Resonant inelastic x-ray scattering (RIXS) is a powerful probe of elementary excitations in solids. It is now widely applied to study magnetic excitations. However, its complex cross section means that RIXS has been more difficult to interpret than inelastic neutron scattering (INS). Here we report $\sim 37$ meV resolution RIXS measurements of the magnetic excitations in ${\mathrm{La}}_2{\mathrm{CuO}}_4$, the antiferromagnetic parent of one system of high-temperature superconductors. At high energies ($\sim 2$ eV), the RIXS spectra show angular-dependent $dd$ orbital excitations in agreement with previous RIXS studies but show new structure. They are interpreted with single-site multiplet calculations. At low energies ($\lesssim 0.3$ eV), we model the wave-vector-dependent single magnon RIXS intensity as the product of the calculated single-ion spin-flip RIXS cross section and the dynamical structure factor $S(\mathbf{Q},\omega )$ of the spin-wave excitations. When $S(\mathbf{Q},\omega )$ is extracted from our data, the wave-vector-dependence of the single-magnon pole intensity shows a similar variation to that observed by INS. Our results confirm that suitably corrected RIXS data can yield the genuine wave-vector and energy dependence of $S(\mathbf{Q},\omega )$ for a cuprate antiferromagnet. In addition to spin waves, our data show structured multimagnon excitations with dispersing peaks in the intensity at energies higher than the single-magnon excitations.

The superconducting transition metal dichalcogenide (TMD) $4Hb\text{−}{\mathrm{TaS}}_2$ consists of alternating layers of $H$ and $T$ structures, which in their bulk form are metallic and Mott insulating, respectively. Recently, this compound has been proposed as a candidate chiral superconductor, due to an observed enhancement of the muon-spin relaxation at $T_c$. $4Hb\text{−}{\mathrm{TaS}}_2$ also exhibits a puzzling $T$-linear specific heat at low temperatures, which is unlikely to be caused by disorder. Elucidating the origin of this behavior is an essential step in discerning the true nature of the superconducting ground state. Here, we propose a simple model that attributes the $T$-linear specific heat to the emergence of a robust multiband gapless superconducting state. We show that an extended regime of gapless superconductivity naturally appears when the pair-breaking scattering rate on distinct Fermi-surface pockets differs significantly, and the pairing interaction is predominantly intrapocket. Using a tight-binding model derived from first-principle calculations, we show that the pair-breaking scattering rate promoted by slow magnetic fluctuations on the $T$ layers, which arise from proximity to a Mott transition, can be significantly different in the various $H$-layer dominated Fermi pockets depending on their hybridization with $T$-layer states. Thus, our results suggest that the ground state of $4Hb\text{−}{\mathrm{TaS}}_2$ consists of Fermi pockets displaying gapless superconductivity, which are shunted by superconducting Fermi pockets that are nearly decoupled from the $T$ layers.

In topological semimetals and nodal superconductors, band crossings between occupied and unoccupied bands form stable nodal points/lines/surfaces carrying quantized topological charges. In particular, in centrosymmetric superconductors, some nodal structures at the Fermi energy $E_F$ carry two distinct topological charges, and thus they are called doubly charged nodes. Here we show that doubly charged nodal surfaces of centrosymmetric superconductors in three dimensions always develop peculiar linking structures with nodal points or lines formed between occupied bands below $E_F$. Such linking structures can naturally explain the inherent relationship between the charge of the node below $E_F$ and the two charges of the nodal surfaces at $E_F$. Based on the Altland-Zirnbauer (AZ) -type tenfold classification of nodes with additional inversion $\mathcal{I}$ symmetry, which is called the $\mathrm{AZ}+\mathcal{I}$ classification, we provide the complete list of linking structures of doubly charged nodes in centrosymmetric superconductors. The linking structures of doubly charged nodes clearly demonstrate that not only the local band structure around the node but also the global band structure plays a critical role in characterizing gapless topological phases.

Charge-density wave (CDW) modulations in underdoped high-temperature cuprate superconductors remain a central puzzle in condensed matter physics. However, despite a substantial experimental verification of this ubiquitous phase in a large class of high $T_c$ cuprates, a complete theoretical explanation of this phase is still missing. Here, we build upon our recent proposal that the CDW in underdoped cuprates (Y- and Bi- based compounds) emerges from a unique cooperation of the $B_{1g}$ bond-buckling phonon with strong electronic correlations. We assume a static mean-field lattice distortion with ${\mathrm{B}}_{1g}$ symmetry, regardless of its origin, with a commensurate wave vector ${\mathbf{q}}^{*}=(2\pi /3,0)/(0,2\pi /3)$. We show that such a phonon-induced CDW (both uni- and biaxial) reconstructs the Fermi surface, leading to electron and hole pockets, with relevant quantum oscillation frequencies in close consistency with the experiments. Furthermore, a systematic analysis of the symmetry of the intra-unit-cell charge modulations on the copper-oxygen planes is provided. We find that the atomic charge modulation on the $\mathrm{Cu}{\mathrm{O}}_2$ unit cell is predominantly of $s$-wave character, in support of the recent experimental observation.

A flat band in fermionic system is a dispersionless single-particle state with a diverging effective mass and nearly zero group velocity. These flat bands are expected to support exotic properties in the ground state, which might be important for a wide range of promising physical phenomena. For many applications, it is highly desirable to have such states in Dirac materials, but so far they have been reported only in some nonmagnetic Dirac systems. In this paper, we propose a realization of topologically protected spin-polarized flat bands generated by domain walls in planar magnetic topological insulators. Using first-principles material design, we suggest a family of intrinsic antiferromagnetic topological insulators with an in-plane sublattice magnetization and high Néel temperature. Such systems can host domain walls in a natural manner. For these materials, we demonstrate the existence of spin-polarized flat bands in the vicinity of the Fermi level and discuss their properties and potential applications.

Screw rotations in nonsymmorphic space group symmetries induce the presence of hourglass and accordion-shape band structures along screw invariant lines whenever spin-orbit coupling is non-negligible. These structures induce topological enforced Weyl points on the band intersections. In this work we show that the chirality of each Weyl point is related to the representations of the cyclic group on the bands that form the intersection. To achieve this, we calculate the Picard group of isomorphism classes of complex line bundles over the two-dimensional sphere with cyclic group action, and we show how the chirality (Chern number) relates to the eigenvalues of the rotation action on the rotation invariant points. Then we write an explicit Hamiltonian endowed with a cyclic action whose eigenfunctions restricted to a sphere realize the equivariant line bundles described before. As a consequence of this relation, we determine the chiralities of the nodal points appearing on the hourglass and accordion shape structures on screw invariant lines of the nonsymmorphic materials ${\mathrm{PI}}_3$ (SG: $\mathrm{P}{6}_3$), ${\mathrm{Pd}}_3\mathrm{N}$ (SG: $\mathrm{P}{6}_{3}22$), ${\mathrm{AgF}}_3$ (SG: $\mathrm{P}{6}_{1}22$), and ${\mathrm{AuF}}_3$ (SG: $\mathrm{P}{6}_{1}22$), and we corroborate these results with the Berry curvature and symmetry eigenvalues calculations for the electronic wave function.

The group V and VI transition metals share a common Fermi surface feature of hole ellipsoids at the $N$ point in the Brillouin zone. In clear contrast to the other Fermi surface sheets, which are purely of $d$ character, these arise from a band that has a significant proportion of $p$ character. By performing local density approximation (LDA), generalized gradient approximation (GGA), strongly constrained and appropriately normed (SCAN) meta-GGA, and $GW$ approximation calculations, we find that the $p$ character part of this band (and therefore the Fermi surface) is particularly sensitive to the exchange-correlation approximation. LDA and GGA calculations inadequately describe this feature, predicting $N$ hole ellipsoid sizes that are consistently too large in comparison to various experimental measurements, whereas quasiparticle self-consistent $GW$ calculations predict a size that is slightly too small (and non-self-consistent $GW$ calculations that use an LDA starting point predict a size that is much too small). Overall, for the metals tested here, SCAN provides the most accurate Fermi surface predictions, mostly correcting the discrepancies between measurements and calculations that were observed when LDA calculations were used. However, none of the tested exchange-correlation approximations succeeds in simultaneously bringing all of the measurable properties of these metals into good experimental agreement, particularly where magnetism is concerned. The SCAN calculations predict antiferromagnetic moments for Cr that are 3 times larger than the experimental value ($1.90{\mu }_B$ compared to $0.62{\mu }_B$).

The multiorbital Hubbard model in the strong-coupling limit is analyzed for the effectively antiferromagnetic Hund's coupling relevant to fulleride superconductors with three orbitals per molecule. The localized spin-orbital model describes the thermodynamics of the half-filled (three electron) state with total spin 1/2, composed of a singlon and a doublon placed on two of the three orbitals. The model is solved using the mean-field approximation, and magnetic and electric ordered states are clarified through the temperature dependences of the order parameters. Combining the model with the band structure from ab initio calculation, we also semiquantitatively analyze the realistic model and the corresponding physical quantities. In the A15-structure fulleride model, there is an antiferromagnetic ordered state, and subsequently the two-orbital ordered state appears at lower temperatures. It is argued that the origin of these orbital orders is related to the $T_h$ point-group symmetry. As for the fcc fulleride model, a time-reversal-broken orbital ordered state is identified. Whereas the spin degeneracy remains in our treatment for a geometrically frustrated lattice, it is expected to be lifted by some magnetic ordering or quantum fluctuations, but not by the spin-orbital coupling, which is effectively zero for fullerides in the strong-coupling regime.

We investigate an optically trapped exciton-polariton condensate and observe temporal coherence beyond 1 ns in duration. Due to the reduction of the spatial overlap with the thermal reservoir of excitons, the coherence time of the trapped condensate is more than an order of magnitude longer than that of an untrapped condensate. This ultralong coherence enables high-precision spectroscopy of the trapped condensate, and we observe periodic beats of the field correlation function due to a fine energy splitting of two polarization modes of the condensate. Our results are important for realizing polariton simulators with spinor condensates in lattice potentials.

Transition metal dichalcogenides (TMDs) are an exciting family of 2D materials; a member of this family, ${\mathrm{MoS}}_2$, became the first studied monolayer semiconductor. In this paper, a generalized phenomenological continuum approach for the optical vibrations of the monolayer TMDs valid in the long-wavelength limit is developed. The equation of motions for nonpolar and polar oscillations include the phonon dispersion up to a quadratic approximation in the phonon wave vector. On the other hand, the polar modes satisfy coupled equations for the displacement vector and the inner electric field. The two-dimensional phonon dispersion curves for in-plane and out-of-plane oscillations are thoroughly analyzed. The model parameters are fitted from density functional perturbation theory calculations. The current formalism provides an effective tool to describe the phonon dispersion curves around the $\mathrm{\Gamma }$ point of the Brillouin zone for a large group of members of the TMD monolayers. A detailed evaluation of the intravalley Pekar-Fröhlich and the $A_1$-homopolar mode deformation potential coupling mechanisms is performed. The effects of metal ions and chalcogen atoms on polaron mass and binding energy are studied. It is argued that both mechanisms should be considered for a correct analysis of the properties of the polaron or of any process that involves the intraband transitions assisted by the electron-phonon interaction.

Square-root topology is a recently emerged subfield describing a class of insulators and superconductors whose topological nature is only revealed upon squaring their Hamiltonians, i.e., the finite energy edge states of the starting square-root model inherit their topological features from the zero-energy edge states of a known topological insulator/superconductor present in the squared model. Focusing on one-dimensional models, we show how this concept can be generalized to $2^n$-root topological insulators and superconductors, with $n$ any positive integer, whose rules of construction are systematized here. Borrowing from graph theory, we introduce the concept of arborescence of $2^n$-root topological insulators/superconductors which connects the Hamiltonian of the starting model for any $n$ through a series of squaring operations followed by constant energy shifts to the Hamiltonian of the known topological insulator/superconductor, identified as the source of its topological features. Our work paves the way for an extension of $2^n$-root topology to higher-dimensional systems.

There has been interest in the spin transport properties of the Aubry-André-Harper model at high temperatures under weak integrability breaking, in particular for small interactions or small fields. We present results that show that the model is diffusive, meaning that the claimed superdiffusion is a finite-size effect.

The iron sulphide ${\mathrm{Fe}}_3{\mathrm{S}}_4$ (greigite) is similar to its oxide counterpart ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (magnetite) as to the crystal structure and ferrimagnetic order, but differs in electronic states. The ab initio calculations have evidenced $p$-type carriers at three spin-minority and three spin-majority Fermi surfaces, which is in contrast to the half-metallic character of magnetite with $n$-type carriers at three spin-minority Fermi surfaces. The transport properties including Hall and Nernst effects have been studied over the range 2–300 K by using nanogranular ceramics prepared by cold isostatic pressing of ${\mathrm{Fe}}_3{\mathrm{S}}_4$ particles with the mean crystallite size of $d_{\mathrm{XRD}}\approx 80$ and 30 nm, respectively. The samples show metalliclike electrical resistivity with large residual value at $T$ → 0 K. The $p$-type character of the charge carriers is reflected by the positive sign of both the thermopower and Hall effect. Temperature dependencies of the electrical resistivity, thermal conductivity, and thermopower are analyzed by considering processes of the grain boundary and defect intragrain scattering; simultaneously the role of magnons and their dynamics in electronic and heat transport is revealed. The Nernst and Hall effects show dominant contributions of anomalous type (ANE and AHE) with signs exactly opposite to those of ${\mathrm{Fe}}_3{\mathrm{O}}_4$, i.e., positive AHE and negative ANE in ${\mathrm{Fe}}_3{\mathrm{S}}_4$. The results are interpreted by evoking the original Callen treatment of thermoelectric and thermomagnetic phenomena using Onsager equations. Scaling between the longitudinal and transverse components of the electrical resistivity and thermoelectric conductivity tensors is checked. The analysis of the temperature dependent AHE using the relation between transverse and longitudinal resistivity ${\rho }_{yx}^A\left(T\right)\sim {\rho }_{xx}{\left(T\right)}^n$ gives the characteristic exponent $n=1.15$, which is close to the $n=1$ predicted by the skew-scattering mechanism.

A different variational approach is proposed at zero temperature for a finite density of charge carriers in order to study ground-state features of the Fröhlich model including electron-electron and electron-phonon interactions. Within the intermediate electron-phonon coupling regime characteristic of large polarons, the approach takes into account on the same footing polaron formation and polaron-polaron correlations which play a relevant role going from low to high charge densities. Including fluctuations on top of the variational approach, the electronic spectral function is calculated from the weak to the intermediate electron-phonon coupling regime finding a peak-dip-hump line shape. The spectra are characterized by a transfer of spectral weight from the incoherent hump to the coherent peak with decreasing the electron-phonon coupling constant or with increasing the particle density. Three different density regimes stem out: the first, at low densities, where the features of a single large polaron with a substantial incoherent spectral weight are not modified by charge carrier interactions; a second one, at intermediate densities, where the polaronic liquid shows a rapid crossover from incoherent to coherent dynamics; the third one, at high densities, where screening effects are so prominent that the system presents a conventional metallic phase. The results obtained in the low to intermediate density regime turn out to be relevant for the interpretation of recent tunneling and photoemission experiments in ${\text{SrTiO}}_3$-based systems.

We study the electronic structure of single-crystal ${\mathrm{Tb}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_3$, a non-charge-ordered mixed-valent semiconductor which exhibits a glassy magnetic ground state. We use the techniques of soft x-ray photoemission, hard x-ray photoemission, x-ray absorption, and resonant photoemission spectroscopy to investigate the occupied and unoccupied electronic states of ${\mathrm{Tb}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_3$. Core level photoemission and x-ray absorption spectroscopy allow us to determine the valence states of Tb, Sr, and Mn ions in ${\mathrm{Tb}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_3$. Model charge transfer multiplet calculations of core level photoemission and x-ray absorption spectra are employed to separate out the ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Mn}}^{4+}$ states and confirm their relative concentrations. Resonant photoemission spectroscopy across the Mn $2p\text{−}3d$ threshold shows clear resonant enhancement of the Mn $3d$ partial density of states and two-hole correlation satellites. A Cini-Sawatzky analysis gives on-site Coulomb energy $U_{dd}\sim 5.5\pm 0.2$ eV for the Mn $3d^n$ states and $U_{pd}$ = 0.7 $\mathrm{eV}\pm 0.2$ eV for the Mn $3d^{n+1}{\underline{L}}^1$ states. The O $1s\text{−}2p$ resonant photoemission is used to identify the O $2p$ two-hole correlation satellite which provides $U_{pp}\sim 3.4\pm 0.2$ eV for the O $2p$ states. Valence band photoemission indicates a small-gap semiconductor ($<100$ meV) consistent with electrical transport measurements. The estimated electronic structure parameters of the on-site Coulomb energies, in combination with the charge transfer energy and the hybridization strength obtained from the model calculations, indicate that ${\mathrm{Tb}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_3$ is a strongly correlated charge transfer type semiconductor.

Optically addressable spin-triplet defects in silicon carbide, such as divacancies and negatively charged nitrogen vacancy $\left({\mathrm{NV}}^{-}\right)$ allow to develop modern quantum technologies operating in the near-infrared range based on the well-developed semiconductor material. Here, by means of both high-frequency (94 GHz) pulsed electron paramagnetic resonance (EPR) and electron-nuclear double Rresonance (ENDOR) techniques the ground state properties of the negatively charged ${\mathrm{NV}}^{-}$ defect in $4H$-SiC were studied. We experimentally determined the ordering of the ground state spin sublevels and established the sign of the zero-field splitting to be positive as predicted by theory. Analysis of nuclear magnetic resonance transitions in ENDOR spectra allowed to determine the sign, symmetry, and absolute values of the hyperfine interaction of the ${\mathrm{NV}}^{-}$ defect electron spin with ${}^{14}\mathrm{N}$ nuclear spin as ${\mathit{A}}_{\parallel }=-1.142\mathrm{MHz}$ and ${\mathit{A}}_{\perp }=-1.184\mathrm{MHz}$. The absolute value of the nuclear quadrupole interaction constant reflecting an interaction between the ${}^{14}\mathrm{N}$ nuclear electric quadrupole moment with the electric field gradient was determined to be $|{\mathit{C}}_q|=2.44\mathrm{MHz}$. This large value is compatible with a threefold coordinated ${}^{14}\mathrm{N}$ nucleus with uniaxial symmetry and proves conclusively the existence of a nearestneighbor ${\mathrm{N}}_{\mathrm{C}}{\mathrm{V}}_{\mathrm{Si}}$ pair in the material. For this ${\mathrm{NV}}^{-}$ defect, an ensemble (Hahn-echo) coherence time of ${\mathit{T}}_{\text{2}}=49\mu \mathrm{s}$ was measured, a value which is in the range previously reported for silicon vacancy spin ensembles and slightly longer than ${\mathit{T}}_{\text{2}}=40\mu \mathrm{s}$ measured here on the divacancy spin ensemble.

The quantum confinement of Rydberg excitons is an important step towards exploiting their large nonlinearities for quantum applications. We observe Rydberg excitons in natural nanoparticles of ${\mathrm{Cu}}_2\mathrm{O}$. We resolve up to the principal quantum number $n=12$ in a bulk ${\mathrm{Cu}}_2\mathrm{O}$ crystal and up to $n=6$ in nanoparticles extracted from the same crystal. The exciton transitions in nanoparticles are broadened and their oscillator strengths decrease as $\propto n^{-4}$ compared to those in the bulk (decreasing as $\propto n^{-3}$). We explain our results by including the effect of quantum confinement of exciton states in the nanoparticles. Our results provide an understanding of the physics of ${\mathrm{Cu}}_2\mathrm{O}$ Rydberg excitons in confined dimensions.

The current-voltage ($IV$) characteristics beyond the linear response regime of magnetic tunnel junction (MTJ) is systematically investigated. We find a clear negative correlation between the two coefficients to characterize the linear ($I\propto V$) and the lowest-order nonlinear ($I\propto V^3$) currents, which holds regardless of the temperature and the thickness of the tunnel barrier. This observation cannot simply be explained by the standard tunneling model such as the Brinkman model, suggesting a mechanism intrinsic to MTJ. We propose a phenomenological model based on the Jullire model that attributes the observed negative correlation to the spin-flip tunneling assisted by a magnon. These results suggest a fundamental law between the linear and the nonlinear response of MTJ.

We discuss the generation of a spin current by an edge plasmon in a graphene ribbon, which is a kind of surface plasmon that is localized near the edges of the ribbon. In contrast with a surface plasmon on the surface of a three-dimensional metal, the electric field of the edge plasmon rotates as a function of the time in the plane of graphene, which means that the optical spin-angular momentum of the edge plasmon is out of plane. We found that the electric-field-induced spin current flows by the inverse Faraday effect between the edges of the ribbon with spin polarization of electrons in the out-of-plane direction. The symmetric mode of the edge plasmon gives a larger magnitude of the spin current than the antisymmetric mode does. Moreover, the magnitude and direction of the spin current are tunable not only by the frequency of the edge plasmon, but also by the Fermi energy of graphene, which enables application to a spin-switching device controlled by a gate voltage.