Spin–orbit coupling controlling the superconducting dome of artificial superlattices of quantum wells

While it is known that a resonant amplification of [Formula: see text] in two-gap superconductors can be driven by using the Fano–Feshbach resonance tuning the chemical potential near a Lifshitz transition, little is known on tuning the [Formula: see text] resonance by cooperative interplay of the Rashba spin–orbit coupling (RSOC) joint with phonon mediated (e-ph) pairing at selected k-space spots. Here, we present first-principles quantum calculation of superconductivity in an artificial heterostructure of metallic quantum wells with 3 nm period where quantum size effects give two-gap superconductivity with RSOC controlled by the internal electric field at the interface between the nanoscale metallic layers intercalated by insulating spacer layers. The key results of this work show that fundamental quantum mechanics effects including RSCO at the nanoscale [Mazziotti et al., Phys. Rev. B, 103, 024523 (2021)] provide key tools in applied physics for quantitative material design of unconventional high temperature superconductors at ambient pressure. We discuss the superconducting domes where [Formula: see text] is a function of either the Lifshitz parameter ([Formula: see text]) measuring the distance from the topological Lifshitz transition for the appearing of a new small Fermi surface due to quantum size effects with finite spin–orbit coupling and the variable e-ph coupling [Formula: see text] in the appearing second Fermi surface linked with the energy softening of the cut off [Formula: see text].