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Energy Gap

The energy difference between the superconducting and normal states, preventing the scattering of electrons and maintaining zero resistance.

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The statement of the theorem

Define the superconducting energy gap

\Delta

using the BCS gap equation, which relates the gap magnitude to the coupling constant

V

and the density of states

N(0)

at the Fermi level:\n

\Delta = \frac{1}{2} \frac{N(0)V}{N(0)} \int_{0}^{2\omega_D} \frac{d\epsilon}{\epsilon} \tanh\left(\frac{\epsilon}{2 k_B T}\right)

\nAlternatively, the gap

\Delta(T)

is the minimum energy required to break a Cooper pair, measured relative to the normal state energy.