Cooper Pairs, Local Pairs, and T_F-Scaled High-T_c Superconductivity

Abstract

The BCS theory of superconductivity predicts a critical temperature given by¹

$$ {\text{T}}_{\text{c}} \simeq 1.13\Theta _{\text{D}} {\text{e}}^{{\text{ - 1/}}\lambda } $$

((1))

, where Θ_D is the material Debye temperature (∼10² K) and λ = 2/g(E_F)V, with g(E_F) the density of states at the Fermi energy ${\text{E}}_{\text{F}} \equiv \hbar ^2 {\text{k}}_{\text{F}}^2 /2{\text{m}}$ and V the model electron-phonon coupling strength. Given that nature provides such small (< 1) values of λ (extracted, e.g., from resistivity measurements in the normal state) Eq. (1) can yield values of T_c no larger than 30 to 40 K. This is popularly known as the “phonon barrier”, which is substantially below the highest T_c value of 125 K reproducibly observed thus far in the new, high-T_c cuprate superconductors.

Support from European Research Office of the U.S. Army is gratefully acknowledged.