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This paper presents a simple formalism for calculating X-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) that has as input orbital-resolved density of states from a single-particle or many-body \textit{ab initio} calculation and is designed to capture itinerant-like features. We use this formalism to calculate both the XAS and RIXS with input from DFT and DFT+DMFT for the recently studied reduced valence nickelates $R_4$Ni$_3$O$_8$ and $R$NiO$_2$ ($R$ a rare earth), and these results are then contrasted with those for the cuprate CaCuO$_2$ and the unreduced nickelate $R_4$Ni$_3$O$_{10}$. In contrast to the unreduced $R_4$Ni$_3$O$_{10}$, the reduced valence nickelates as well as the cuprate show strong orbital polarization due to the dominance of $x^2-y^2$ orbitals for the unoccupied $3d$ states. We also reproduce two key aspects of a recent RIXS experiment for $R_4$Ni$_3$O$_8$: (i) a charge transfer feature between $3d$ and oxygen $2p$ states whose energy we find to decrease as one goes from $R$NiO$_2$ to $R_4$Ni$_3$O$_8$ to the cuprate, and (ii) an energy-dependent polarization reversal of the fluorescence line that arises from hybridization of the unoccupied $z^2$ states with $R$ 5d states. We end with some implications of our results for the nature of the $3d$ electrons in reduced valence nickelates.

${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}$ (SCOC) is a model undoped cuprate with $I4/mmm$ crystallographic symmetry, and a simple magnetic space group ${C}_{A}mca$ with associated magnetic point group $mmm{1}^{\ensuremath{'}}$. However, recent second harmonic spectroscopy in the antiferromagnetic phase has challenged this picture, suggesting instead a magnetic point group $4/m{m}^{\ensuremath{'}}{m}^{\ensuremath{'}}$ that coexists with the antiferromagnetism and breaks the two orthogonal mirror planes containing the tetragonal $c$ axis. Here, we analyze the symmetry of SCOC in light of the second harmonic results, and discuss possible ground states that are consistent with the data.

The discovery of superconductivity in a d(9-delta) nickelate has inspired disparate theoretical perspectives regarding the essential physics of this class of materials. A key issue is the magnitude of the magnetic superexchange, which relates to whether cuprate-like high-temperature nickelate superconductivity could be realized. We address this question using Ni L-edge and O K-edge spectroscopy of the reduced d(9-1/3) trilayer nickelates R4Ni3O8 (where R = La, Pr) and associated theoretical modeling. A magnon energy scale of similar to 80 meV resulting from a nearest-neighbor magnetic exchange of J = 69(4) meV is observed, proving that d(9-delta) nickelates can host a large superexchange. This value, along with that of the Ni-O hybridization estimated from our O K-edge data, implies that trilayer nickelates represent an intermediate case between the infinite-layer nickelates and the cuprates. Layered nickelates thus provide a route to testing the relevance of superexchange to nickelate superconductivity.

The discovery of superconductivity in a d^{9-δ} nickelate has inspired disparate theoretical perspectives regarding the essential physics of this class of materials. A key issue is the magnitude of the magnetic superexchange, which relates to whether cuprate-like high-temperature nickelate superconductivity could be realized. We address this question using Ni L-edge and O K-edge spectroscopy of the reduced d^{9-1/3} trilayer nickelates R_{4}Ni_{3}O_{8} (where R=La, Pr) and associated theoretical modeling. A magnon energy scale of ∼80 meV resulting from a nearest-neighbor magnetic exchange of J=69(4) meV is observed, proving that d^{9-δ} nickelates can host a large superexchange. This value, along with that of the Ni-O hybridization estimated from our O K-edge data, implies that trilayer nickelates represent an intermediate case between the infinite-layer nickelates and the cuprates. Layered nickelates thus provide a route to testing the relevance of superexchange to nickelate superconductivity.

Calculations of the electronic structure of NdNiO${}_{2}$, recently found to be superconducting, reveal important similarities and differences to cuprates, which may shed light on the origin of cuprate high-temperature superconductivity.

An overview of an exotic type of liquid Materials with interacting quantum spins that nevertheless do not order magnetically down to the lowest temperatures are candidates for a materials class called quantum spin liquids (QSLs). QSLs are characterized by long-range quantum entanglement and are tricky to study theoretically; an even more difficult task is to experimentally prove that a material is a QSL. Broholm et al. take a broad view of the state of the field and comment on the upcoming challenges. Science , this issue p. eaay0668

Second harmonic generation (SHG) on the pyrochlore metal ${\mathrm{Cd}}_{2}{\mathrm{Re}}_{2}{\mathrm{O}}_{7}$ indicates the presence of three order parameters setting in below an inversion breaking transition. Here, we explore a possible structural explanation and relate it not only to the SHG data but also to neutron and x-ray diffraction, where we find that such a structural scenario can explain certain reflection extinctions observed in single crystal x-ray data. From this analysis, we suggest future experiments that could be done to resolve this matter. Finally, we comment on the Landau-violating nature of the inversion breaking transition and its relation to similar phenomena observed in improper ferroelectrics.

A recent study has revealed that the low carrier density electron gas (2DEG) induced at the interface of EuO and (111) ${\mathrm{KTaO}}_{3}$ exhibits a broken symmetry phase with a strong in-plane anisotropy of the resistivity. We present a minimal tight-binding model of this (111) 2DEG, including the large spin-orbit coupling from the Ta ions, which reveals a hexagonal Fermi surface with a highly enhanced $2{k}_{F}$ electronic susceptibility. We argue that repulsive electronic interactions, together with a ferromagnetic EuO substrate, favor a magnetic stripe instability leading to a partially gapped Fermi surface. Such a stripe state, or its vestigial nematicity, could explain the observed transport anisotropy. We propose a $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ theory for the low energy $j=3/2$ states, which captures the key results from our tight-binding study, and further reveals the intertwined dipolar and octupolar modulations underlying this magnetic stripe order. We conclude by speculating on the relation of this stripe order to the superconductivity seen in this material.

A variety of copper tellurium oxide minerals are known, and many of them exhibit either unusual forms of magnetism, or potentially novel spin liquid behavior. Here, I review a number of the more interesting materials with a focus on their crystalline symmetry and, if known, the nature of their magnetism. Many of these exist (so far) in mineral form only, and most have yet to have their magnetic properties studied. This means a largely unexplored space of materials awaits our exploration., Comment: Contribution to a dedicated issue of the Journal of Magnetism and Magnetic Materials in memory of Art Freeman

High-temperature cuprate superconductivity remains a defining problem in condensed-matter physics. Among myriad approaches to addressing this problem has been the study of alternative transition metal oxides with similar structures and 3d electron count that are suggested as proxies for cuprate physics. None of these analogues has been superconducting, and few are even metallic. Here, we report that the low-valent, quasi-two-dimensional trilayer compound Pr4Ni3O8 avoids a charge-stripe-ordered phase previously reported for La4Ni3O8, leading to a metallic ground state. X-ray absorption spectroscopy shows that metallic Pr4Ni3O8 exhibits a low-spin configuration with significant orbital polarization and pronounced character in the unoccupied states above the Fermi energy, a hallmark of the cuprate superconductors. Density functional theory calculations corroborate this finding, and reveal that the orbital dominates the near-Ef occupied states as well. Belonging to a regime of 3d electron count found for hole-doped cuprates, Pr4Ni3O8 thus represents one of the closest analogues to cuprates yet reported and a singularly promising candidate for high-Tc superconductivity if electron doping could be achieved. A careful study of the low-valent, quasi-two-dimensional trilayer metallic nickelate Pr4Ni3O8 is presented, revealing this system to be a close analogue of cuprate systems, and offering tantalizing hope that it may superconduct if appropriate electron doping can be achieved.

Trilayer nickelates, which exhibit a high degree of orbital polarization combined with an electron count (d8.67) corresponding to overdoped cuprates, have been identified as a promising candidate platform for achieving high-Tc superconductivity. One such material, La4Ni3O8, undergoes a semiconductor-insulator transition at ~105 K, which was recently shown to arise from the formation of charge stripes. However, an outstanding issue has been the origin of an anomaly in the magnetic susceptibility at the transition and whether it signifies formation of spin stripes akin to single layer nickelates. Here we report single crystal neutron diffraction measurements (both polarized and unpolarized) that establish that the ground state is indeed magnetic. The ordering is modeled as antiferromagnetic spin stripes that are commensurate with the charge stripes, the magnetic ordering occurring in individual trilayers that are essentially uncorrelated along the crystallographic c-axis. Comparison of the charge and spin stripe order parameters reveals that, in contrast to single-layer nickelates such as La2-xSrxNiO4 as well as related quasi-2D oxides including manganites, cobaltates, and cuprates, these orders uniquely appear simultaneously, thus demonstrating a stronger coupling between spin and charge than in these related low-dimensional correlated oxides., Comment: 34 pages, 10 figures (including SI). Accepted by Physical Review Letters

Averievite, ${\mathrm{Cu}}_{5}{\mathrm{V}}_{2}{\mathrm{O}}_{10}(\mathrm{CsCl})$, is an oxide mineral composed of ${\mathrm{Cu}}^{2+}$ kagome layers sandwiched by ${\mathrm{Cu}}^{2+}\text{\ensuremath{-}}{\mathrm{V}}^{5+}$ honeycomb layers. We have synthesized this oxide and investigated its properties from ab initio calculations along with susceptibility and specific heat measurements. The data indicate a Curie-Weiss temperature of 185 K as well as long-range magnetic order at 24 K due to the significant interlayer coupling from the honeycomb copper ions. This order is suppressed by substituting copper by isoelectronic zinc, suggesting that Zn-substituted averievite is a promising spin liquid candidate. A further proposed substitution that replaces ${\mathrm{V}}^{5+}$ by ${\mathrm{Ti}}^{4+}$ not only dopes the material but is predicted to give rise to a two-dimensional electronic structure featuring Dirac crossings. As such, averievite is an attractive platform for $S=1/2$ kagome physics with the potential for realizing novel electronic states.

We report investigations on the magnetotransport in LaSb, which exhibits extremely large magnetoresistance (XMR). Foremost, we demonstrate that the resistivity plateau can be explained without invoking topological protection. We then determine the Fermi surface from Shubnikov - de Haas (SdH) quantum oscillation measurements and find good agreement with the bulk Fermi pockets derived from first principle calculations. Using a semiclassical theory and the experimentally determined Fermi pocket anisotropies, we quantitatively describe the orbital magnetoresistance, including its angle dependence. We show that the origin of XMR in LaSb lies in its high mobility with diminishing Hall effect, where the high mobility leads to a strong magnetic field dependence of the longitudinal magnetoconductance. Unlike a one-band material, when a system has two or more bands (Fermi pockets) with electron and hole carriers, the added conductance arising from the Hall effect is reduced, hence revealing the latent XMR enabled by the longitudinal magnetoconductance. With diminishing Hall effect, the magnetoresistivity is simply the inverse of the longitudinal magnetoconductivity, enabling the differentiation of the electron and hole contributions to the XMR, which varies with the strength and orientation of the magnetic field. This work demonstrates a convenient way to separate the dynamics of the charge carriers and to uncover the origin of XMR in multi-band materials with anisotropic Fermi surfaces. Our approach can be readily applied to other XMR materials., 34 pages, 8 figures

An argument by contradiction shows that the pseudogap state in the high-temperature superconducting cuprates is due to the superconducting pairing rather than being an independent or even competing state.

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature T$_{cdw}$. Here we investigate, using photoemission, X-ray scattering and scanning tunneling microscopy, the canonical CDW compound 2H-NbSe$_2$ intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude that impacts the electronic dispersion, giving rise to an energy gap. The phase transition at T$_{cdw}$ marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in `pseudogap' states., main manuscript plus supplementary information

We discuss the nodal structure of odd-parity superconductors in the presence of non-symmorphic crystal symmetries, both with and without spin-orbit coupling, and with and without time reversal symmetry. We comment on the relation of our work to previous work in the literature, and also the implications for unconventional superconductors such as UPt$_3$., 6 pages, 2 figures

The currently accepted magnetic ground state of ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ (the $\ensuremath{-}++\ensuremath{-}$ state) preserves inversion symmetry. This is at odds, though, with recent experiments that indicate a magnetoelectric ground state, leading to the speculation that orbital currents or more exotic magnetic multipoles might exist in this material. Here, we analyze various magnetic configurations and demonstrate that two of them, the magnetoelectric $\ensuremath{-}+\ensuremath{-}+$ state and the nonmagnetoelectric $++++$ state, can explain these recent second-harmonic generation (SHG) experiments, obviating the need to invoke orbital currents. The SHG-probed magnetic order parameter has the symmetry of a parity-breaking multipole in the $\ensuremath{-}+\ensuremath{-}+$ state and of a parity-preserving multipole in the $++++$ state. We speculate that either might have been created by the laser pump used in the experiments. An alternative is that the observed magnetic SHG signal is a surface effect. We suggest experiments that could be performed to test these various possibilities and also address the important issue of the suppression of the RXS intensity at the ${L}_{2}$ edge.

We classify line nodes in superconductors with strong spin-orbit interactions and time-reversal symmetry, where the latter may include non-primitive translations in the magnetic Brillouin zone to account for coexistence with antiferromagnetic order. We find four possible combinations of irreducible representations of the order parameter on high symmetry planes, two of which allow for line nodes in pseudo-spin triplet pairs and two that exclude conventional fully gapped pseudo-spin singlet pairs. We show that the former can only be realized in the presence of band-sticking degeneracies, and verify their topological stability using arguments based on Clifford algebra extensions. Our classification exhausts all possible symmetry protected line nodes in the presence of spin-orbit coupling and a (generalized) time-reversal symmetry. Implications for existing non-symmorphic and antiferromagnetic superconductors are discussed., Comment: 4+ pages, 4 tables, supplementary material, changed title, added table

A brief overview is given of the problem of high temperature superconductivity in the cuprates, with emphasis on theoretical ideas.

Understanding the underlying mechanism and phenomenology of colossal magnetoresistance in manganites has largely focused on atomic and nanoscale physics such as double exchange, phase separation, and charge order. Here we consider a more macroscopic view of manganite materials physics, reporting on the ferromagnetic domain behavior in a bilayer manganite sample with a nominal composition of ${\text{La}}_{2\ensuremath{-}2x}{\text{Sr}}_{1+2x}{\text{Mn}}_{2}{\text{O}}_{7}$ with $x=0.38$, studied using in situ Lorentz transmission electron microscopy. The role of magnetocrystalline anisotropy on the structure of domain walls was elucidated. Upon cooling, the magnetic domain contrast was seen to appear first at the Curie temperature within the a-b plane. With further reduction in temperature, the change in area fraction of magnetic domains was used to estimate the critical exponent describing the ferromagnetic phase transition. The ferromagnetic phase transition was accompanied by a distinctive nanoscale granular contrast close to the Curie temperature, which we infer to be related to the presence of ferromagnetic nanoclusters in a paramagnetic matrix, which has not yet been reported in bilayer manganites.

It is shown that the Weyl semimetal TaAs can have a significant polar vector contribution to its optical activity. This is quantified by ab initio calculations of the resonant x-ray diffraction at the Ta L1 edge. For the Bragg vector (400), this polar vector contribution to the circular intensity differential between left and right polarized x-rays is predicted to be comparable to that arising from linear dichroism. Implications this result has in regards to optical effects predicted for topological Weyl semimetals are discussed., 5 pages, 3 figures

Recent experiments have addressed the nature of the charge order seen in underdoped cuprates. Here, I show that x-ray absorption and linear dichroism are an excellent probe of such order. Ab-initio calculations reveal that a d-wave charge density wave order involving the oxygen ions is a much better description of the data than alternate models., Comment: 3 pages, 3 figures

Recently, a general formalism was presented for gyrotropic, ferroelectric, and multipolar order in spin-orbit coupled metals induced by spin-spin interactions. Here, I point out that the resulting order parameters are equivalent to expectation values of operators that determine natural circular dichroic signals in optical and x-ray absorption. Some general properties of these operator equivalents and the resulting dichroisms are mentioned, and I list several material examples in this connection, including Weyl semimetals. The particular case of the tensor order in the pyrochlore superconductor Cd2Re2O7 is treated in more detail, including calculations of the x-ray absorption and circular dichroism at the O K edge., v3 is a significant extension of the previous version, including a new table and a figure presenting ab initio results on Cd2Re2O7

Charge order has emerged as a generic feature of doped cuprates, leading to important questions about its origin and its relation to superconductivity. Recent experiments on two classes of hole doped cuprates indicate a novel d-wave symmetry for the order. These were motivated by earlier spin fluctuation theoretical studies based on an expansion about hot spots in the Brillouin zone that indicated such order would be competitive with d-wave superconductivity. Here, we reexamine this problem by solving strong coupling equations in the full Brillouin zone. Our results find that bond-oriented order, as seen experimentally, is strongly suppressed, indicating that the charge order must have a different origin., Comment: 5 pages, 4 figures plus Supplemental materials

Low energy inelastic neutron scattering on single crystals of the kagome spin-liquid compound ${\mathrm{ZnCu}}_{3}{(\mathrm{OD})}_{6}{\mathrm{Cl}}_{2}$ (herbertsmithite) reveals antiferromagnetic correlations between impurity spins for energy transfers $\ensuremath{\hbar}\ensuremath{\omega}l0.8\phantom{\rule{0.28em}{0ex}}\mathrm{meV} (\ensuremath{\sim}J/20)$. The momentum dependence differs significantly from higher energy scattering which arises from the intrinsic kagome spins. The low energy fluctuations are characterized by diffuse scattering near wave vectors (100) and $\left(00\frac{3}{2}\right)$, which is consistent with antiferromagnetic correlations between pairs of nearest-neighbor Cu impurities on adjacent triangular (Zn) interlayers. The corresponding impurity lattice resembles a simple cubic lattice in the dilute limit below the percolation threshold. Such an impurity model can describe prior neutron, NMR, and specific heat data. The low energy neutron data are consistent with the presence of a small spin gap $(\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}0.7\phantom{\rule{0.28em}{0ex}}\mathrm{meV})$ in the kagome layers, similar to that recently observed by NMR. The ability to distinguish the scattering due to Cu impurities from that of the planar kagome Cu spins provides an important avenue for probing intrinsic spin-liquid physics.

This chapter provides an introduction to unconventional superconductors. It traces their development from the early days of helium-3 to the modern world of Majorana fermions. It discusses heavy fermion superconductors, cuprates, and their iron-based cousins. It emphasizes the fact that in almost all cases, an accepted microscopic theory has yet to emerge due to the difficulty of constructing a theory of superconductivity outside the Migdal–Eliashberg framework.

Angle-resolved photoemission data in the superconducting state of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ show a kink in the dispersion along the zone diagonal, which is related via a Kramers-Kr\"onig analysis to a drop in the low energy scattering rate. As one moves towards $(\ensuremath{\pi},0)$, this kink evolves into a spectral dip. The occurrence of these anomalies in the dispersion and line shape throughout the zone indicates the presence of a new energy scale in the superconducting state.

The doping dependence of the low-temperature spectral function is precisely determined from angle resolved photoemision (ARPES) measurements. It is found that, as the doping decreases, the maximum of the superconducting gap increases, but the slope of the gap near the nodes decreases. Though consistent with d-wave symmetry, the gap with underdoping cannot be fit by the simple cos(kx)-cos(ky) form. We suggest that this arises due to the increasing importance of long range interactions as one approaches the insulator. It is also shown that the shape of the spectral function at the (π, 0) point below T c can be explained by the interaction of the electrons with a collective mode whose energy matches that of the magnetic resonance as obtained by inelastic neutron scattering data, and points to the intimate relation of magnetic correlatins to high Tc superconductivity.

Motivated by neutron scattering data, we develop a model of electrons interacting with a magnetic resonance and use it to analyze angle resolved photoemission and tunneling data in the superconducting state of Bi{sub 2}Sr {sub 2}CaCu{sub 2}O{sub 8+{delta}} . We not only can explain the peak-dip-hump structure observed near the ({pi},0) point, and its particle-hole asymmetry as seen in superconductor-insulator-normal tunneling spectra, but also its evolution throughout the Brillouin zone, including a velocity ''kink'' near the d -wave node.

We study the Fermi surface of Bi2Sr2CaCu2O8 using angle resolved photoemission spectroscopy (ARPES) with a momentum resolution of approximately 0.01 of the Brillouin zone. We show that, contrary to recent suggestions, the ARPES derived Fermi surface is a large hole barrel centered at (pi,pi), independent of the incident photon energy. We caution that the photon energy and k dependence of the matrix elements, if not properly accounted for, can lead to misinterpretation of ARPES intensities.

The photoemission line shape near (pi, 0) in Bi(2)Sr(2)CaCu(2)O(8+delta) below T(c) is characterized by a sharp peak, followed at higher energy by a dip and hump. We study the evolution of this line shape as a function of momentum, temperature, and doping. We find the hump scales with the peak and persists above T(c) in the pseudogap state. We present strong evidence that the peak-dip-hump structure arises from the interaction of electrons with a collective mode of wave vector (pi, pi). The inferred mode energy and its doping dependence agree well with a magnetic resonance observed by neutron scattering.

The self-energy {Sigma}({bold k},{omega}), the fundamental function that describes the effects of many-body interactions on an electron in a solid, is usually difficult to obtain directly from experimental data. In this paper we show that by making certain reasonable assumptions, the self-energy can be directly determined from angle-resolved photoemission data. We demonstrate this method on data for the high-temperature superconductor Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+x} in the normal, superconducting, and pseudogap phases. {copyright} {ital 1999} {ital The American Physical Society}

We argue that incoherent pair tunneling in a cuprate superconductor junction with an optimally doped superconducting and an underdoped normal lead can be used to detect the presence of pairing correlations in the pseudogap phase of the underdoped lead. We estimate that the junction characteristics most suitable for studying the pair tunneling current are close to recently manufactured cuprate tunneling devices., ReVTeX 3.1; 4 pages, 2 EPS figures (included)

We use the gradient of the energy-integrated angle resolved photoemission (ARPES) intensity in order to define precisely the Fermi surface (FS) in BSCCO superconductors. We show that, independent of the photon energy, the FS is a hole barrel centered at ({pi},{pi}), Then, the superconducting gap along the FS is precisely determined from ARPES measurements on over-doped and underdoped samples of Bi2212. As the doping decreases, the maximum gap increases, but the slope of the gap near the nodes decreases. Though consistent with d-wave symmetry, the gap with underdoping cannot be fit by the simple cos(k{sub x})-cos(k{sub y}) form. A comparison of our ARPES results with available penetration depth data indicates that the renormalization of the linear T suppression of the superfluid density at low temperatures due to quasiparticle excitations around the d-wave nodes is large and doping dependent.