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A Superconductor Made by a Metal Heterostructure at the Atomic Limit Tuned at the "Shape Resonance": MgB2

We have studied the variation of Tc with charge density and lattice parameters in Mg1-xAlxB2 superconducting samples at low Al doping x<8%. We show that high Tc occurs where the chemical potential is tuned at a "superconducting shape resonance" near the energy Ec of the quantum critical point (QCP) for the dimensional transition from 2D to 3D electronic structure in a particular subband of the natural superlattice of metallic atomic boron layers. At the "shape resonance" the electrons pairs see a 2D Fermi surface at EF-w0 and a 3D Fermi surface at EF+wo, where wo is the energy cut off of the pairing interaction. The resonant amplification occurs in a narrow energy range where EF-Ec is in the range of 2wo.