One of interesting open questions for the high transition temperature (Tc) superconductivity in sulfur hydrides is why high pressure phases of H3S have extremely high Tc's. Recently, it has been pointed out that the presence of the van Hove singularities (vHs) around the Fermi level is crucial. However, while there have been quantitative estimates of Tc based on the Migdal-Eliashberg theory, the energy dependence of the density of states (DOS) has been neglected to simplify the Eliashberg equation. In this study, we go beyond the constant DOS approximation and explicitly consider the electronic structure over 40 eV around the Fermi level. In contrast with the previous conventional calculations, this approach with a sufficiently large number of Matsubara frequencies enables us to calculate Tc without introducing the empirical pseudo Coulomb potential. We show that while H3S has much higher Tc than H2S for which the vHs is absent, the constant DOS approximation employed so far seriously overestimates (underestimates) Tc by ∼ 60 K (∼ 10 K) for H3S (H2S). We then discuss the impact of the strong electron-phonon coupling on the electronic structure with and without the vHs and how it affects the superconductivity. Especially, we focus on (1) the feedback effect in the self-consistent calculation of the self-energy, (2) the effect of the energy shift due to the zero-point motion, and (3) the effect of the changes in the phonon frequencies due to strong anharmonicity. We show that the effect of (1)- (3) on Tc is about 10-30 K for both H3S and H2S. Eventually, Tc is estimated to be 181 K for H3S at 250 GPa and 34 K for H2S at 140 GPa, which explains the pressure dependence of Tc observed in the experiment. In addition, we evaluate the lowest order vertex correction beyond the Migdal-Eliashberg theory and discuss the validity of the Migdal approximation for sulfur hydrides.

We theoretically give an infinite number of metastable crystal structures for the superconducting sulfur hydride HxS under pressure. Previously predicted crystalline phases of H2S and H3S have been thought to have important roles for the experimentally observed low and high Tc, respectively. The newly found structures are long-period modulated crystals where slab-like H2S and H3S regions intergrow in a microscopic scale. The extremely small formation enthalpy for the H2S-H3S boundary indicated with the first-principles calculations suggests possible alloying of these phases through formation of local H3S regions. The modulated structures and gradual alloying transformations between them explain peculiar pressure dependence of Tc in sulfur hydride observed experimentally, as well as could they prevail in the experimental samples under various compression schemes.

Pyrochlore oxides possessing "all-in-all-out" spin ordering have attracted burgeoning interest as a rich ground of emergent states. This ordering has two distinct types of magnetic domains (all-in-all-out or all-out-all-in) with broken time-reversal symmetry, and a non-trivial metallic surface state has been theoretically demonstrated to appear at their domain wall. Here, we report on observation of this metallic conduction at the single all-in-all-out/all-out-all-in magnetic domain wall formed at the heterointerface of two pyrochlore iridates. By utilizing different magnetoresponses of them with different lanthanide ions, the domain wall is controllably inserted at the heterointerface, the surface state being detected as anomalous conduction enhancement with a ferroic hysteresis. Our establishment paves the way for further investigation and manipulation of this new type of surface transport.

Recent progress in the fully nonempirical calculation of the superconducting transition temperature (T ) is reviewed. Especially, this study focuses on three representative light-element high-T superconductors, i.e., elemental Li, sulfur hydrides, and alkali-doped fullerides. Here, it is discussed how crucial it is to develop the beyond Migdal-Eliashberg (ME) methods. For Li, a scheme of superconducting density functional theory for the plasmon mechanism is formulated and it is found that T is dramatically enhanced by considering the frequency dependence of the screened Coulomb interaction. For sulfur hydrides, it is essential to go beyond not only the static approximation for the screened Coulomb interaction, but also the constant density-of-states approximation for electrons, the harmonic approximation for phonons, and the Migdal approximation for the electron-phonon vertex, all of which have been employed in the standard ME calculation. It is also shown that the feedback effect in the self-consistent calculation of the self-energy and the zero point motion considerably affect the calculation of T . For alkali-doped fullerides, the interplay between electron-phonon coupling and electron correlations becomes more nontrivial. It has been demonstrated that the combination of density functional theory and dynamical mean field theory with the ab initio downfolding scheme for electron-phonon coupled systems works successfully. This study not only reproduces the experimental phase diagram but also obtains a unified view of the high-T superconductivity and the Mott-Hubbard transition in the fullerides. The results for these high-T superconductors will provide a firm ground for future materials design of new superconductors.