Scaling of the critical temperature with the Fermi temperature in diborides

Abstract

The experimental determination of the scaling of the superconducting critical temperature ${(T}_{c})$ vs the Fermi temperature ${(T}_{f})$ of the holes in the boron \ensuremath{\sigma} subband is presented. The Fermi level has been tuned near the ``shape resonance,'' i.e., the two- to three-dimensional crossover of the Fermi surface of the boron \ensuremath{\sigma} subband by changing the Al/Mg content in ${\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{B}}_{2}.$ The product ${k}_{f}{\ensuremath{\xi}}_{0}$ of the Fermi wave vector ${(k}_{f})$ times the superconducting Pippard coherence length $({\ensuremath{\xi}}_{0}),$ that is a measure of the pairing strength, remains constant, ${k}_{f}{\ensuremath{\xi}}_{0}=90$ for $x>0.66.$ This high-${T}_{c}$ phase occurs in the boron superlattice under a tensile microstrain in the range $3%<\ensuremath{\varepsilon}<6%.$