Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-Tc Superconductivity

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2 Delta/k(B)T(c) approximate to 6.5 (where Delta is the pairing gap and T-c is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N-0 and the height of the jump delta gamma(T-c) in the coefficient gamma of the fermionic specific heat at T-c are strongly peaked. In the cuprates, delta gamma(T-c) is peaked at this gap ratio when Delta corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in delta gamma(T-c) also to coincide with a normal state maximum in gamma, which is indicative of a pairing fluctuation pseudogap above T-c.

Automated summary

This study provides clear evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio, reflecting the optimal robustness of paired fermion condensates.