Theory for phonon-induced superconductivity in MgB${}_2$

Abstract

We analyze superonductivity in MgB${}_2$ observed below $T_c=39$ K resulting from electron-phonon coupling involving a mode at $\hslash {\omega }_1=24$ meV and most importantly the in-plane B-B $E_{2g}$ vibration at $\hslash {\omega }_2=67$ meV. The quasiparticles originating from $\pi$- and $\sigma$-states couple strongly to the low-frequency mode and the $E_{2g}$-vibrations respectively. Using two-band Eliashberg theory, ${\lambda }_{\pi }=1.4$ and ${\lambda }_{\sigma }=0.7$, we calculate the gap functions ${\Delta }^i(\omega ,0)$ ($i=\pi$, $\sigma$). Our results provide an explanation of recent tunneling experiments. We get $H_{c_2}^{ab}/H_{c_2}^c\approx 3.9$.

revised version, accepted for publication in PRB

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• Collective modes in superconductors including Coulomb repulsion
• Is Delta_{pi}-gap-only superconductivity possible in Mg_{1-x}Al_{x}B_{2} and Mg(B_{1-y}C_{y})_{2} alloys?