Sh. Simon, TOWARDS A FERMI-LIQUID THEORY OF THE NU=1 2 STATE - MAGNETIZED COMPOSITE FERMIONS/, Journal of physics. Condensed matter, 8(48), 1996, pp. 10127-10148
The fermionic Chern-Simons approach has had remarkable success in the
description of quantum Hall states at even-denominator filling fractio
ns v = 1/2m. In this paper we review a number of recent works concerne
d with modelling this state as a Landau-Silin Fermi liquid. We win the
n focus on one particular problem with constructing such a Landau theo
ry that becomes apparent in the limit of high magnetic field, or equiv
alently the limit of small electron band mass m(b). In this limit, the
static response of electrons to a spatially varying magnetic field is
largely determined by kinetic energy considerations. We then remedy t
his problem by attaching an orbital magnetization to each fermion to s
eparate the current into magnetization and transport contributions, as
sociated with the cyclotron and guiding centre motions respectively. T
his leads us to a description of the v = 1/2m state as a Fermi liquid
of magnetized composite fermions which correctly predicts the m(b)-dep
endence of the static and dynamic response in the limit m(b) --> 0. As
an aside, we derive a sum rule for the Fermi liquid coefficients far
the Chern-Simons Fermi liquid. This paper is intended to be readable b
y people who may not be completely familiar with this field.