First-Principles Calculation of the Real-Space Order Parameter and Condensation Energy Density in Phonon-Mediated Superconductors

Combining Eliashberg Theory with Density Functional Theory for the Accurate Prediction of Superconducting Transition Temperatures and Gap Functions

We propose a practical alternative to Eliashberg equations for the ab initio calculation of superconducting transition temperatures and gap functions. Within the recent density functional theory for superconductors, we develop an exchange-correlation functional that retains the accuracy of Migdal's approximation to the many-body electron-phonon self-energy, while having a simple analytic form. Our functional is based on a parametrization of the Eliashberg self-energy for a superconductor with a single Einstein frequency, and enables density functional calculations of experimental excitation gaps. By merging electronic structure methods and Eliashberg theory, the present approach sets a new standard in quality and computational feasibility for the prediction of superconducting properties.

Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride

The discovery of superconductivity at 200 kelvin in the hydrogen sulfide system at high pressures¹ demonstrated the potential of hydrogen-rich materials as high-temperature superconductors. Recent theoretical predictions of rare-earth hydrides with hydrogen cages^2,3 and the subsequent synthesis of LaH₁₀ with a superconducting critical temperature (T_c) of 250 kelvin^4,5 have placed these materials on the verge of achieving the long-standing goal of room-temperature superconductivity. Electrical and X-ray diffraction measurements have revealed a weakly pressure-dependent T_c for LaH₁₀ between 137 and 218 gigapascals in a structure that has a face-centred cubic arrangement of lanthanum atoms⁵. Here we show that quantum atomic fluctuations stabilize a highly symmetrical [Formula: see text] crystal structure over this pressure range. The structure is consistent with experimental findings and has a very large electron-phonon coupling constant of 3.5. Although ab initio classical calculations predict that this [Formula: see text] structure undergoes distortion at pressures below 230 gigapascals^2,3, yielding a complex energy landscape, the inclusion of quantum effects suggests that it is the true ground-state structure. The agreement between the calculated and experimental T_c values further indicates that this phase is responsible for the superconductivity observed at 250 kelvin. The relevance of quantum fluctuations calls into question many of the crystal structure predictions that have been made for hydrides within a classical approach and that currently guide the experimental quest for room-temperature superconductivity^6-8. Furthermore, we find that quantum effects are crucial for the stabilization of solids with high electron-phonon coupling constants that could otherwise be destabilized by the large electron-phonon interaction⁹, thus reducing the pressures required for their synthesis.

Direct evaluation of the isotope effect within the framework of density functional theory for superconductors

Within recent developments of density functional theory, its numerical implementation and of the superconducting density functional theory is nowadays possible to predict the superconducting critical temperature, [Formula: see text], with sufficient accuracy to anticipate the experimental verification. In this paper we present an analytical derivation of the isotope coefficient within the superconducting density functional theory. We calculate the partial derivative of [Formula: see text] with respect to atomic masses. We verified the final expression by means of numerical calculations of isotope coefficient in monatomic superconductors (Pb) as well as polyatomic superconductors (CaC₆). The results confirm the validity of the analytical derivation with respect to the finite difference methods, with considerable improvement in terms of computational time and calculation accuracy. Once the critical temperature is calculated (at the reference mass(es)), various isotope exponents can be simply obtained in the same run. In addition, we provide the expression of interesting quantities like partial derivatives of the deformation potential, phonon frequencies and eigenvectors with respect to atomic masses, which can be useful for other derivations and applications.

Time-Domain ab Initio Modeling of Electron-Phonon Relaxation in High-Temperature Cuprate Superconductors

Superconducting pairing due to electron-phonon coupling is investigated in recent pump-probe experiments. Combining time-dependent density functional theory and nonadiabatic molecular dynamics, we report the first direct modeling of such experiments and show how the electron-phonon relaxation depends on chemical bonding, electron-phonon coupling, and electronic state density. The relaxation rate is determined primarily by the nonadiabatic charge-phonon coupling strength, which in turn depends on the strength of chemical interactions between the key atoms, reflected in the wave function delocalization. The differences in the electronic density of states constitute the secondary factor. Having obtained good agreement with the experimental data on YBa₂Cu₃O_6.5, we predict that the relaxation slows if Y is replaced with Sc or Ba with Sr, while the relaxation accelerates if O is replaced with S, indicating that YBa₂Cu₃S_6.5 can exhibit improved superconducting performance.