Super Efimov Effect of Resonantly Interacting Fermions in Two Dimensions

We study a system of spinless fermions in two dimensions with a short-range interaction fine-tuned to a p-wave resonance. We show that three such fermions form an infinite tower of bound states of orbital angular momentum l = +/- 1 and their binding energies obey a universal doubly exponential scaling E-3((n)) proportional to exp(-2e(3 pi n/4+theta)) at large n. This super Efimov effect'' is found by a renormalization group analysis and confirmed by solving the bound state problem. We also provide an indication that there are l = +/- 2 four-body resonances associated with every three-body bound state at E-4((n)) proportional to exp(-2e(3 pi n/4+theta-0.188)). These universal few-body states may be observed in ultracold atom experiments and should be taken into account in future many-body studies of the system.