Possibility of BCS-BEC crossover in $\kappa$-type organic superconductors

The realization of BCS-BEC crossover in superconductors, which smoothly connects Bardeen-Cooper-Schrieffer (BCS) theory with Bose-Einstein Condensation (BEC) in fermion systems, is an intriguing recent topic in strongly correlated electron systems. The organic superconductor $\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$ ($\kappa$-HgBr) under pressure is one of the leading candidates, owing to its unique metallic spin-liquid nature and tunable electron correlation. We theoretically investigate the extended Hubbard model for $\kappa$-HgBr and discuss the possibility of the BCS-BEC crossover by systematically calculating superconducting correlation function, coherence length, superfluid weight, and chemical potential. Our findings show that the BCS-BEC crossover can be observed when competing phases, such as Mott insulators and charge and/or spin orders, are suppressed by appropriate hole doping. $\kappa$-HgBr is just the case because both the Mott insulating phase and magnetic orders are absent due to its nonstoichiometric Hg composition and geometrical frustration. We further propose that other $\kappa$-type organic superconductors could serve as potential candidates of the BCS-BEC crossover if their band fillings and degree of geometrical frustration are systematically tuned.