In materials with strong local Coulomb interactions, simple defects such as atomic substitutions strongly affect both macroscopic and local properties of the system. A nonmagnetic impurity, for instance, is seen to induce magnetism nearby. Even without disorder, models of such correlated systems are generally not soluble in two or three dimensions, and so few exact results are known for the properties of such impurities. Nevertheless, some simple physical ideas have emerged from experiments and approximate theories. Here the authors review what we can learn about this problem from one-dimensional (1D) antiferromagnetically correlated systems. Experiments on the high-$T_c$ cuprate normal state which probe the effect of impurities on local charge and spin degrees of freedom are discussed, and compared with theories of single impurities in correlated hosts, as well as phenomenological effective Kondo descriptions. Subsequently, theories of impurities in $d$-wave superconductors including residual quasiparticle interactions are reviewed and compared with experiments in the superconducting state. Existing data exhibit a remarkable similarity to impurity-induced magnetism in the 1D case, implying the importance of electronic correlations for the understanding of these phenomena, and suggesting that impurities may provide excellent probes of the still poorly understood ground state of the cuprates.

A deeper look into iron selenide: In the past 10 years, iron-based superconductors have created more puzzles than they have helped resolve. Some of the most fundamental outstanding questions are how strong the interactions are and what the electron pairing mechanism is. Now two groups have made contributions toward resolving these questions in the intriguing compound iron selenide (FeSe) (see the Perspective by Lee). Gerber et al. used photoemission spectroscopy coupled with x-ray diffraction to find that FeSe has a very sizable electron-phonon interaction. Quasiparticle interference imaging helped Sprau et al. determine the shape of the superconducting gap and find that the electron pairing in FeSe is orbital-selective. Science , this issue p. 71 , p. 75 ; see also p. 32

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.

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe${}_{1-x}$Se${}_x$, intercalated FeSe materials, and monolayer FeSe and FeTe${}_{1-x}$Se${}_x$ on SrTiO${}_3$. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

We discuss the influence on spin-fluctuation pairing theory of orbital selective strong correlation effects in Fe-based superconductors, particularly Fe chalcogenide systems. We propose that a key ingredient for an improved itinerant pairing theory is orbital selectivity, i.e., incorporating the reduced coherence of quasiparticles occupying specific orbital states. This modifies the usual spin-fluctuation theory via suppression of pair scattering processes involving those less coherent states and results in orbital selective Cooper pairing of electrons in the remaining states. We show that this paradigm yields remarkably good agreement with the experimentally observed anisotropic gap structures in both bulk and monolayer FeSe, as well as LiFeAs, indicating that orbital selective Cooper pairing plays a key role in the more strongly correlated iron-based superconductors.

We discuss the large gap anisotropy found for the $A_{1g}$ ($s$ wave) state in random-phase approximation spin fluctuation and functional renormalization-group calculations and show how the simple arguments leading to isotropic sign-switched $s$-wave states in these systems need to be supplemented by a consideration of pair scattering within Fermi-surface sheets and between the individual electron sheets as well. In addition, accounting for the orbital makeup of the states on the Fermi surface is found to be crucial.