Аннотация:We report first principles calculations of the superconducting properties of fcc potassium under high pressure. Using a completely ab initio method we predict a superconducting phase transition at $18\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. A maximum critical temperature of about $2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is observed around $23\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, the pressure at which the crossover between the fcc phase and the KIII structure experimentally occurs. At higher pressure, when the fcc phase is experimentally unstable, we find, in the phononically stable range, values of ${T}_{c}$ up to $11\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. In order to understand the underlying mechanisms inducing superconductivity in potassium, we study the effect of pressure on the electronic and vibrational properties, showing a progressive phonon softening near the $K$ point of the Brillouin zone and a concomitant enhancement of the electron-phonon coupling constant $\ensuremath{\lambda}$. Interestingly, we find that the pressure induced $s\text{\ensuremath{-}}d$ charge transfer causes an increasing anisotropy of the superconducting gap $\ensuremath{\Delta}$. Although similar to dense Li in many respects, K displays interesting peculiar features.
