From Cooper pairs to tightly bound bosons: T_c dome and pair size evolution
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T_c / E_F
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ξ_pair / (1/k_F)
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Δ / E_F
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Regime
The BCS-BEC crossover (Eagles 1969, Leggett 1980, Nozières-Schmitt-Rink 1985): tuning 1/(k_F a) from −∞ (BCS: Cooper pairs, Δ≪E_F) through unitarity (1/k_F a=0, strongly correlated) to +∞ (BEC: tightly bound molecules). T_c/E_F forms a dome: suppressed in both limits, maximal near unitarity. Pair size ξ = ℏv_F/πΔ (BCS) → a_B/√2 (BEC). High-T_c cuprates sit on the BCS-BEC crossover, explaining the pseudogap regime above T_c.