Semisuper Efimov effect induced by resonant pair exchange in mixed dimensions

We introduce a new member to the class of semisuper Efimov effects, where an infinite number of bound states emerge with their binding energies obeying the universal scaling law $E_n\sim e^{-2(\pi n\mathrm{/}\gamma {)}^2}$ for sufficiently high excitation $n\in \mathbb{N}$. Our system consists of a pair of two-component fermions in three dimensions at infinite scattering length, which furthermore interact with a boson confined in two dimensions so as to form a three-body bound state at zero energy. When another boson is added, the exchange of the resonant pair of fermions between two bosons leads to the semisuper Efimov effect of four such particles with the scaling exponent $\gamma$ determined by the mass ratio of bosons to fermions. If bosons exist in three dimensions, an infinite number of bound states do not emerge, but some of them may survive for a large mass ratio, making our findings potentially relevant to two-neutron halo nuclei as well as ultracold atoms.