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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 seedoi:10.1088/0953-8984/13/33/318 fatcat:uf775bx3mzduxcpijzm6tu542e