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By means of first-principles calculations, we studied stable latticestructures and estimated superconducting transition temperature of CaSi$_2$ athigh pressure. Our simulation showed stability of the AlB$_2$ structure in apressure range above 17 GPa. In this structure, doubly degenerated opticalphonon modes, in which the neighboring silicon atoms oscillate alternately in asilicon plane, show prominently strong interaction with the conductionelectrons. In addition there exists a softened optical mode (out-of-plan motionof silicon atoms), whose strength of the electron-phonon interaction is nearlythe same as the above mode. The density of states at the Fermi level in theAlB$_2$ structure is higher than that in the trigonal structure. These findingsand the estimation of the transition temperature strongly suggest that higher$T_{\rm c}$ is expected in the AlB$_2$ structure than the trigonal structureswhich are known so far.

Theoretical evidences for enhanced superconducting transition temperature of CaSi$_2$ in a high-pressure AlB$_2$ phase