We study non-Hermitian Josephson junctions formed by multiple superconductors and discover the emergence of exceptional points entirely determined by the interplay of the distinct superconducting phases and non-Hermiticity due to normal reservoirs. In particular, in Josephson junctions with three and four superconductors, we find stable lines and surfaces of exceptional points protected by non-Hermitian topology and highly tuneable by the superconducting phases. We also discover that, in Josephson junctions formed by laterally coupled superconductors, exceptional points can result from hybridized Andreev bound states and lead to the enhancement of supercurrents controlled by dissipation. Our work unveils the potential of multiterminal Josephson junctions for realizing higher-dimensional topological non-Hermitian superconducting phenomena.

We present a generative diffusion model specifically tailored to the discovery of surface structures. The generative model takes into account substrate registry and periodicity by including fixed substrate atoms and $z$-directional confinement. Using a rotational equivariant neural network architecture, we design a method that trains a denoiser network for diffusion alongside a forcefield for guided sampling of low-energy surface phases. An effective data-augmentation scheme for training the denoiser network is introduced to allow for scaling the structure generation far beyond structure sizes represented in the training data. We showcase the generative model by investigating multiple surface systems and propose an atomistic structure model for a silver-oxide domain boundary of unprecedented size.

Starting from a low-energy continuum model for the band dispersion of the $2\times 2$ charge-ordered phase of the kagome metals ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ $(A=\mathrm{K}, \mathrm{Rb}, \mathrm{Cs})$, we show that nematicity can develop in this state driven either by three inequivalent $1\times 4$ charge fluctuations preemptive of a $1\times 4$ charge order (CO), or by an actual zero-momentum $d$-wave charge Pomeranchuk instability (PI). We perform an analysis that starts from a Kohn-Luttinger theory in the particle-hole sector, which allows us to establish a criterion for the development of an attractive nematic channel near the onset of the $1\times 4$ CO and near the $d$-wave charge PI, respectively. We derive an effective charge-fermion model for the $d$-wave PI with a nematic susceptibility given via a random phase approximation (RPA) summation. By contrast, for the finite momentum CO, the RPA scheme breaks down and needs to be improved upon by including Aslamazov-Larkin contributions to the nematic pairing vertex. We then move to the derivation of the Ginzburg-Landau potentials for the $1\times 4$ CO and for the $d$-wave PI, and we obtain the corresponding analytical expression for the nematic susceptibility at the nematic transition temperature $T$ $\sim T_{\text{nem}}$ in both cases. The nematic response functions obtained in this way are interpreted starting from the two charge-fermion models, and we underline under which assumptions one recovers the Ginzburg-Landau result. Finally, we show an enhancement of the nematic character that is rooted in the coupling of the order parameters to elastic deformations. Our work establishes a relation between the nematicity observed in some of the iron-based superconductors, where the nematic phase might be driven by spin fluctuations, and the vanadium-based kagome metals, where charge fluctuations likely induce nematicity. The two microscopic mechanisms we propose for the stabilization of the nematic state in ${A\mathrm{V}}_3{\mathrm{Sb}}_5$, i.e., the zero-momentum $d$-wave PI and the fluctuations of the finite momentum CO, are distinguishable by diffusive scattering experiments, meaning that it is possible to gauge which of the two theories, if any, is the most likely to describe this phase. Both mechanisms might also be relevant for the recently discovered titanium-based family $A{\mathrm{Ti}}_3{\mathrm{Sb}}_5$, where nematicity has also been observed.

Flat bands, particularly the class possessing nontrivial quantum geometry, attract wide interest in multidisciplinary fields as a fertile playground for exotic transport phenomena and correlated phases. The chiral symmetry provides a generic principle for realizing ideal flat bands at the boundary of a topological phase. However, boundary flat bands enforced by traditional chiral symmetry are trivial in quantum geometry as the symmetry operator is a constant unitary matrix. Recently, we generalized the chiral symmetry by allowing dependence on partial momentum components and introduced the concept termed subchiral symmetry. Notably, systems lacking chiral symmetry but possessing subchiral symmetry can have boundary flat bands with intriguing properties, such as topological spin textures and quantized $\pi$ Berry phases. This Letter reports an experimental realization and observation of such topological boundary flat bands and the concomitant topological spin textures in a two-dimensional circuit system. Our study provides a scheme for topologically nontrivial flat bands and a forward-looking experimental platform for the exploration of novel physics emerging in flat bands.

Nonreciprocal transport, characterized by its direction-selective nature, holds significant potential for applications in various devices. In this study, we investigate nonreciprocal heat transport in Majorana systems, specifically focusing on the Kitaev chiral spin liquid under external magnetic fields. Our theoretical examination focuses on effects of open boundaries in which the Majorana edge modes exist, and the inversion symmetry is broken, which leads to the Dzyaloshinskii-Moriya interaction (DMI). Through perturbation theory, we demonstrate that DMI induces asymmetric hopping, resulting in the asymmetry of the Majorana band. The results of nonreciprocal heat currents are presented for various directions of external magnetic fields, and we discuss the relation between the current and the field directions. The potential exists to manipulate both of the directions and magnitude of the nonreciprocal current by varying external magnetic fields and apply to heat transfer devices.

We report the magnetization and the ${}^{51}\mathrm{V}$ NMR measurements in the polar magnet $\mathrm{Ga}{\mathrm{V}}_4\mathrm{S}{\mathrm{e}}_8$ in which a magnetic skyrmion lattice appears in the structural domain with the polar axis parallel to the magnetic field. Although we successfully separate the ${}^{51}\mathrm{V}$ NMR signals in the domain from those in the other structural domains, only the high-frequency region of NMR spectrum is observed due to a significant increase of the spin-echo decay rate in the low-frequency region. In ${\mathbf{B}}_{\mathrm{ext}}\parallel \left[111\right]$, we find the NMR signals from the supermagnetized cycloidal state in the parallel domains as well as from the conical state in domains where the polar axis is tilted from the magnetic field. No NMR signal from the skyrmion lattice state is observed, suggesting a significant increase of the decay rate by additional low-energy excitations caused by dynamics of the skyrmions. In ${\mathbf{B}}_{\mathrm{ext}}\parallel \left[001\right]$, where all the structural domains are magnetically equivalent, multiple NMR peaks converge into one peak at the saturation magnetic field. This field dependence is explained by the closing of magnetic cones as approaching the forced-ferromagnetic state.

The spatial structure of in-gap Yu-Shiba-Rusinov (YSR) bound states induced by a magnetic impurity in a superconductor is the essential ingredient for the possibility of engineering collective impurity states. Recently, a saddle-point approximation [M. Uldemolins et al., Phys. Rev. B 105, 144503 (2022)] revealed how the spatial form of a YSR state is controlled by an anisotropic exponential decay length, and an anisotropic prefactor, which depends on the Fermi velocity and Fermi-surface curvature. Here we analyze scanning tunnel microscope (STM) data on YSR states in ${\mathrm{NbSe}}_2$, focusing on the key issue that the exponential decay length predicted theoretically from the small superconducting gap is much larger than the observed extent of YSR states. We confirm that the exponential decay can be neglected in the analysis of the anisotropy. Instead, we extract the anisotropic prefactor directly from the data, matching it to the theoretical prediction, and we establish that the theoretical expression for the prefactor alone captures the characteristic flowerlike shape of the YSR state. Surprisingly, we find that up to linear order in the superconducting gap the anisotropic prefactor that determines the shape of YSR states is the same as the anisotropic response to the impurity in the underlying normal metal. Our work points out the correct way to analyze STM data on impurities in small-gap superconductors and reveals the importance of the normal band structure's curvature and Fermi velocity in designing multi-impurity in-gap states in superconductors.

We address the topological classification of one-dimensional chiral symmetric interfaces embedded into a two-dimensional substrate. A proof of the validity of a topological classification based on the Green's function by explicit evaluation of the topological invariant is presented. Further, we show that due to entanglement between the in-gap modes and the substrate, the full physics of the substrate that is contained in the Green's function is required. This is done by considering a classification scheme derived from the reduced ground state projector, for which we show that an uncritical handling produces erroneous changes in the topological index due to entanglement driven gap closures. We illustrate our results by applying them to a tight-binding model of a spiral magnetic interface in a $s$-wave superconductor.

I present a tensorial approach to the description of $\mathbf{k}/–\mathbf{k}$-symmetric, time-reversal-odd splitting of electronic bands in magnetic materials, which can be of nonrelativistic origin and was recently given the name of “altermagnetism”. I demonstrate that tensors provide a general framework to discuss magnetic symmetry using both spin groups and magnetic point groups, which have often been contrasted in recent literature. I also provide a natural classification of altermagnets in terms of the lowest-order tensorial forms that are permitted in each of the 69 altermagnetic point groups. This approach clarifies the connection between altermagnetism and well-known bulk properties, establishing that the vast majority of altermagnetic materials must also be piezomagnetic and MOKE-active, and provides a rational criterion to search for potential altermagnets among known materials and to test them when the magnetic structure is unknown or ambiguous.

We performed a comprehensive study of light-induced superconducting-like responses in La-based cuprate superconductors, $\mathrm{L}{\mathrm{a}}_{2-x-y}\mathrm{N}{\mathrm{d}}_y\mathrm{S}{\mathrm{r}}_x\mathrm{Cu}{\mathrm{O}}_4$, which exhibit charge stripe orders or a short-range charge density wave (CDW) order depending on the concentration of Nd and Sr, by using near-infrared optical pump and terahertz probe spectroscopy. The light-induced plasma edge was observed in the $c$-axis terahertz reflectivity for all the samples far above $T_c$, regardless of long-range stripe or short-range CDW order. Remarkably, the frequency of light-induced plasma edge above $T_c$ coincides with that of Josephson plasma resonance of $\mathrm{L}{\mathrm{a}}_{2-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Cu}{\mathrm{O}}_4$ at the similar doping in the low-temperature superconducting phase, imposing a strong constraint on the interpretation of the phenomenon. We elucidated a close correlation between the emergence of the light-induced $c$-axis plasma edge and the CDW order or fluctuations in the temperature-doping phase diagram, unveiling the intimate interplay between the equilibrium CDW and the light-induced coherent charge carriers along the $c$ axis in nonequilibrium. The possibility of the existence of incoherent Cooper pairs above $T_c$ that show up upon the photoexcitation is discussed from the optical conductivity analysis.

The evolution of charge and orbital ordering phenomena in optimally doped $R_{5/8}{\mathrm{Ca}}_{3/8}{\mathrm{MnO}}_3$ (RCMO, $R=\text{rare earth}$) manganite perovskites has been investigated through average structure synchrotron x-ray and neutron powder diffraction techniques. We demonstrate the intricate relationship between the $B{\mathrm{O}}_6$ octahedral rotation magnitude and lattice strain distortions acting in this series and how they tune macroscopic signatures describing ordering behavior. Through careful symmetry-motivated crystallographic analysis, we show that for the range of RCMO compositions which famously contain maxima in the colossal magnetoresistance (CMR) response, their lattice strain states are in close proximity to that associated with a novel orbital order:charge disordered state we have recently unveiled in the quadruple manganite perovskites ${\mathrm{Na}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Mn}}_7{\mathrm{O}}_{12}$. We establish that this order is the primary state which competes with the ferromagnetic metallic state which ultimately leads to phase coexistence and the emergence of CMR. Our results lend themselves to aiding a further understanding of how particular chemical complexities can control charge and orbital ordering phenomena and also the general properties of manganite perovskites and other related systems via strain effects.

To investigate the role of the excitons for the origin of the pressure-induced phase transition (BGT) from the black-colored insulator (BI) to the golden-yellow-colored metal (GM) of samarium monosulfide, optical reflectivity, Sm $3d$ x-ray absorption spectroscopy (XAS), and x-ray diffraction (XRD) with the creation of excitons by photoexcitation (PE) are reported. In the pump-probe reflectivity measurement, following a huge reflectivity change of about 22%, three different relaxation times with a vibration component were observed. The fast component with the relaxation time ($\tau$) of less than 1 ps is due to the excitation and relaxation of electrons into the conduction band, and the slowest one with $\tau >\mathrm{several}$ 100 ps originates from the appearance of the photo-induced (PI) state. The components with $\tau \sim 10$ ps and vibration originate from the appearance of the PI state and the interference between the reflection lights at the sample surface and the boundary between the BI and PI states, suggesting that the electronic structure of the PI phase is different from that of the BI state. XAS spectra indicate that the Sm mean valence is shifted from the ${\text{Sm}}^{2+}$ dominant to the intermediate between ${\text{Sm}}^{2+}$ and ${\text{Sm}}^{3+}$ by PE but did not change to that of the GM phase across BGT, consistent with the reflectivity data. The XRD result after PE shows that the PI state has much less lattice contraction than the GM phase. These results suggest that the BGT cannot be achieved solely by creating excitons after PE but requires other effects, such as a lattice contraction.

We investigate the emergence of helical edge modes in a Heisenberg antiferromagnet on a triangular lattice, driven by a topological mechanism similar to that proposed by Dong et al. [Phys. Rev. Lett. 130, 206701 (2023)] for chiral spin waves in ferromagnets. The spin-frame field theory of a three-sublattice antiferromagnet allows for a topological term in the energy that modifies the boundary conditions for certain polarizations of spin waves and gives rise to edge modes. These edge modes are helical: modes with left and right circular polarizations propagate in opposite directions along the boundary in a way reminiscent of the electron edge modes in two-dimensional topological insulators. The field-theoretic arguments are verified in a realistic lattice model of a Heisenberg antiferromagnet with superexchange interactions that exhibits helical edge modes. The strength of the topological term is proportional to the disparity between two inequivalent superexchange paths. These findings suggest potential avenues for realizing magnonic edge states in frustrated antiferromagnets without requiring Dzyaloshinskii-Moriya interactions or nontrivial magnon band topology.

Sum rules for linear response functions give powerful and experimentally relevant relations between frequency moments of response functions and ground-state properties. In particular, renewed interest has been drawn to optical conductivity and density-density sum rules and their connection to quantum geometry in topological materials. At the same time, recent studies have also illustrated the connection between quantum geometry and second-order nonlinear response functions in quantum materials, motivating the search for exact sum rules for second-order response that can provide experimental probes and theoretical constraints for geometry and topology in these systems. Here, we begin to address these questions by developing a general formalism for deriving sum rules for second-order response functions. Using generalized Kramers-Kronig relations, we show that the second-order Kubo formula can be expressed in terms of a spectral density that is a sum of Dirac delta functions in frequency. We show that moments of the spectral density can be expressed in terms of averages of equal-time commutators, yielding a family of generalized sum rules; furthermore, these sum rules constrain the large-frequency asymptotic behavior of the second-harmonic generation rate. We apply our formalism to study generalized $f$-sum rules for the second-order density-density response function and the longitudinal nonlinear conductivity. We show that for noninteracting electrons in solids, the generalized $f$-sum rule can be written entirely in terms of matrix elements of the Bloch Hamiltonian. Finally, we derive a family of sum rules for rectification response, determining the large-frequency asymptotic behavior of the time-independent response to a harmonic perturbation.

This paper presents theoretical and experimental studies on the superconductivity of $\mathrm{Pb}{}_{0.64}{\mathrm{Bi}}_{0.36}$ alloy, which is a prototype of strongly coupled superconductors and exhibits one of the strongest coupling under ambient pressure among the materials studied so far. The critical temperature, the specific heat in the superconducting state, and the magnetic critical fields are experimentally determined. Deviations from the single-gap $s$-wave BCS-like behavior are observed. The electronic structure, phonons, and electron-phonon interactions are analyzed in relation to the metallic Pb, explaining why the Pb-Bi alloy exhibits such a large value of the electron-phonon coupling parameter $\lambda \simeq 2$. Superconductivity is studied using the isotropic Eliashberg formalism as well as the anisotropic density functional theory for superconductors. We find that while Pb is a two-gap superconductor with well-defined separate superconducting gaps, in the Pb-Bi alloy an overlapped three-gap-like structure is formed with a strong anisotropy. Furthermore, the chemical disorder, inherent to this alloy, leads to strong electron scattering, which is found to reduce the critical temperature.

The ${\mathrm{NV}}^{-}$ color center in diamond has been demonstrated as a powerful nanosensor for quantum metrology due to the sensitivity of its optical and spin properties to external electric, magnetic, and strain fields. In view of these applications, we use quantum embedding to derive a many-body description of strain- and electric-field-induced Stark effects on the ${\mathrm{NV}}^{-}$ center. We quantify how strain longitudinal to the axis of ${\mathrm{NV}}^{-}$ shifts the excited states in energy, while strain with a component transverse to the ${\mathrm{NV}}^{-}$ axis splits the degeneracies of the ${}^{3}E$ and ${}^{1}E$ states. The largest effects are for the optically relevant ${}^{3}E$ manifold, which splits into $E_x$ and $E_y$ with transverse strain. From these responses we extract strain susceptibilities for the $E_{x/y}$ states within the quasilinear regime. Additionally, we study the many-body dipole matrix elements of the ${\mathrm{NV}}^{-}$ and find a permanent dipole 1.6 D at zero strain, which is somewhat smaller than that obtained from recent density functional theory calculations. We also determine the transition dipole between the $E_x$ and $E_y$ and how it evolves with strain.

We present a minimal pole method for analytically continuing matrix-valued imaginary frequency correlation functions to the real axis, enabling precise access to off-diagonal elements and thus improving the interpretation of self-energies and susceptibilities in quantum simulations. Traditional methods for matrix-valued analytic continuation tend to be either noise sensitive or make ad hoc positivity assumptions. Our approach avoids these issues via the construction of a compact pole representation with shared poles through exponential fits, expanding upon prior work focused on scalar functions. We test our method across various scenarios, including fermionic and bosonic response functions, with and without noise, and for both continuous and discrete spectra of real materials and model systems. Our findings demonstrate that this technique addresses the shortcomings of existing methodologies, such as artificial broadening and positivity violations. The paper is supplemented with a sample implementation in python.

We demonstrate the nonreciprocity of electrically and thermally generated incoherent magnon transport using the magnetization direction of a Py wire placed on top of an ultrathin YIG film. We show that the transport properties of thermally generated magnons under a Py wire depend on the relative orientation between the temperature gradient and the Py-magnetization direction. The symmetries of this nonreciprocal magnon transport match with those predicted by the remote dipolar interaction between YIG and Py magnons, controlled by the chirality of the YIG magnon dipolar stray fields. We also show that the directional magnon generation by the spin Seebeck effect from the Py wire displays the symmetries expected from the chiral spin Seebeck effect.

Magnetic skyrmions are chiral spin textures which have attracted intense research for their fundamentally novel physics and potential applications as spintronic information carriers. The stability which makes them so potentially useful is a result of their underlying nontrivial topology. While skyrmions were originally predicted and observed in crystalline materials lacking inversion symmetry, some of the most promising host systems for skyrmions are multilayer thin films, where skyrmions have been stabilized at ambient conditions, which is critical for their use in real-world devices. The skyrmions found in multilayer thin films have additional three-dimensional structure, with their domain wall helicities twisting through the thickness of the film to create a hybrid skyrmion composed of a Bloch-type core with Néel-type caps of opposite chiralities at the surfaces. In this paper, we show that this three-dimensional variation creates additional knotted topological structure, providing an explanation for their exceptional stability in ambient conditions. We show that hybrid skyrmions can be described as half-integer hopfions, and that their field lines have the knotted structure of the Hopf fibration. Furthermore, we show that the topological charge of partially twisted hybrid skyrmions can be related to the domain wall helicity at the surfaces, providing a straightforward way to connect experimental measurements to underlying topology.

We investigate the entanglement properties of the non-Hermitian Su-Schrieffer-Heeger model from the perspective of the generalized Brillouin zone (GBZ). The non-Bloch entanglement entropy is defined on a quasireciprocal lattice, obtained by performing an ordinary Fourier transformation on the non-Bloch Hamiltonian. We demonstrate that the broken bulk-boundary correspondence is recovered in terms of the non-Bloch entanglement entropy. When the GBZ is circular, we show that the non-Bloch entanglement entropy is well-defined (real and positive-definite) in large parameter regions, except close to the exceptional points (EPs). In the critical region, we found that each Fermi point contributes precisely 1 to the central charge $c$ of the logarithmic scaling. At the EP, the central charge becomes negative due to the presence of the exceptional bound state. For the case of a noncircular GBZ, long-range hopping emerges in the quasireciprocal lattice and the von Neumann entropy on the GBZ is no longer real. However, the non-Bloch edge entanglement entropy remains real, which serves as a reliable topological indicator and respects the bulk-boundary correspondence. We compute the topological phase diagram and reveal the critical behavior along the exceptional phase boundaries.