporated into an effective mass of the new composite particles. The fluctuations of the Chern-Simons gauge field, which describes formally the flux attachment, induce new interactions between the Composite Fermions. The effective interaction is investigated with particular emphasis on the role of the electron spin at filling factor $\nu=1/2$. For a system with equal numbers of spin-up and spin-down electrons it is found that the dominant effective interaction is attractive in the spin-singlet channel. This can induce a ground state consisting of Cooper pairs of Composite Fermions that is separated from the excited states by a gap. The results are used to understand recent spin polarization measurements done in the region of the Fractional Quantum Hall Effect at different constant filling factors.