Effects of $p$-wave Interactions on Borromean Efimov Trimers in Heavy-Light Fermi Systems

We investigate the effects of $p$-wave interactions on Efimov trimers in systems comprising two identical heavy fermions and a light particle, with mass ratios larger than $13.6$. Our focus lies on the borromean regime where the ground-state trimer exists in the absence of dimers. Using pair-wise Lennard-Jones potentials and concentrating on the $L^{\pi} = 1^{-}$ symmetry, we explore the critical value of the interspecies $s$-wave scattering length $a_{c}$ at which the borromean state appears in several two-component particle systems. Our exploration encompasses the universal properties of $a_{c}$ and the influence of $p$-wave fermion-fermion interactions on its value. We find that, in the absence of $p$-wave fermion-fermion interactions, $a_{c}$ is determined universally by the van der Waals radius and mass ratio. However, the introduction of $p$-wave fermion-fermion interactions unveiled a departure from this universality. Our calculations show that the critical interspecies scattering length $a_{c}$ now depends on the details of the fermion-fermion $p$-wave interaction. And, the presence of $p$-wave fermion-fermion interactions favors the formation of the borromean state. Additionally, our investigation reveals that Efimov effect in the $1^{-}$ symmetry persist even when the fermion-fermion interaction reaches the $p$-wave unitary limit.