High-temperature superconductivity in the Ca-Sc-H system

The discovery of high critical temperature Tc in compressed H3S has been followed by the prediction and experimental confirmation of even higher superconducting temperatures with Tc approaching room temperature in LaH10 and CaH6. These works established the mechanism of the electron-phonon interaction and the dominant role of hydrogen in these materials. In the present work we focus on CaH6 and we follow the classic McMillan paper, which writes the electron-phonon coupling parameter angstrom as a ratio of an electronic contribution n over a force constant k = M(m2) which contains the phonon contribution. First the numerator of McMillan's expression, the Hopfield-McMillan parameter n, is computed using the theory of Gaspari and Gyorffy (GG), and the force constants in the denominator are obtained from the paper of Quan et al. The resulting angstrom is used in the Allen-Dynes equation to calculate Tc. We present an analysis of the different terms of the GG equation and conclude that the sp channel of hydrogen has the most important contribution to obtain high values of Tc, as in the other hydrogenated materials. In addition, we further separate the three terms of the GG expression and assess the role of the phase shifts term versus the partial densities of states and free scatterers. We compare these quantities in CaH6 to those in SH3 and LaH10 and, in contrast to what is expected for high values of angstrom, we conclude that in CaH6 the coupling parameter angstrom is the better indicator of high Tc than n. However, we have found that in the strong coupling limit of large angstrom the high values of Tc are strongly dependent on the parameter n and make Tc a decreasing function of n. Unfortunately most of the researchers of these materials have ignored the importance of the parameter n partly because the computational packages they are using do not separately compute n. Our view is that the parameters n, K, and angstrom must be examined on an equal footing as we study how to achieve high Tc at low pressures. Finally, we present the following findings: (a) using the virtual crystal approximation and an extension of the Allen-Dynes finding that at the strong coupling limit Tc depends on n, we predict that the alloy Ca1-xScxH6 can reach higher Tc than CaH6. (b) If the higher hydrogen content material CaH10 can be made in the Fm3m structure it would have significantly higher Tc than CaH6.