Towards a Fermi Liquid Theory of the $ν$=1/2 State : Magnetized Composite Fermions

Abstract

The Fermionic Chern-Simons approach has had remarkable success in the description of quantum Hall states at even denominator filling fractions $ν=\frac{1}{2m}$. In this paper we review a number of recent works concerned with modeling this state as a Landau-Silin Fermi liquid. We will then focus on one particular problem with constructing such a Landau theory that becomes apparent in the limit of high magnetic field, or equivalently 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 this problem by attaching an orbital magnetization to each fermion to separate the current into magnetization and transport contributions, associated with the cyclotron and guiding center motions respectively. This leads us to a description of the $ν=\frac{1}{2m}$ state as a Fermi liquid of magnetized composite fermions which correctly predicts the $m_b$ dependence of the static and dynamic response in the limit $m_b \rightarrow 0$. As an aside, we derive a sum rule for the Fermi liquid coefficients for the Chern-Simons Fermi liquid. This paper is intended to be readable by people who may not be completely familiar with this field.