BCS Superconductivity

Cooper pairs · energy gap · phonon-mediated pairing

Δ = 1.5 meV
T/T_c = 0.30
λ = 0.30
Physics: BCS gap equation: 1 = λ ∫ tanh(E_k/2k_BT) / 2E_k dε where E_k = √(ξ_k² + Δ²); at T=0, gap 2Δ(0) = 3.52 k_B T_c (universal BCS ratio). T_c ≈ 1.13 ℏω_D exp(−1/λ) where ω_D is Debye frequency. Cooper pairs: phonon-mediated attraction overcomes Coulomb repulsion for electrons near the Fermi surface; bound state below E_F. Josephson effect: supercurrent through thin insulator I = I_c sin(φ), φ = phase difference. Record T_c = 138 K for HgBaCaCuO (1993); room-temperature superconductivity observed in H₃S at 203 K (250 GPa, 2015).