| We consider the fractional quantum Hall (FQH) bi-layer system at total filling fraction 1/2 in the small tunneling regime. The system is two-component, and described by the first-quantized 331 Halperin state for two distinguishable species of electrons. This FQH state emerges by a two-part-process where the Laughlin states are formed in each layer and the fermions between layers form pairs. The multiple zeros in the Halperin state, as in the Laughlin state, ensure that the amplitude of the states for the states together to be close is vanishingly small (i.e. there is electron inhibition in a layer from approaching each other). We find that as (d/lB), where d characterizes the quasi-2D tunneling barrier thickness for the system under consideration and lB is the magnetic length, is allowed to decrease from (d/lB) > 1 to (d/lB) ~ 0.2 at a given (moderate) tunneling strength (η), the system undergoes a first order transition from a compressible state with weak electron correlations (Haldane pseudo-potentials) to an incompressible state with strong electron correlations. We also find that as η is increased, for (d/lB) ~ 0.5, the electrons find it energetically favorable to be in the superposition of two layers and the system, consequently, loses its two-component character. This system is now described by Moore-Read Pfaffian. The Pfaffian is also the candidate wave function to describe the half filling of the second Landau level(LL). In the second-quantization formalism, we show that the attractive nature of the electron correlations in this LL facilitates the p-wave pairing between the electrons. |
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