Feshbach shape resonance in multiband superconductivity in heterostructures

We report experimental data showing the Feshbach shape resonance in the electron doped MgB2 where the chemical potential is tuned by Al, Sc, and C substitutions. The scaling of the critical temperature T-c as a function of the Lifshitz parameter z = E-Gamma-E-F where E-F is the chemical potential and Er is the energy of the Gamma critical point where the a Fermi surface changes from the 3D to a 2D topology, is reported. The resonant amplification of T,(z) driven by the interband pairing is assigned to a Feshbach shape resonance characterized by quantum superposition of pairs in states corresponding to different spatial location and different parity. It is centered at z = 0 where the chemical potential is tuned to a Van Hove-Lifshits feature for the change of Fermi surface dimensionality in the electronic energy spectrum in one of the subbands. In this heterostructure at atomic limit the multiband superconductivity is in the clean limit because the disparity and negligible overlap between electron wavefunctions in different subbands suppresses the single electron interband impurity scattering rate. The emerging scenario from these experimental data suggests that the Feshbach shape resonance could be the mechanism for high T, in particular nanostructured architectures.