The Amplification of the Superconducting Tc by Combined Effect of Tuning of the Fermi Level and the Tensile Micro-Strain in Al1-xmgxb2

The increase of Tc with x in Al1-xMgxB2 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 ? holes in the superlattice of boron mono-layers intercalated by Al1-xMgx 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 ? in the range 3% < ? < 6% shows the increasing electron-lattice interaction. The linear scaling, for 0.66 < x < 1, of Tc vs. the Fermi temperature TF of the ? holes shows a constant coupling strength with kF?0 = 90 (where kF is the Fermi wave vector and ?o is the Pippard coherence length) that points toward a vibronic pairing mechanism.