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We have studied the lattice dynamics, electron-phonon coupling, andsuperconducting properties of $\alpha$-MoB$_2$, as a function of appliedpressure, within the framework of density functional perturbation theory usinga mixed-basis pseudopotential method. We found that phonon modes located alongthe A$-$H, H$-$L, and L$-$A high-symmetry paths exhibit large phonon linewidthsand contribute significantly to the electron-phonon coupling constant. Althoughlinewidths are particularly large for the highest-frequency optical phononmodes (dominated by B vibrations), their contribution to the electron-phononcoupling constant is marginal. The latter is largely controlled by the acousticlow-frequency modes of predominantly Mo character. It was observed that at apressure of $90$~GPa, where $\alpha$-MoB$_2$ forms, the phonon-mediated pairingfalls into the strong-coupling regime, and the estimate for the superconductingcritical temperature $T_c$ agrees well with experimental observations. Whenfurther increasing the applied pressure, a reduction of $T_c$ is predicted,which correlates with a hardening of the acoustic low-frequency phonon modesand a decrease of the electron-phonon coupling parameter.

Electron-phonon coupling and superconductivity in $\alpha$-MoB$_2$ as a function of pressure