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Electron energy-loss spectroscopy (EELS) was combined with heat capacitymeasurements to follow the change of superconductivity with systematic Aldoping of MgB$_2$. By using x-ray diffraction and Vegard's law to assess theactual Al content in the samples, changes in behavior were found to be muchmore in agreement with theoretical predictions than in earlier studies. EELSdata show that $\sigma$-band hole states disappear above 33% Al, approximatelythe composition at which the $\sigma$ band Fermi surface is predicted to loseits cylindrical shape in reciprocal space and break apart into ellipsoidalpockets. At this composition, the $\sigma$ gap obtained from the heat capacitydata falls to the level of the $\pi$ gap, implying that band filling results inthe loss of strong superconductivity on the $\sigma$ band. However,superconductivity is not quenched completely, but persists with $T_c < 7$ K upto about 55% Al, the Al concentration at which the entire $\sigma$ band ispredicted to fall below the Fermi surface. Since, in the region $0.33 \alt x\alt 0.55$, only the $\pi$ band has appreciable density of states, it becomesthe stronger of the 2 bands, thus inverting the 2-band hierarchy of MgB$_2$

physical review letters

Inversion of Two-Band Superconductivity at the Critical Electron Doping of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">(</mml:mo><mml:mi>Mg</mml:mi><mml:mo>,</mml:mo><mml:mi>Al</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi mathvariant="normal">B</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

Inversion of Two-Band Superconductivity at the Critical Electron Doping of(Mg,Al)B2