Development of density-functional theory for a plasmon-assisted superconducting state: application to lithium under high pressures

The 2021 room-temperature superconductivity roadmap

Designing materials with advanced functionalities is the main focus of contemporary solid-state physics and chemistry. Research efforts worldwide are funneled into a few high-end goals, one of the oldest, and most fascinating of which is the search for an ambient temperature superconductor (A-SC). The reason is clear: superconductivity at ambient conditions implies being able to handle, measure and access a single, coherent, macroscopic quantum mechanical state without the limitations associated with cryogenics and pressurization. This would not only open exciting avenues for fundamental research, but also pave the road for a wide range of technological applications, affecting strategic areas such as energy conservation and climate change. In this roadmap we have collected contributions from many of the main actors working on superconductivity, and asked them to share their personal viewpoint on the field. The hope is that this article will serve not only as an instantaneous picture of the status of research, but also as a true roadmap defining the main long-term theoretical and experimental challenges that lie ahead. Interestingly, although the current research in superconductor design is dominated by conventional (phonon-mediated) superconductors, there seems to be a widespread consensus that achieving A-SC may require different pairing mechanisms.In memoriam, to Neil Ashcroft, who inspired us all.

Emerging properties of carbon based 2D material beyond graphene

Graphene turns out to be the pioneering material for setting up boulevard to a new zoo of recently proposed carbon based novel two dimensional (2D) analogues. It is evident that their electronic, optical and other related properties are utterly different from that of graphene because of the distinct intriguing morphology. For instance, the revolutionary emergence of Dirac cones in graphene is particularly hard to find in most of the other 2D materials. As a consequence the crystal symmetries indeed act as a major role for predicting electronic band structure. Since tight binding calculations have become an indispensable tool in electronic band structure calculation, we indicate the implication of such method in graphene's allotropes beyond hexagonal symmetry. It is to be noted that some of these graphene allotropes successfully overcome the inherent drawback of the zero band gap nature of graphene. As a result, these 2D nanomaterials exhibit great potential in a broad spectrum of applications, viz nanoelectronics, nanooptics, gas sensors, gas storages, catalysis, and other specific applications. The miniaturization of high performance graphene allotrope based gas sensors to microscopic or even nanosized range has also been critically discussed. In addition, various optical properties like the dielectric functions, optical conductivity, electron energy loss spectra reveal that these systems can be used in opto-electronic devices. Nonetheless, the honeycomb lattice of graphene is not superconducting. However, it is proposed that the tetragonal form of graphene can be intruded to form new hybrid 2D materials to achieve novel superconducting device at attainable conditions. These dynamic experimental prospects demand further functionalization of these systems to enhance the efficiency and the field of multifunctionality. This topical review aims to highlight the latest advances in carbon based 2D materials beyond graphene from the basic theoretical as well as future application perspectives.

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.

Nonempirical Calculation of Superconducting Transition Temperatures in Light-Element Superconductors

Recent progress in the fully nonempirical calculation of the superconducting transition temperature (T_c ) is reviewed. Especially, this study focuses on three representative light-element high-T_c 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_c 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_c . 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_c superconductivity and the Mott-Hubbard transition in the fullerides. The results for these high-T_c superconductors will provide a firm ground for future materials design of new superconductors.

Possible "Magnéli" Phases and Self-Alloying in the Superconducting Sulfur Hydride

We theoretically give an infinite number of metastable crystal structures for the superconducting sulfur hydride H_{x}S under pressure. Previously predicted crystalline phases of H_{2}S and H_{3}S have been thought to have important roles for experimentally observed low and high T_{c}, respectively. The newly found structures are long-period modulated crystals where slablike H_{2}S and H_{3}S regions intergrow on a microscopic scale. The extremely small formation enthalpy for the H_{2}S-H_{3}S boundary indicated by first-principles calculations suggests possible alloying of these phases through the formation of local H_{3}S regions. The modulated structures and gradual alloying transformations between them not only explain the peculiar pressure dependence of T_{c} in sulfur hydride observed experimentally, but also could prevail in the experimental samples under various compression schemes.

Exotic s-wave superconductivity in alkali-doped fullerides

Alkali-doped fullerides (A3C60 with A = K, Rb, Cs) show a surprising phase diagram, in which a high transition-temperature (Tc) s-wave superconducting state emerges next to a Mott insulating phase as a function of the lattice spacing. This is in contrast with the common belief that Mott physics and phonon-driven s-wave superconductivity are incompatible, raising a fundamental question on the mechanism of the high-Tc superconductivity. This article reviews recent ab initio calculations, which have succeeded in reproducing comprehensively the experimental phase diagram with high accuracy and elucidated an unusual cooperation between the electron-phonon coupling and the electron-electron interactions leading to Mott localization to realize an unconventional s-wave superconductivity in the alkali-doped fullerides. A driving force behind the exotic physics is unusual intramolecular interactions, characterized by the coexistence of a strongly repulsive Coulomb interaction and a small effectively negative exchange interaction. This is realized by a subtle energy balance between the coupling with the Jahn-Teller phonons and Hund's coupling within the C60 molecule. The unusual form of the interaction leads to a formation of pairs of up- and down-spin electrons on the molecules, which enables the s-wave pairing. The emergent superconductivity crucially relies on the presence of the Jahn-Teller phonons, but surprisingly benefits from the strong correlations because the correlations suppress the kinetic energy of the electrons and help the formation of the electron pairs, in agreement with previous model calculations. This confirms that the alkali-doped fullerides are a new type of unconventional superconductors, where the unusual synergy between the phonons and Coulomb interactions drives the high-Tc superconductivity.

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

We show that the superconducting order parameter and condensation energy density of phonon-mediated superconductors can be calculated in real space from first principles density functional theory for superconductors. This method highlights the connection between the chemical bonding structure and the superconducting condensation and reveals new and interesting properties of superconducting materials. Understanding this connection is essential to describe nanostructured superconducting systems where the usual reciprocal space analysis hides the basic physical mechanism. In a first application we present results for MgB2, CaC6 and hole-doped graphane.