Composite Fermion Pairing in the ν=1/2+1/2 Bilayer at Large Layer Spacing

We study interlayer pairing of composite fermions in the ν=1/2+1/2 quantum Hall bilayer. In the large layer spacing limit, ignoring disorder and for perfectly balanced wells, the interlayer pairing interaction mediated by the Chern-Simons gauge fields in the two layers is singular with both attractive (out-of-phase) and repulsive (in-phase) components. If only the singular attractive interaction is included the pairing gap obtained by solving the Eliashberg equations is proportional to the inverse of the layer spacing squared [1]. Analyzing these equations in the so-called local approximation [2] we find when the less singular repulsive interactions are included the energy gap is strongly suppressed, but still falls off as inverse layer spacing squared, consistent with recent RG analysis [3]. The (in some cases analytic) local approximation solutions are then used as a starting point to iterate the full Eliashberg equations to assess the validity of the approximation in this limit.
[1] N. Bonesteel, I. McDonald, C. Nayak, PRL 77, 3009 (1996); Z. Wang, I. Mandal, S. B. Chung, and S. Chakravarty, Ann. Phys. 351, 727 – 738 (2014)
[2] H. Wang, S. Raghu, G. Torroba, PRB 95, 165137 (2017)
[3] I. Sodemann, I. Kimchi, C. Wang, and T. Senthil, PRB 95, 085135 (2017)