BCS Superconductor Energy Gap Calculator

Superconductivity & condensed matter physics: Calculate Bardeen-Cooper-Schrieffer (BCS) energy gap ($\Delta(T)$), thermodynamic critical magnetic field ($H_c(T)$), condensation energy, and penetration depth.

Superconducting Material Properties

Material Preset:

Critical Temperature $T_c$ (K):

Operating Temperature $T$ (K):

Zero-Temp Field $B_c(0)$ (mT):

Zero-Temp Penetration $\lambda_0$ (nm):

BCS Coherence Length $\xi_0$ (nm):

Superconducting State Performance

Energy Gap $\Delta(T)$

meV (Cooper binding)

Zero-Temp Gap $\Delta(0)$

meV ($1.764 \, k_B T_c$)

Critical Field $B_c(T)$

mT (thermodynamic)

London Penetration $\lambda_L(T)$

nm (screening depth)

Ginzburg-Landau $\kappa$

Type I vs Type II boundary

Condensation Energy $U_0$

$\text{kJ}/\text{m}^3$ ($B_c^2 / 2\mu_0$)

BCS Energy Gap & Critical Field vs Temperature

At $T = T_c$, both the energy gap and critical field collapse to zero via second-order phase transition.

Microscopic BCS Theory Formulation

The 1957 Bardeen-Cooper-Schrieffer (BCS) microscopic theory explains superconductivity through electron-phonon interactions forming Cooper pairs of opposite spin and momentum:

          $$\Delta(0) = 1.764 \, k_B T_c$$
          $$\Delta(T) \approx \Delta(0) \tanh\left( 1.74 \sqrt{\frac{T_c}{T} - 1} \right) \quad (T < T_c)$$
          $$B_c(T) = B_c(0) \left[ 1 - \left(\frac{T}{T_c}\right)^2 \right]$$
        

The Ginzburg-Landau parameter $\kappa = \lambda_L / \xi_0$ distinguishes Type I ($\kappa < 1/\sqrt{2} \approx 0.707$, complete Meissner expulsion) from Type II ($\kappa > 0.707$, Abrikosov vortex state with mixed phase between $B_{c1}$ and $B_{c2}$).

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BCS Superconductor Energy Gap Calculator

Superconducting Material Properties

Superconducting State Performance

BCS Energy Gap & Critical Field vs Temperature

Microscopic BCS Theory Formulation

Frequently Asked Questions