Pairing in half-filled Landau level

TL;DR

This paper reexamines pairing mechanisms in half-filled Landau levels using full frequency-dependent interactions, revealing a continuous transition to chiral pairing states and highlighting differences from previous low-frequency approximations.

Contribution

It introduces a full frequency-dependent analysis of composite fermion pairing, showing continuous transitions and differences in angular momentum channels compared to prior models.

Findings

Continuous transition from Halperin-Lee-Read to chiral pairing state.

High frequency interactions can compensate for repulsive low frequency interactions.

Phase diagrams differ notably for angular momentum channels, especially for .

Abstract

Pairing of composite fermions in half-filled Landau level state is reexamined by solving the BCS gap equation with full frequency dependent current-current interactions. Our results show that there can be a \emph{continuous} transition from the Halperin-Lee-Read state to a chiral odd angular momentum Cooper pair state for short-range contact interaction. This is at odds with the previously established conclusion of first order pairing transition, in which the low frequency effective interaction was assumed for the entire frequency range. We find that even if the low frequency effective interaction is repulsive, it is compensated by the high frequency regime, which is attractive. We construct the phase diagrams and show that $\ell=1$ angular momentum channel is quite different from higher angular momenta $\ell\ge 3$. Remarkably, the full frequency dependent analysis applied to the bilayer Hall system with a total filling fraction $\nu=\frac{1}{2}+\frac{1}{2}$ is quantitatively changed from the previously established results but not qualitatively.