First-principles studies of high-pressure superconducting hydrides

Abstract

Room-temperature superconductivity (SC) has been one of the most challenging subjects in modern physics. The discovery of superconductivity at 203 K in H$_3$S have demonstrated the potential for achieving room-temperature superconductivity in compressed H-rich materials. First-principles density-functional theory (DFT) calculations together with the Migdal-Eliashberg formalism have predicted that rare-earth metal hydrides such as yttrium, lanthanum, cerium hydrides host high superconducting transition temperature ($T_{\rm c}$) SC at megabar pressures, the origin of which is based on phonon-mediated electron pairing. Subsequently, such a conventional SC of LaH$_{10}$ was experimentally observed with a $T_{\rm c}$ of 250-260 K at a pressure of $\sim$170 GPa. The $T_{\rm c}$ of LaH$_{10}$ sets an new record for the highest temperature among experimentally available superconducting materials including curpates, and iron-based superconductors. Therefore, the experimental relization of room-temperature SC in LaH$_{10}$ has stimulated interests of the high $T_{\rm c}$ community towards compressed hydrides rich materials.\\

Firstly, I studied the pressure dependence of the superconducting transition temperature of compressed LaH$_{10}$. Nearly simultaneously, two experimental groups synthesized a lanthanum hydride LaH$_{10}$ with a clathrate-like structure at megabar pressures and measured a $T_{\rm c}$ between 250${\sim}$260 K at a pressure of ${\sim}$170 GPa. Although the two experiments agreed well with high values of $T_{\rm c}$ in the fcc phase of compressed LaH$_{10}$, the dependence of $T_{\rm c}$ on pressure is conflicting with each other. Therefore, the two different experimental observations on the pressure dependence of $T_{\rm c}$ of fcc LaH$_{10}$ raise an open question of whether $T_{\rm c}$ increases or decreases with increasing pressure, together with its microscopic underlying mechanism. Here, based on first-principles calculations, we reveal that for the fcc-LaH$_{10}$ phase, softening of the low-frequency optical phonon modes of H atoms dramatically occurs as pressure decreases, giving rise to a significant increase of the electron-phonon coupling (EPC) constant. Meanwhile, the electronic band structure near the Fermi energy is insensitive to change with respect to pressure. These results indicate that the pressure-dependent phonon softening is unlikely associated with Fermi-surface nesting, but driven by effective screening with the electronic states near the Fermi energy. It is thus demonstrated that the strong variation of EPC with respect to pressure plays a dominant role in the decrease of $T_{\rm c}$ with increasing pressure, supporting the measurements of Drozdov $et$ $al$.\\

Secondly, I studied the multiband nature of the room-temperature superconductivity in compressed LaH$_{10}$. Motivated by the experimentally realization of fcc LaH$_{10}$ under pressure, a number of DFT studies have been intensively performed to show that fcc LaH$_{10}$ having a high crystalline symmetry of the space group $Fm$$\overline{3}m$ (No. 225) with the point group O$_h$ features the peculiar bonding characters, van Hove singularities near the Fermi energy $E_{\rm F}$, and strong electron-phonon coupling with H-derived phonon modes. These unique bonding, electronic, and phononic properties of fcc LaH$_{10}$ have been associated with increased EPC constant, leading to the emergence of a room-temperature SC. However, the detailed nature of how fcc LaH$_{10}$ forms the large EPC constant and high $T_{\rm c}$ remains to be clarified. In this study, using the DFT calculations and the Migdal-Eliashberg formalism, we reveal the presence of two nodeless, anisotropic superconducting gaps on the Fermi surface (FS). Here, the small gap is mostly associated with the hybridized states of H $s$ and La $f$ orbitals on the three outer FS sheets, while the large gap arises mainly from the hybridized state of neighboring H $s$ or $p$ orbitals on the one inner FS sheet. Further, we find that compressed YH$_{10}$ with the same sodalite-like clathrate structure has the two additional FS sheets, enhancing EPC constant and $T_{\rm c}$. It is thus demonstrated that the nature of room-temperature SC in compressed LaH$_{10}$ and YH$_{10}$ features the multiband pairing of hybridized electronic states with large EPC constants.\\

Finally, I studied the Effect of hole doping on Superconductivity in Compressed CeH$_{9}$ at High Pressures. The main bottleneck for the research of high-$T_{\rm c}$ hydrides has been associated with difficulties both raising $T_{\rm c}$ and lowering the pressure of stability simultaneously. Near simultaneously, two experimental groups reported the successful synthesis of cerium hydride CeH$_9$ at 80$-$100 GPa. Its theoretically predicted $T_{\rm c}$ value was around 75 K, much lower than those of and LaH$_{10}$. In order to alleviate this bottleneck in CeH$_9$, we here investigate the effect of hole doping on superconductivity, which leads to a significant increase in $T_{\rm c}$. our first-principles calculations reveal that the strongly hybridized electronic states of Ce-4$f$ and H-1$s$ orbitals produce the topologically nontrivial Dirac nodal lines around the Fermi energy $E_{\rm F}$, which are protected by crystalline symmetries. By hole doping, $E_{\rm F}$ shifts down toward the symmetry-driven van Hove singularity to increase the density of states, which in turn significantly raises a superconducting transition temperature $T_{\rm c}$. We show that the hole doping with Ce$^{3+}$ ions can be well electronically miscible in CeH$_9$ because both Ce$^{3+}$ and Ce behave similarly as cations. Therefore, the interplay of crystalline symmetry, band topology, and hole doping contributes to enhance $T_{\rm c}$ in compressed CeH$_9$, which can also be demonstrated in another superconducting rare-earth hydride LaH$_{10}$.