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 of destabilizing composite fermions. However, composite Fermions are stabilized when the short-range Coulomb interaction is strong enough. Projecting into the Hilbert space where composite fermions are stabilized, we derive the effective Hamiltonian for CF's. Based on this Hamiltonian we discuss the condition for pairing of composite fermions within mean-field theory. We show that the pairing condition is satisfied at nu = 5/2 for GaAs/AlGaAs heterojunctions because of the screening effect of the long-range Coulomb interaction 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 composite fermions because of the reduction of the short-range Coulomb interaction. 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.