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BCS Gap, Self-Consistent

What you are seeing: the superconducting gap Δ(T)\Delta(T) from the BCS self-consistent gap equation, normalized to the zero-temperature gap. At T=TcT = T_c, Δ\Delta vanishes; the universal ratio 2Δ(0)/kBTc=3.5282\Delta(0)/k_B T_c = 3.528.

Figure 1. Δ(T)\Delta(T) from BCS gap equation; universal-shape curve.
N(0) V0.30
T / Tc0.30

WHAT TO TRY

  • Raise T toward T_c: the gap Delta(T) collapses to zero with the characteristic vertical-tangent BCS shape, and the glowing gap band on the Fermi surface narrows to nothing. Above T_c the metal is normal.
  • Increase the coupling N(0)V: the zero-temperature gap and T_c both grow, but their ratio 2 Delta(0)/k_B T_c stays pinned near the universal 3.53. That fixed ratio is the hallmark prediction of BCS theory.
  • Read the gap band on the Fermi surface: it is the energy a Cooper pair must pay to break, which is why a clean superconductor below the gap carries current with no dissipation.