Extension of Bilbro–McMillan charge density wave-superconductivity coexistence relation to quantum régimes: Application to superconducting domes around quantum critical points

•Study of quantum critical points.•Heuristic explanation of superconducting domes.•Interaction between superconductivity and charge density waves.

Quantum critical points (QCP) accompanied by superconductivity are ubiquitous in condensed matter physics. In general, the transition temperature T0T0 of an ordered state, e.g. antiferromagnetic, goes to zero under the influence of an external parameter, e.g. pressure. Superconductivity appears before the disappearance of the ordered state, but reaches its maximum TcTc when T0=0T0=0. Presently, the implications of the QCP׳s on superconductivity are a subject of debate. It is proposed here that both transition temperatures satisfy the relation T˜02+T˜c2=1, where the tilde indicates normalization to the maximum values. Inspired from the basic postulate of SO(N)SO(N) theories of superconductors, it is proposed as an extension from Bilbro–McMillan relation.