The amplification of the superconducting Tc by combined effect of tuning the Fermi level and the tensile micro-strain in Al1-x Mgx B2

The increase of T(c) with x in Al(1-x)Mg(x)B(2) is controlled by the Fermi level tuning at a shape resonance ( i.e., the 2D-3D cross-over, at x = 0.66, of the topology of the Fermi surface of sigma holes in the superlattice of boron mono-layers intercalated by Al(1-x)Mg(x) ions) and by the tensile "micro-strain" in the boron sub-lattice (due to the lattice misfit between the boron and the intercalated layers). The softening of the E(2g) phonon frequency with increasing boron tensile micro-strain epsilon in the range 3% < epsilon < 6% shows the increasing electron-lattice interaction. The linear scaling, for 0.66 < x < 1, of T(c) vs. the Fermi temperature T(F) of the sigma holes shows a constant coupling strength with k(F)xi(o) = 90(where k(F) is the Fermi wave vector and xi(o) is the Pippard coherence length) that points toward a vibronic pairing mechanism.