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Theory for phonon-induced superconductivity in MgB$_2$

C. Joas·I. Eremin·D. Manske·K. H. Bennemann
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Abstract

We analyze superonductivity in MgB$_2$ observed below $T_c=39$ K resulting from electron-phonon coupling involving a mode at $\hbar ω_1 = 24$ meV and most importantly the in-plane B-B $E_{2g}$ vibration at $\hbar ω_2=67$ meV. The quasiparticles originating from $π$- and $σ$-states couple strongly to the low-frequency mode and the $E_{2g}$-vibrations respectively. Using two-band Eliashberg theory, $λ_π = 1.4$ and $λ_σ = 0.7$, we calculate the gap functions $Δ^{i}(ω,0)$ ($i=π$, $σ$). Our results provide an explanation of recent tunneling experiments. We get $H^{ab}_{c_2}/H^{c}_{c_2} \approx 3.9$.

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C. Joas, I. Eremin, D. Manske, K. H. Bennemann. 2002-02-13. Theory for phonon-induced superconductivity in MgB$_2$. https://doi.org/10.1103/physrevb.65.132518

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