Superconductivity 2D — BCS Cooper Pairs, Meissner Effect & R(T)

Cooper pairs in the crystal lattice

Resistance vs Temperature R(T)

Temperature: 2.0 K Magnetic field H: 0 Oe

T = 2.0 K

Tc = 4.2 K

State: SUPERCONDUCTING

R = 0.000 Ω

BCS gap: —

BCS Theory (1957 Nobel Prize)

Below T_c, electrons form Cooper pairs via phonon-mediated attraction and condense into a state that flows without scattering — resistance drops to exactly zero. The Meissner effect expels magnetic flux via surface screening currents. Type II materials (Nb, YBCO) let flux penetrate as quantized Abrikosov vortices between H_c1 and H_c2. BCS gap: 2Δ ≈ 3.52 k_B T_c.