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In many articles and web pages I found people claiming that the maximum critical temperature for superconductivity in the BCS framework is about 40K.

Sometime, more accurate writers report that the above temperature is the maximum critical temperature achievable with electron-phonon coupling.

In both cases I never sow a reliable proof of these statements, so I'm asking if they are correct and where I can find a reference (a paper or simply few physical considerations) leading to this result.

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It was quite strange to find this question I asked 5 years now that 200 K phonon mediated superconductivity is here! – Pie86 Apr 15 at 16:08
up vote 6 down vote accepted

The thermal energy required to break the Cooper pairs determines the value of Tc in BCS superconductors. In the work of McMillan, (Physical Review 167 (2), 1968 p 331-344), he shows that with considerations to phonon excitations in materials, the limitation of phonon vibrational energies is the limiting factor in BCS transition temperatures. In his work, McMillan estimated the upper Tc for electron-phonon superconductors is 28K.

The superconductivity in MgB2, with a Tc of ~40K is a form of BCS electron phonon coupling, but is isolated to only a few phonon modes, which enhances the effect of the coupling.

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