Given a superconductor's transition temperature Tc, BCS weak-coupling theory predicts the zero-temperature gap and a handful of derived energy scales universally. Provide the total density of states at the Fermi level N(0) to also obtain the Sommerfeld coefficient, specific-heat jump, condensation-energy density, and thermodynamic critical field.
Let R ≡ 2Δ(0)/(kB Tc) be the coupling-strength ratio (BCS weak-coupling: R = 3.528).
Universal predictions (from Tc and R only):
Δ(0) = (R/2) kB Tc; pair-breaking gap 2Δ(0) = R kB Tc.νpb = 2Δ(0)/h.λpb = h c / 2Δ(0).Tgap = 2Δ(0)/kB = R Tc.ΔC / (γ Tc) = 1.43.Δ(T)/Δ(0) ≈ tanh[1.74 · √((Tc−T)/T)] for T < Tc.With N(0) provided:
γV = (π²/3) kB² N(0).ΔC(Tc) = 1.43 · γV Tc.Ucond = (1/2) N(0) Δ(0)².Bc(0) = √(2μ0 Ucond) = Δ(0) · √(μ0 N(0)).Constants (CODATA): h = 6.62607015×10−34 J·s, c = 2.99792458×108 m/s, kB = 1.380649×10−23 J/K, qe = 1.602176634×10−19 C, μ0 = 1.25663706212×10−6 N/A².