The amplification of the superconducting T c by combined effect of tuning of the Fermi level and the tensile micro-strain in Al 1 − x Mg x B 2

The increase of Tc 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 σ 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 E2g phonon frequency with increasing boron tensile micro-strain e in the range 3% < e < 6% shows the increasing electron-lattice interaction. The linear scaling, for 0.66 < x < 1, of Tc vs. the Fermi temperature TF of the σ holes shows a constant coupling strength with kFξ0 = 90 (where kF is the Fermi wave vector and ξ0 is the Pippard coherence length) that points toward a vibronic pairing mechanism.