High-temperature superconductivity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>LaH</mml:mi><mml:mn>10</mml:mn></mml:msub></mml:math>
D. A. Papaconstantopoulos, Michael J. Mehl, Po-Hao Chang
Abstract
The recent discovery of a high critical temperature ${T}_{c}$ in compressed ${\mathrm{H}}_{3}\mathrm{S}$ has been followed by the prediction of Liu et al. of ${T}_{c}\ensuremath{\approx}250$ K in the clathrate ${\mathrm{LaH}}_{10}$ structure. This report has been confirmed experimentally by Somayazulu et al. and Drozdov et al. Additional theoretical work by Wang et al. and Quan et al. further established the mechanism of electron-phonon interaction and the dominant role of hydrogen. In the present Rapid Communication we follow the classic McMillan paper, which separates the electron and phonon contributions to the electron-phonon coupling $\ensuremath{\lambda}$. We first compute the numerator of McMillan's expression, the Hopfield parameter $\ensuremath{\eta}$, using the theory of Gaspari and Gyorffy (GG), and obtain the force constants in the denominator from Wang et al. and Quan et al. The resulting $\ensuremath{\lambda}$ is used in the Allen-Dynes equation to calculate ${T}_{c}$. The value of ${T}_{c}$ reaches a maximum in the range of 236--263 K at pressures of 255 GPa and decreases for smaller or larger pressures. We provide a thorough analysis of the different terms of the GG equation and draw the conclusion that the $sp$ channel of the hydrogen is the most important contribution to obtain high values of ${T}_{c}$ in this material. Consistent with Wang et al., we find large values of $\ensuremath{\lambda}$ that decrease with increasing pressure. In addition, we find that the hydrogen sites are the largest contributors to the total value of the coupling constant $\ensuremath{\lambda}$. That is, the acoustic mode associated with La contributes only 2% to the total $\ensuremath{\lambda}$, while the optic modes associated with H contribute 18% for the H1 site and 80% for the H2 site. These relative contributions to $\ensuremath{\lambda}$ are consistent with those given by Wang et al. and by Quan et al. Thus, our results strongly support the view that ${\mathrm{LaH}}_{10}$ is a metallic hydrogen superconductor.