Infrared properties of Mg${}_{1-x}$Al${}_x($B${}_{1-y}$C${}_y$)${}_2$ single crystals in the normal and superconducting state

Abstract

The reflectivity $R(\omega )$ of $ab$-oriented Mg${}_{1-x}$Al${}_x$(B${}_{1-y}$C${}_y$)${}_2$ single crystals has been measured by means of infrared microspectroscopy for $1300<\omega <17000$ cm${}^{-1}$. An increase with doping of the scattering rates in the $\pi$ and $\sigma$ bands is observed, being more pronounced in the C doped crystals. The $\sigma$-band plasma frequency also changes with doping due to the electron doping, while the $\pi$-band one is almost unchanged. Moreover, a $\sigma \to \sigma$ interband excitation, predicted by theory, is observed at ${\omega }_{IB}\simeq 0.47$ eV in the undoped sample, and shifts to lower energies with doping. By performing theoretical calculation of the doping dependence ${\omega }_{IB}$, the experimental observations can be explained with the increase with electron doping of the Fermi energy of the holes in the $\sigma$-band. On the other hand, the $\sigma$ band density of states seems not to change substantially. This points towards a $T_c$ reduction driven mainly by disorder, at least for the doping level studied here. The superconducting state has been also probed by infrared synchrotron radiation for $30<\omega <150$ cm${}^{-1}$ in one pure and one C-doped sample. In the undoped sample ($T_c$ = 38.5 K) a signature of the $\pi$-gap only is observed. At $y$ = 0.08 ($T_c$ = 31.9 K), the presence of the contribution of the $\sigma$-gap indicates dirty-limit superconductivity in both bands.

arXiv comment12 pages, 9 figures

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