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Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen–Cooper–Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund’s interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials. The progress and the outstanding issues in understanding the correlated phases in the unconventional iron-based superconductors is reviewed.

Physical properties of multi-orbital materials depend not only on the strength of the effective interactions among the valence electrons but also on their type. Strong correlations are caused by either Mott physics that captures the Coulomb repulsion among charges, or Hund physics that aligns the spins in different orbitals. We identify four energy scales marking the onset and the completion of screening in orbital and spin channels. The differences in these scales, which are manifest in the temperature dependence of the local spectrum and of the charge, spin and orbital susceptibilities, provide clear signatures distinguishing Mott and Hund physics. We illustrate these concepts with realistic studies of two archetypal strongly correlated materials, and corroborate the generality of our conclusions with a model Hamiltonian study. Strong correlation effects in metals lead to unconventional emergent behavior that depends on the nature of interactions at the microscopic scale. Deng et al. identify distinct signatures of the so-called Mott and Hund regimes, which may guide the theoretical understanding of correlated materials.

Correlated electron materials display a rich variety of notable properties ranging from unconventional superconductivity to metal-insulator transitions. These properties are of interest from the point of view of applications but are hard to treat theoretically, as they result from multiple competing energy scales. Although possible in more weakly correlated materials, theoretical design and spectroscopy of strongly correlated electron materials have been a difficult challenge for many years. By treating all the relevant energy scales with sufficient accuracy, complementary advances in Green’s functions and quantum Monte Carlo methods open a path to first-principles computational property predictions in this class of materials.

Copper oxide superconductors do not superconduct unless electrons or holes are added to the parent compounds. A theoretical study reveals how the electrons or holes affect the host material microscopically in an asymmetric way. The introduction of holes in a parent compound consisting of copper oxide layers results in high-temperature superconductivity. It is also possible to dope the cuprate parent compound with electrons 1 , 2 , 3 . The physical properties of these electron-doped materials bear some similarities to but also significant differences from those of their hole-doped counterparts. Here, we use a recently developed first-principles method 4 to study the electron-doped cuprates and elucidate the deep physical reasons behind their behaviour being so different from that of the hole-doped materials. The crystal structure of the electron-doped compounds is characterized by a lack of apical oxygens, and we find that it results in a parent compound that is a Slater insulator—a material in which the insulating behaviour is the result of the presence of magnetic long-range order. This is in sharp contrast with the hole-doped materials, which are insulating owing to the strong electronic correlations but not owing to magnetism.

Understanding characteristic energy scales is a fundamentally important issue in the study of strongly correlated systems. In multiband systems, an energy scale is affected not only by the effective Coulomb interaction but also by the Hund’s coupling. Direct observation of such energy scale has been elusive so far in spite of extensive studies. Here, we report the observation of a kink structure in the low energy dispersion of NiS 2− x Se x and its characteristic evolution with x , by using angle resolved photoemission spectroscopy. Dynamical mean field theory calculation combined with density functional theory confirms that this kink originates from Hund’s coupling. We find that the abrupt deviation from the Fermi liquid behavior in the electron self-energy results in the kink feature at low energy scale and that the kink is directly related to the coherence-incoherence crossover temperature scale. Our results mark the direct observation of the evolution of the characteristic temperature scale via kink features in the spectral function, which is the hallmark of Hund’s physics in the multiorbital system. A decisive spectroscopic evidence of the Hund’s coupling energy scale in multi-orbital correlated systems has been lacking. Here, the authors identify a kink feature due to Hund´s coupling in the spectral function of NiS 2 x Se x as they track its evolution across the Mott-insulator transition.

The intermetallic FeSi exhibits an unusual temperature dependence in its electronic and magnetic degrees of freedom, epitomized by the cross-over from a low-temperature nonmagnetic semiconductor to a high-temperature paramagnetic metal with a Curie–Weiss-like susceptibility. Many proposals for this unconventional behavior have been advanced, yet a consensus remains elusive. Using realistic many-body calculations, we here reproduce the signatures of the metal-insulator cross-over in various observables: the spectral function, the optical conductivity, the spin susceptibility, and the Seebeck coefficient. Validated by quantitative agreement with experiment, we then address the underlying microscopic picture. We propose a new scenario in which FeSi is a band insulator at low temperatures and is metalized with increasing temperature through correlation induced incoherence. We explain that the emergent incoherence is linked to the unlocking of iron fluctuating moments, which are almost temperature independent at short timescales. Finally, we make explicit suggestions for improving the thermoelectric performance of FeSi based systems.

In his comment1, Katanin reanalyzes our LDA + DMFT results for the temperature-dependent static local spin susceptibility of Sr2RuO4 and V2O3 fitting them to a Curie–Weiss (CW) form, χ(T) ≃ a/(T + θ). Invoking Wilson’s analysis of the impurity susceptibility of the spin-½ one-channel Kondo model (1CKM) in the wide-band limit, he extracts spin Kondo temperatures using TK = θ/√2, obtaining TK = 350 K and 100 K for Sr2RuO4 and V2O3, respectively. Noting that these are significantly smaller than the scales Tᵒⁿˢᵉᵗ_(sp) = 2300 K and 1000 K reported in ref. 2, he argues that our Tᵒⁿˢᵉᵗ_(sp) scales “do not characterize the screening process”.

We develop a new implementation of the Gutzwiller approximation in combination with the local density approximation, which enables us to study complex 4f and 5f systems beyond the reach of previous approaches. We calculate from first principles the zero-temperature phase diagram and electronic structure of Pr and Pu, finding good agreement with the experiments. Our study of Pr indicates that its pressure-induced volume-collapse transition would not occur without change of lattice structure—contrarily to Ce. Our study of Pu shows that the most important effect originating the differentiation between the equilibrium densities of its allotropes is the competition between the Peierls effect and the Madelung interaction and not the dependence of the electron correlations on the lattice structure.

We develop an efficient approach for computing two-particle response functions and interaction vertices for multiorbital strongly correlated systems based on the rotationally-invariant slave-boson framework. The method is applied to the degenerate three-orbital Hubbard-Kanamori model for investigating the origin of the s-wave orbital antisymmetric spin-triplet superconductivity in the Hund's metal regime, previously found in the dynamical mean-field theory studies. By computing the pairing interaction considering the particle-particle and the particle-hole scattering channels, we identify the mechanism leading to the pairing instability around Hund's metal crossover arises from the particle-particle channel, containing the local electron pair fluctuation between different particle-number sectors of the atomic Hilbert space. On the other hand, the particle-hole spin fluctuations induce the s-wave pairing instability before entering the Hund's regime. Our approach paves the way for investigating the pairing mechanism in realistic correlated materials

Uranium compounds can manifest a wide range of fascinating many-body phenomena, and are often thought to be poised at a crossover between localized and itinerant regimes for 5 f electrons. The antiferromagnetic dipnictide USb 2 has been of recent interest due to the discovery of rich proximate phase diagrams and unusual quantum coherence phenomena. Here, linear-dichroic X-ray absorption and elastic neutron scattering are used to characterize electronic symmetries on uranium in USb 2 and isostructural UBi 2 . Of these two materials, only USb 2 is found to enable strong Hund’s rule alignment of local magnetic degrees of freedom, and to undergo distinctive changes in local atomic multiplet symmetry across the magnetic phase transition. Theoretical analysis reveals that these and other anomalous properties of the material may be understood by attributing it as the first known high temperature realization of a singlet ground state magnet, in which magnetism occurs through a process that resembles exciton condensation. Electrons in uranium-based materials are often on the border between localised and itinerant behaviour, which can lead to unusual magnetic behaviour. Here the authors combine experiment and theory to show that USb 2 may be an unusually high temperature example of a singlet-ground-state magnet.