= Superconducting energy gap
{title2=$\Delta,2\Delta$}
In this fully gapped isotropic <BCS quasiparticle spectrum>, $\Delta$ is the minimum single-<quasiparticle> excitation <energy>. The interval between $-\Delta$ and $+\Delta$ has width $2\Delta$. A process that creates two <quasiparticles> from the <BCS ground state> has an energetic threshold $2\Delta$, subject also to its transition-selection rules.<Microscopic Quantum Interference Effects in the Theory of Superconductivity by Leon Neil Cooper>[1972 lecture, excitation spectrum and correlated background, pp.78–80]{ref}
For example, two independently created excitations with $\xi_1=\xi_2=0$ cost $E_1+E_2=2\Delta$. With the chosen cutoff example this is $1.46574\ \mathrm{meV}$, while adding one excitation costs at least $0.732871\ \mathrm{meV}$. This factor of two matters when comparing <photon> absorption with the <Giaever superconducting tunnelling experiment>. <Quantum tunnelling> from a normal metal can add one excitation to a sample exhibiting <superconductivity>; with two gapped electrodes, their excitation costs add. A minimum excitation cost is an energetic condition; the measured onset can additionally depend on <temperature> and on the available transitions.
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