Effect of Gauge Fluctuations on Excitonic Instabilities of Composite Fermi Liquids

The effects of Chern-Simons gauge fluctuations on exciton condensation of Composite Fermions (CFs) in two-component CF liquids are studied within the Random Phase Approximation (RPA). Two cases are considered. Case (i): Two coupled CF liquids formed from half-filled (Chern number C=1) Landau levels. This system is unstable to interlayer CF pairing [1], and the resulting paired state may correspond to the observed ν=1/2+1/2 bilayer quantum Hall state at small layer spacing [2]. Case (ii): Coupled C=1 and C=-1 CF liquids, corresponding, possibly, to a state recently observed in tMoTe₂ in zero field [3]. For this case, gauge fluctuations suppress interlayer CF pairing, opening the door to CF exciton condensation [4]. Given the markedly different effects that gauge fluctuations have on CF pairing for these cases it is of interest to study their effect on CF exciton condensation. Here we follow [5], in which correlation energy as a function of CF exciton order parameter was calculated within the RPA for case (i) and shown to suppress CF exciton condensation, in order to study the effect of gauge fluctuations for case (ii) in a way which allows for directly comparing and contrasting the two cases.

[1] NEB, I.A. McDonald, and C. Nayak, PRL 77, 3009 (1996); H. Deng, L. Mendoza, and NEB, PRB 109, 085134 (2024)

[2] I. Sodemann, I. Kimchi, C. Wang and T. Senthil, PRB, 95, 085135 (2017)

[3] K. Kang et al., Nature 628, 522 (2024)

[4] Z.D. Shi, H. Goldman, Z. Dong, and T. Senthil, arXiv:2402.12436

[5] R. Cipri and NEB, PRB 89, 085109 (2014)