Pressure effects on the superconducting transition in nH-CaAlSi

We present a combined experimental and theoretical study of the effects of pressure on T-c of the hexagonal layered superconductors nH-CaAlSi (n=1, 5, and 6), where nH denotes the different stacking variants that were recently discovered. Experimentally, the pressure dependence of T-c has been investigated by measuring the magnetic susceptibility of single crystals up to 10 kbars. In contrast to previous results on polycrystalline samples, single crystals with different stacking sequences display different pressure dependences of T-c. 1H-CaAlSi shows a decrease in T-c with pressure, whereas 5H- and 6H-CaAlSi exhibit an increase in T-c with pressure. Ab initio calculations for 1H-, 5H-, and 6H-CaAlSi reveal that an ultrasoft phonon branch associated with out-of-plane vibrations of the Al-Si layers softens with pressure, leading to a structural instability at high pressures. For 1H-CaAlSi, the softening is not sufficient to cause an increase in T-c, which is consistent with the present experiments but adverse to previous reports. For 5H and 6H, the softening provides the mechanism to understand the observed increase in T-c with pressure. Calculations for hypothetical 2H and 3H stacking variants reveal qualitative and quantitative differences.