# What are virtual excitations in the context of superconductors?

In a superconductor I have read that the energy gap can be defined as the energy difference between the ground state and the virtual excitations of the system. Is this the energy required to form a cooper pair?

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## 1 Answer

In a superconductor (in BCS theory, at the very least), the ground state exists of a condensate of Cooper pairs (and regular unpaired electrons). The first excited state is the state where one of these Cooper pairs is broken up into two regular unpaired electrons. Hence, rather than the energy to make a pair, it is the energy needed to break up a the first Cooper pair.

In case you're studying superconductivity at a QFT level: This is precisely the content of the Bogoliubov transformation of the BCS Hamiltonian: rather than study the Hamiltonian in terms of the electron creation and annihilation operators $\hat a_k$ and $\hat a_k^\dagger$, one can define new fields $\alpha_k$ and $\alpha_k^\dagger$, where the creation operator $\alpha_k^\dagger$ exactly creates a broken up electron pair.

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This answer is correct enough as far as I understand BCS Theory :-) – user17581 Jan 17 '13 at 23:04