Nonempirical Calculation of Superconducting Transition Temperatures in Light‐Element Superconductors

Abstract

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.

Superconducting Hydrogen Sulfide

“…As such, the Im structure has been intensively investigated by many theoreticians, with including the effect of anharmonicityand quantum hydrogen‐bond symmetrization . The T c has been calculated using many flavors of Eliashberg theory, and most of the results show general agreement with the experiment (Figure ). However, the uncertainties in both experiment and calculations should be kept in mind.…”

Relation between Crystal Structure and Transition Temperature of Superconducting Metals and Alloys

“…Various theoretical calculations of T c were published in the literature using band structure calculations [19][20][21][22][23][24]. These methods were recently reviewed in [25] with the emphasis of obtaining the T c of the hydrogen sulfide under pressure. These calculations are extensive and time consuming, but brought out important insights into the nature of superconductivity.…”

Ab initio Eliashberg Theory: Making Genuine Predictions of Superconducting Features

“…So far, ab initio superconductivity prediction are limited to phonon-driven superconductors, while important classes such as cuprates and iron based superconductors, are still out of reach due to the lack understanding of the microscopic pairing mechanism 41) and treatment 42) of the Coulomb interactions. In this respect, Superconducting Density Functional Theory 43) (SCDFT), has been the leading theory which includes Coulomb interactions solely by first principles.…”