Superconductivity (SC) arises when electrons form Cooper pairs that move collectively without resistance. In the weak-coupling regime, this pairing is described by the Bardeen-Cooper-Schrieffer (BCS) theory, where electrons form weakly bound, overlapping Cooper pairs. In the opposite, strong-coupling limit, electrons form tightly bound bosonic pairs that undergo Bose–Einstein condensation (BEC). The smooth evolution between these two regimes—the BCS-BEC crossover—has been extensively studied in ultracold atomic gases [34,35,36]. Whether and how this crossover occurs in solids, particularly in strongly correlated electron systems, is now an active frontier in condensed matter physics. [37].

Organic superconductors, especially those of the κ-type, offer a promising platform for exploring this crossover. These materials have a quasi-two-dimensional anisotropic triangular lattice and host strong electron–electron interactions and geometrical frustration [38]. Among them, κ-(BEDT-TTF)₄Hg_2.89Br₈ (κ-HgBr) is a promising candidate to realize the BCS-BEC crossover [39], possessing a spin-liquid-like metallic state and superconductivity near the Mott insulating phase. Importantly, its electron correlation strength can be tuned via external pressure, offering a rare opportunity to explore strongly correlated superconductivity across different regimes.

In our recent work [40], we theoretically investigated the possibility of a BCS-BEC crossover in κ-HgBr and related compounds by studying an extended Hubbard model on an anisotropic triangular lattice, including intradimer degrees of freedom. Using a variational Monte Carlo method, we evaluated several physical observables relevant to superconductivity, such as the superconducting correlation function P_SC, coherence length ξ, superfluid weight D_s, and chemical potential μ, across a range of electron interaction strengths and doping levels.

Our key finding is that the BCS-BEC crossover emerges at a hole doping rate of δ = 0.06, where superconductivity remains robust even in the strongly correlated regime. Figure 3a illustrates the behavior of P_SC ~  < c⁺c⁺cc > as a function of the on-site Coulomb interaction U/t for different doping rates. For δ = 0, superconductivity is suppressed by a transition to a Mott insulating phase. For δ = 0.11, a charge-ordered stripe phase appears, again destroying superconductivity. Only for δ = 0.06, P_SC exhibit a dome-shaped profile: it first increases and then decreases with increasing U/t, a hallmark of the BCS-BEC crossover. The superconducting gap, however, increases monotonically with U/t, indicating that while local pair formation strengthens, long-range coherence weakens.

This inverse behavior between the gap amplitude and P_SC is a characteristic signature of the crossover. It reflects the transition from BCS-type long-range coherence to BEC-type local pairing. In addition, as shown in Fig. 3b, the coherence length k_Fξ becomes of order unity in this region, satisfying another important criterion for the crossover.

Further insight is gained by analyzing the superfluid weight D_s. While it decreases with increasing U/t, a deviation from its expected trend suggests a reduction in superfluid density n_s, consistent with the formation of tightly bound pairs that are less mobile. The chemical potential μ also shows nontrivial behavior: while it does not drop below zero as in dilute Fermi gases, it decreases beyond a certain U/t, signaling a decoupling of fermionic quasiparticles from the Fermi surface.

These findings point to a unique form of the BCS-BEC crossover in strongly correlated lattice systems. Unlike in ultracold gases, where the crossover is driven by tuning an attractive interaction, here it emerges from repulsive electron interactions mediated by spin exchange mechanisms. Moreover, the presence or absence of competing phases, such as Mott or stripe order, plays a crucial role. In κ-HgBr, geometrical frustration suppresses these competing states, allowing superconductivity to survive and enabling the crossover to be realized.

From an experimental perspective, our results suggest strategies to access the BCS-BEC crossover in organic materials. Tuning U/t via physical or chemical pressure, controlling the doping level, and enhancing geometrical frustration are all promising approaches. For example, the application of pressure increases the transfer integral t, effectively reducing U/t and potentially moving the system through the crossover regime. Chemical substitution in the anion layers can provide additional tuning knobs, and recent advances in electric-double-layer transistor techniques may even allow controlled doping in undoped systems [41].

Our study highlights how the interplay of strong correlations, frustration, and doping can give rise to unconventional superconducting states. The BCS-BEC crossover, long considered a theoretical curiosity in solid-state systems, may be within reach in organic materials like κ-HgBr. This opens the door to further exploration of exotic pairing mechanisms and could provide new insights into high-temperature superconductivity and quantum criticality. We hope that our work will motivate both theoretical and experimental efforts to deepen our understanding of this rich crossover phenomenon in complex electron systems.

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[Source: https://link.springer.com/article/10.1007/s43673-025-00165-7]