Maximum 2Δ0/kBTc for electron-phonon superconductors

J. P. Carbotte; F. Marsiglio; B. Mitrović

doi:10.1103/PhysRevB.33.6135

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Maximum 2Δ0/kBTc for electron-phonon superconductors

J. P. Carbotte, F. Marsiglio, B. Mitrović

DOI 10.1103/PhysRevB.33.6135 · Physical Review B

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Abstract

For an electron-phonon superconductor the question of a possible maximum value for the size of the ratio 2Δ0/kBTc is addressed. Here Δ0 is the gap edge and Tc the critical temperature. We were able to obtain well-converged solutions of the Eliashberg equations for a δ-function electron-phonon spectral density centered at ΩE with ΩE as low as 0.75 meV, in which case 2Δ0/kBTc is still rising and equal to ∼9. In the limit ΩE→0, we can prove analytically that both Δ0 and Tc scale like (ΩE)1/2 so that their ratio remains finite. A rough estimate gives a value of about 7 for the ratio in this limit. In the course of the discussion a new upper bound on Δ0 is established and tested.