Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity.

Area of Science:

• Condensed matter physics
• Superconductivity
• Quantum gases

Background:

• Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) represent distinct regimes of fermion pairing.
• A crossover between BCS and BEC is well-established in cold atomic Fermi gases.
• The existence of this crossover in high-temperature superconducting cuprates remains an open question.

Purpose of the Study:

• To investigate the presence of a BCS-BEC crossover in high-temperature superconducting cuprates.
• To identify universal indicators of this crossover in cuprate systems.
• To correlate findings with observations in cold atomic Fermi gases.

Main Methods:

• Analysis of the universal magic gap ratio (2Δ/k_{B}T_{c}≈6.5) as an indicator of optimal condensate robustness.
• Measurement of the condensate fraction (N_{0}) and the jump in the fermionic specific heat coefficient (δγ(T_{c})).
• Correlation of the gap ratio with the antinodal spectroscopic gap and normal state specific heat behavior.

Main Results:

• Unambiguous evidence for a BCS-BEC crossover in cuprates identified via the magic gap ratio.
• Strong peaks in condensate fraction (N_{0}) and specific heat jump (δγ(T_{c})) at the magic gap ratio.
• The antinodal spectroscopic gap corresponds to the pairing gap, and its peak coincides with a normal state pseudogap.

Conclusions:

• The BCS-BEC crossover is a universal phenomenon present in cuprate superconductors.
• The magic gap ratio serves as a robust indicator for optimal pairing and condensate formation.
• Pairing fluctuations above T_{c} contribute to a pseudogap in the normal state of cuprates.