Recent experiments on certain Fe-based superconductors have hinted at a role for paired electrons in "incipient" bands that are close to, but do not cross the Fermi level. Related theoretical works disagree on whether or not strong-coupling superconductivity is required to explain such effects, and whether a critical interaction strength exists. In this work, we consider various versions of the model problem of pairing of electrons in the presence of an incipient band, within a simple multiband weak-coupling BCS approximation. We categorize the problem into two cases: case(I) where superconductivity arises from the "incipient band pairing" alone, and case(II) where it is induced on an incipient band by pairing due to Fermi-surface based interactions. Negative conclusions regarding the importance of incipient bands have been drawn so far largely based on case(I), but we show explicitly that models under case(II) are qualitatively different, and can explain the non-exponential suppression of Tc, as well as robust large gaps on an incipient band. In the latter situation, large gaps on the incipient band do not require a critical interaction strength. We also model the interplay between phonon and spin fluctuation driven superconductivity and describe the bootstrap of electron-phonon superconductivity by spin fluctuations coupling the incipient and the regular bands. Finally, we discuss the effect of the dimensionality of the incipient band on our results. We argue that pairing on incipient bands may be significant and important in several Fe-based materials, including LiFeAs, FeSe intercalates and FeSe monolayers on strontium titanate, and indeed may contribute to high critical temperatures in some cases.

We investigate superconductivity in a two-band system with an electronlike and a holelike band, where one of the bands is away from the Fermi level (or "incipient"). We argue that the incipient band contributes significantly to spin-fluctuation pairing in the strong coupling limit where the system is close to a magnetic instability and can lead to a large T_{c}. In this case, T_{c} is limited by a competition between the frequency range of the coupling (set by an isolated paramagnon) and the coupling strength itself, such that a domelike T_{c} dependence on the incipient band position is obtained. The coupling of electrons to phonons is found to further enhance T_{c}. The results are discussed in the context of experiments on monolayers and intercalates of FeSe.

The discovery of two-dimensional (2D) materials comes at a time when computational methods are mature and can predict novel 2D materials, characterize their properties, and guide the design of 2D materials for applications. This article reviews the recent progress in computational approaches for 2D materials research. We discuss the computational techniques and provide an overview of the ongoing research in the field. We begin with an overview of known 2D materials, common computational methods, and available cyber infrastructures. We then move onto the discovery of novel 2D materials, discussing the stability criteria for 2D materials, computational methods for structure prediction, and interactions of monolayers with electrochemical and gaseous environments. Next, we describe the computational characterization of the 2D materials' electronic, optical, magnetic, and superconducting properties and the response of the properties under applied mechanical strain and electrical fields. From there, we move on to discuss the structure and properties of defects in 2D materials, and describe methods for 2D materials device simulations. We conclude by providing an outlook on the needs and challenges for future developments in the field of computational research for 2D materials.

We present the derivation of an ab initio and parameter-free effective electron-electron interaction that goes beyond the screened random phase approximation and accounts for superconducting pairing driven by spin fluctuations. The construction is based on many-body perturbation theory and relies on the approximation of the exchange-correlation part of the electronic self-energy within time-dependent density functional theory. This effective interaction is included in an exchange-correlation kernel for superconducting density functional theory in order to achieve a completely parameter free superconducting gap equation. First results from applying the new functional to a simplified two-band electron gas model are consistent with experiments.

We study the electron-phonon coupling strength near the interface of monolayer and bilayer FeSe thin films on SrTiO3, BaTiO3, and oxygen-vacant SrTiO3 substrates, using ab initio methods. The calculated total electron-phonon coupling strength λ = 0.2-0.3 cannot account for the high Tc ∼ 70 K observed in these systems through the conventional phonon-mediated pairing mechanism. In all of these systems, however, we find that the coupling constant of a polar oxygen branch peaks at q = 0 with negligible coupling elsewhere, while the energy of this mode coincides with the offset energy of the replica bands measured recently by angle-resolved photoemission spectroscopy experiments. But the integrated coupling strength for this mode from our current calculations is still too small to produce the observed high Tc, even through the more efficient pairing mechanism provided by the forward scattering. We arrive at the same qualitative conclusion when considering a checkerboard antiferromagnetic configuration in the Fe layer. In light of the experimental observations of the replica band feature and the relatively high Tc of FeSe monolayers on polar substrates, our results point towards a cooperative role for the electron-phonon interaction, where the crossinterface interaction acts in conjunction with a purely electronic interaction. We also discuss a few scenarios where the coupling strength obtained here may be enhanced.

We numerically investigate the Spin Density Functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding paper I. As a test system we employ a free electron gas featuring an exchange-splitting, a phononic pairing field and a Coulomb repulsion. SpinSCDFT results are compared with Sarma, the Bardeen Cooper and Schrieffer theory and with an Eliashberg type of approach. We find that the spectrum of the superconducting Kohn-Sham SpinSCDFT system is not in agreement with the true quasi particle structure. Therefore, starting from the Dyson equation, we derive a scheme that allows to compute the many body excitations of the superconductor and represents the extension to superconductivity of the G0W0 method in band structure theory. This superconducting G0W0 method vastly improves the predicted spectra.

We present a first-principles approach to describe magnetic and superconducting systems and the phenomena of competition between these electronic effects. We develop a density functional theory: SpinSCDFT, by extending the Hohenberg-Kohn theorem and constructing the non-interacting KohnSham system. An exchange-correlation functional for SpinSCDFT is derived from the Sham Schlüter connection between the SpinSCDFT Kohn-Sham and a self-energy in Eliashberg approximation. The reference Eliashberg equations for superconductors in the presence of magnetism are also derived and discussed.

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.