Composite fermion pairing theory in single-layer systems

We study the pairing state of composite fermions (CF's) at even denominator Landau level fillings. We introduce the composite fermion operators by the Rajaraman-Sondhi nonunitary transformation. The resulting Hamiltonian has a non-Hermitian term. We show that this non-Hermitian term has the effect o f destabilizing composite fermions. However, composite Fermions are stabili zed when the short-range Coulomb interaction is strong enough. Projecting i nto the Hilbert space where composite fermions are stabilized, we derive th e effective Hamiltonian for CF's. Based on this Hamiltonian we discuss the condition for pairing of composite fermions within mean-field theory. We sh ow that the pairing condition is satisfied at nu = 5/2 for GaAs/AlGaAs hete rojunctions because of the screening effect of the long-range Coulomb inter action induced by the filled Landau levels. We also consider the condition for the pairing state at nu = 3/2 and nu = 1/2. The absence of the pairing state at half filled high Landau levels is understood as the breakdown of c omposite fermions because of the reduction of the short-range Coulomb inter action. The instability of the nu = 5/2 state against an in-plane magnetic field is also understood as the breakdown of composite fermions. Comparison of the ground state energy reveals the polarization of spins.