The Euler class is a $\mathbb{Z}$-valued topological invariant that characterizes a pair of real bands in a two-dimensional Brillouin zone. One of the symmetries that permits its definition is ${\mathcal{C}}_{2z}\mathcal{T}$, where ${\mathcal{C}}_{2z}$ denotes a twofold rotation about the $z$ axis and $\mathcal{T}$ denotes time-reversal symmetry. Here, we study three-dimensional spinless insulators characterized by the Euler class, focusing on the case where additional ${\mathcal{C}}_{4z}$ or ${\mathcal{C}}_{6z}$ rotational symmetry is present, and investigate the relationship between the Euler class of the occupied bands and their rotation eigenvalues. We first consider two-dimensional systems and clarify the transformation rules for the real Berry connection and curvature under point-group operations, using the corresponding sewing matrices. Applying these rules to ${\mathcal{C}}_{4z}$ and ${\mathcal{C}}_{6z}$ operations, we obtain explicit formulas that relate the Euler class to the rotation eigenvalues at high-symmetry points. We then extend our analysis to three-dimensional systems, focusing on the difference in the Euler class between the two $C_{2z}T$-invariant planes. We derive analytic expressions that relate the difference in the Euler class to two types of representation-protected invariants and analyze their phase transitions. We further construct tight-binding models and perform numerical calculations to support our analysis and elucidate the bulk-boundary correspondence.

Compelling evidence exists for electronic phase separation in cuprate high-$T_c$ superconductors, emerging near 1/8 hole doping. At these dopings and low temperatures, intertwined charge and spin stripes coexist with more uniformly doped regions in the two-dimensional (2D) copper-oxide planes. Each region is capable of developing superconducting pairing, either as a pair density wave (PDW) within the stripes or as a uniform $d$-wave condensate ($d$-SC) in the more homogeneous regions. Using neutron scattering on single crystals of ${\mathrm{La}}_{1.875-y}{\mathrm{Nd}}_y{\mathrm{Sr}}_{0.125}{\mathrm{CuO}}_4$, we demonstrate that the onset temperatures for spin stripe order ($T_N$) and superconductivity ($T_c$) merge as the average ordered moment vanishes in LSCO ($y=0$), whereas Nd doping stabilizes static stripe order and suppresses $T_c$. Because the spin stripes possess the same in-plane periodicity ($8a$) as the PDW and establish the framework within which the PDW resides, the stabilization of spin stripe order enhances PDW correlations. Thus, the competition between $d$-wave pairing in the uniform regions and PDW pairing in the stripe-ordered regions can be controlled by the Nd concentration in ${\mathrm{La}}_{1.875-y}{\mathrm{Nd}}_y{\mathrm{Sr}}_{0.125}{\mathrm{CuO}}_4$, allowing the superconducting $T_c$ to vary by nearly an order of magnitude at a fixed 1/8-hole doping.

We present a first-principles study based on density functional theory (DFT) on the electronic and structural properties of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$, a layered transition metal chalcogenide that has been considered as a possible candidate for an excitonic insulator. Our systematic DFT results however provide a nonexcitonic mechanism for the experimentally observed electronic and structural phase transitions in ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$, in particular explaining why sulfur substitution of selenium reduces the distortion angle in the low-temperature phase and potassium dosing closes the gap in the electronic structure. Moreover, the calculations show that these two effects couple to each other. Further, our first-principles calculations predict several changes in both the crystal structure and electronic structure under the effects of uniform charge dosing and uniaxial strain, which could be tested experimentally.

The $R_5{\mathrm{Pb}}_3\mathrm{O}$ family was discovered decades ago, but has remained largely unexplored. Here, we report single-crystal growth and basic characterization for the La and Ce members of this family. At room temperature, these compounds adopt a tetragonal structure $(I4/mcm)$, where $R$ and Pb atoms form linear chains along the $c$ axis. We identify a second-order structural phase transition at 260 and 145 K for $R=$ La and Ce, respectively. Single-crystal x-ray diffraction reveals a lattice modulation below the transition temperature, resulting in $R\text{−}\mathrm{Pb}$ pairs in the $z$ direction. The broken symmetry in the low-temperature phases results in a primitive structure with space group $P4/ncc$. Transport and diffraction measurements, in agreement with density functional theory calculations, support that the $R_5{\mathrm{Pb}}_3\mathrm{O}$ $(R=\mathrm{La} \text{and} \mathrm{Ce})$ series hosts an electron-phonon coupling driven charge density wave (CDW) at low temperatures. The CDW ordering temperature is suppressed by more than 100 K by the La to Ce substitution, suggesting high-pressure sensitivity. Therefore, this family offers the potential for investigating competing orders in oxides, with heavier rare-earth members still to be explored.

The tremendous interest in the technology and underlying physics of all-optical switching of magnetization brings up the question of how fast the switching can occur and how high the frequency of writing the data with ultrafast laser pulses can be. To answer this question, we excited a GdFe ferrimagnetic alloy, the magnetization of which can be reversed by single laser pulses, a phenomenon known as toggle switching, by two pulses with a certain time delay in between. Using photoemission electron microscopy and Kerr microscopy for magnetic domain imaging, we explore the effects of varying fluences of the first and second pulse as well as the time delay between the two pulses. Our results show that when the fluence of the first pulse is adjusted just above the threshold of single-pulse switching, a second pulse with about $60\%$ of the fluence of the first pulse, arriving only $3\mathrm{p}\mathrm{s}$ later, switches the magnetization back. This reswitching persists up to about $40\mathrm{p}\mathrm{s}$ pulse separation. We interpret the latter as the time required for the sample to cool down and remagnetize after the first pulse. For shorter time delays below about $2\mathrm{p}\mathrm{s}$, no reswitching occurs. However, the effect of the two pulses adds up, enabling switching for fluences of both pulses below the threshold for single-pulse switching. Atomistic spin dynamics simulations are used to model the experimental data, successfully confirming our results.

${\mathrm{CuGeO}}_3$ has long been studied as a prototypical example of the spin-Peierls transition in a $S=1/2$ Heisenberg chain. Despite intensive investigation of this quasi-one-dimensional material, systematic measurements and calculations of the phonon excitations in the dimerized phase have not to date been possible, leaving certain aspects of the spin-Peierls phenomenon unresolved. We perform state-of-the-art density functional theory (DFT) calculations to compute the electronic structure and phonon dynamics in the low-temperature dimerized phase. We also perform high-resolution neutron spectroscopy to measure the full phonon spectrum over multiple Brillouin zones. We find excellent agreement between our numerical and experimental results that extend to all measurement temperatures. Notable features of our phonon spectra include a number of steeply dispersive modes, nonmonotonic dispersion features, and specific phonon anticrossings, which we relate to the mode eigenvectors. By calculating the magnetic interactions within DFT and studying the effects of different phonon modes on the superexchange paths, we discuss the possibility of observing spin-phonon hybridization effects in experiments performed both in and out of equilibrium.

In conventional magnetic tunnel junctions (MTJs), the tunnel magnetoresistance (TMR) typically increases with barrier thickness as electron transmission in the antiparallel configuration decays faster than that of the parallel configuration. In this work, we reveal an anomalous scaling effect in altermagnetic tunnel junctions (AMTJs), where the TMR decreases anomalously with an increasing barrier thickness. The anomalous scaling originates from the overlapping spin-split branches forming a transmission path that cannot be suppressed in the antiparallel state. Such phenomenon is explained by a double-barrier model and is further demonstrated using ab initio quantum transport simulations in two-dimensional ${\mathrm{V}}_2{\mathrm{Te}}_2\mathrm{O}/{\mathrm{Cr}}_2{\mathrm{Se}}_2\mathrm{O}/{\mathrm{V}}_2{\mathrm{Te}}_2\mathrm{O}$ and ${\mathrm{V}}_2{\mathrm{Te}}_2\mathrm{O}/\mathrm{ZnSe}/{\mathrm{V}}_2{\mathrm{Te}}_2\mathrm{O}$ AMTJs. Our work identifies a peculiar unexpected transport characteristic of an AMTJ, providing a fundamental limit on AMTJ device design and illustrating the potential optimal design of an AMTJ at the ultrascaled monolayer limit.

Helimagnets, characterized by a helical arrangement of magnetic moments, possess unique internal degrees of freedom, including the spin phase, defined by the phase of the helical magnetic structure. Electrical detection of the spin phase is essential for both practical applications and fundamental research in helimagnets. Here, we demonstrate the electrical detection of the spin phase in a van der Waals nanoscale chiral helimagnet ${\mathrm{CrNb}}_3{\mathrm{S}}_6$ using nonlocal spin valve measurements. Due to the short spin diffusion length in ${\mathrm{CrNb}}_3{\mathrm{S}}_6$ ($\sim 5$ nm), the surface magnetic moment direction, which corresponds to the spin phase, can be detected via spin currents. The experimentally observed magnetic field dependence of the nonlocal spin valve signal is consistent with that of the surface magnetic moment in the helical magnetic structure, as supported by micromagnetic simulations. Our results establish spin currents as a powerful tool for detecting the spin phase in helimagnets, opening avenues for utilizing the spin phase as a novel internal degree of freedom in nanoscale spintronic devices.

Motivated by the highest superconducting transition temperature ($T_c$) in multilayer cuprates, we investigated the trilayer Hubbard model by adopting large-scale dynamical cluster quantum Monte Carlo simulations. Focusing on the systems with hole dopings within the two outer layers (OLs) higher than the inner layer (IL), which is believed to be relevant to the realistic multilayer cuprates, our exploration discovered that the IL and OL manifest strong differentiation in a wide range of hole doping combinations. Specifically, the OLs remain metallic while the IL shows a distinct transition from the pseudogap to superconducting state. More importantly, the highest $T_c$ of the composite trilayer system can be largely enhanced compared to the single layer model and the imbalanced hole dopings between IL and OL are generically beneficial for global superconductivity (SC). We further provide strong numerical evidence on the possibility of $d$-wave SC solely hosted in the IL. Our investigation provides insight into the origin of highest $T_c$ in multilayer cuprates.

In this work, we investigate the softening of the in-plane transverse acoustic phonon driven by electronic nematicity in ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$ using inelastic x-ray scattering, with a focus on the optimally doped sample ($x=0.31$) sample—a system exhibiting signatures of a putative nematic quantum critical point and minimal disorder among iron pnictides. We observe only a modest softening of the phonon frequency and no evidence of critical damping, suggesting that the nematic quantum critical fluctuations couple only weakly to the lattice from our quantum critical model. Given the close proximity of the structural and magnetic transition temperatures in the underdoped sample—which implies that spin-nematic fluctuations couple strongly to the lattice—we conjecture that the quantum critical nematic fluctuations are predominantly orbital in origin.

Infinite-layer (IL) nickelates have rapidly emerged as a new class of superconductors. However, due to the technical challenges of their topotactic synthesis, they have so far been realized primarily as thin films or polycrystalline powder samples, limiting comprehensive investigations of fundamental physical properties such as the lattice dynamics. Here, we present a time-of-flight inelastic neutron scattering study on a sample composed of a large number of coaligned bulk crystals of the IL nickelate ${\mathrm{LaNiO}}_2$. We observe several dispersive phonon branches, which are in good agreement with lattice dynamical calculations based on density-functional perturbation theory. In addition, we compare the characteristics of selected ${\mathrm{LaNiO}}_2$ phonon modes to those of isostructural cuprate superconductors. Our findings provide a reference point for future experimental and theoretical efforts aimed at understanding the interplay between lattice dynamics and electronic properties in IL nickelates.

Nonlinear transmission measurements of silicon are used to determine the two- and three-photon absorption coefficients for photon energies above the indirect band gap of Si in the range of $1.14–2.07\mathrm{eV}$. By careful characterization of the temporal and spatial profiles of the ultrashort optical pulses, the nonlinear transmission as a function of peak optical intensity can be determined. Two- and three-photon absorption coefficients are acquired by fitting both an analytical and numerical model to the transmission traces, from which two distinct spectral regimes emerge with a clear threshold at $1.7\mathrm{eV}$—this corresponds to half the direct band gap in Si. At photon energies above the threshold, the nonlinear transmission traces are dominated by two-photon absorption, whereas below the threshold three-photon absorption is dominant with a nondetectable contribution from indirect two-photon absorption. This result is at variance with the current understanding of above-band-gap nonlinear absorption in Si, which is exclusively attributed to two-photon absorption processes.

We investigate single-photon nonlinear refractive index change and frequency shift of epsilon-near-zero (ENZ) sub-wavelength nanoparticles. We apply the rigorous quantum Langevin-noise approach in the framework of Green's tensor quantization method to realistic ENZ materials with causal dispersion and derive closed-form analytical solutions for structures with spherical geometry. This is achieved by employing a fully nonperturbative methodology for the analysis of open quantum systems with single-photon Kerr-type nonlinearity. The analytical results are validated numerically using the established quasi-normal-mode expansion method and extended to nonspherical nanoparticle geometries that can be experimentally fabricated using state-of-the-art electron-beam lithography. Our findings establish a rigorous benchmark for understanding single-photon nonlinear optical effects in Kerr-type ENZ nanostructures with losses and are of importance to emerging quantum technology applications, including on-chip single-photon nondemolition detection, quantum sensing, spectroscopy, and controlled quantum gates driven by photon blockade effects at the nanoscale.

Brillouin light scattering is a powerful technique to measure microwave excitations present in a magnetic system. In microfocused mode, the light is focused on the sample using a microscope objective. This substantially accelerates the measurement but results in mixing the response of all microwave excitations into a single spectrum, such that modeling is required to disentangle the contribution of each spin wave. By assuming that a spectrum collected in microfocused mode can be approximated as the sum of all back-scattering spectra that can be collected by the microscope objective, we develop a simple and direct way of interpreting spectra. The model is compared to experimental data collected on a 50-nm-thick CoFeB magnetic film. The model allows an understanding of the influence of the optical properties of a sample, of the dispersion relation of the spin wave eigenexcitations, and of their thickness profiles, as well as of their populations onto the magnitudes and the line shapes of the characteristic features of a spectrum.

Topological insulators (TIs) of the bismuth telluride type are the most investigated among TIs. However, the studies were focused solely on the natural cleavage surface (111) which exhibits a slightly anisotropic Dirac state. Being a strong TI, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ should support topological surface states (TSSs) on any surface. Up to now, direct ARPES measurements of such surfaces have not been performed due to the complexity of preparing the surfaces different from (111). The few early density functional theory (DFT) studies were done for arbitrary side surfaces. In this study, we succeeded in preparing a side surface of a satisfactory quality for ARPES measurements. Also, using the DFT calculations, we explicitly showed the cause of the giant anisotropy of the TSS and its dependence on the projection of the bulk states onto the selected crystallographic plane. Calculations of the surface spectra for several planes that can form facets on the prepared side surface made it possible to identify the $\left(10\overline{1}\right)$ surface, the spectrum of which is in perfect agreement with the ARPES measurements.

The first-principles calculation of Bloch state derivatives is numerically challenging yet indispensable for evaluating the quantum response functions of materials. Here, we propose a band-resolved automatic differentiation (BRAD) approach for efficiently calculating quantum response properties, by developing a forward-mode automatic differentiation framework based on a modified Nelson's method. The BRAD approach offers two key advantages over existing methods: (i) The calculation is carried out in a band-by-band manner, removing the need for a time-consuming full-band summation. (ii) Bloch state derivatives can be computed to arbitrary orders through automatic differentiation, eliminating the need for manual analytical derivations and complex computational implementations. We demonstrate the reliability of our approach by computing the nonlinear optical responses of monolayer ${\mathrm{WS}}_2$ and further highlight its usefulness in studying high-order quantum response properties.

We investigate the emergence of topological and correlated electronic phases in a twisted bilayer Kagome lattice constructed from carbonyl-triphenyl (CTP) supermolecules. Using symmetry-adapted moiré supercells and ab initio electronic structure calculations, we find that moiré modulation preserves the underlying Kagome node-localized wavefunctions while introducing momentum-selective interlayer hybridization. At a commensurate twist angle of $\theta =10.{83}^{\circ }$, a nontrivial topological index ${\mathbb{Z}}_2=1$ is found from the non-Abelian Wilson loop analysis across the combined subspace of the near Fermi flatbands (FFBs). In contrast, at a twist angle of $\theta =11.{46}^{\circ }$, while the net Chern number ($C$) of the full subspace remains zero, individual FFB acquires nonzero $C=\pm 1$ despite the absence of explicit spin polarization. This topological response arises from Berry curvature redistribution driven by moiré-induced inversion symmetry breaking. Both topological phases are accompanied by the van Hove singularities near the Fermi level, suggesting a favorable environment for interaction-driven instabilities. Our results establish twisted supermolecular Kagome bilayers as a chemically tunable platform for realizing frustration-enhanced topological states and potential correlated quantum phases in organic systems.

Charge carrier mobilities are critical parameters in halide perovskite solar cells, governing their average carrier velocity under an applied electric field and overall efficiency. Recent advances in first-principles calculations of electron-phonon interactions and carrier mobilities have enabled predictive computations for perovskite solar cells. However, the flexible octahedral frameworks and cationic displacements in these materials challenge the harmonic approximation, leading to significant difficulties in accurately calculating transport properties. To address these issues, we combine temperature-dependent effective potentials with the ab initio Boltzmann transport equations to compute carrier mobilities in a representative lead-free perovskite, ${\mathrm{CsSnBr}}_3$. At room temperature, the electron (hole) Hall mobilities in ${\mathrm{CsSnBr}}_3$ are 106 (256) ${\mathrm{cm}}^2/\left(\mathrm{Vs}\right)$ when neglecting anharmonic effects and 59 (145) ${\mathrm{cm}}^2/\left(\mathrm{Vs}\right)$ when included. This overestimation of the harmonic approximation arises from the neglect of scattering coming from soft modes. We provide a workflow for performing first-principles carrier mobility calculations in anharmonic systems, advancing the predictive modeling of perovskite solar cells.

We measure the spin-wave Doppler shift induced by the transfer of angular momentum from the diffusive spin-polarized electric current onto coherent spin waves in epitaxial MgO/Fe/MgO thin films. We follow this Doppler shift as a function of the temperature and determine that the degree of spin polarization of the current increases from 77 to $86\%$ when cooling the device from 303 to 10 K. Interpreting these measurements within the two-current model, we separate the contributions from electron-surface, electron-phonon, and electron-magnon scatterings to the spin-dependent resistivity of iron.

We study the dissipative dynamics of a class of interacting “gamma-matrix” spin models coupled to a Markovian environment. For spins on an arbitrary graph, we construct a Lindbladian that maps to a non-Hermitian model of free Majorana fermions hopping on the graph with a background classical ${\mathbb{Z}}_2$ gauge field. We show, analytically and numerically, that the steady states and relaxation dynamics are qualitatively independent of the choice of the underlying graph, in stark contrast to the Hamiltonian case. We also show that the exponentially many steady states provide a concrete example of mixed-state topological order, in the sense of strong-to-weak spontaneous symmetry breaking of a one-form symmetry. While encoding only classical information, the steady states still exhibit long-range quantum correlations. Afterward, we examine the relaxation processes toward the steady state by numerically computing decay rates, which we generically find to be finite, even in the dissipationless limit. However, we identify symmetry sectors where fermion-parity conservation is enhanced to fermion-number conservation, where we can analytically bound the decay rates and prove that they vanish in the limits of both infinitely weak and infinitely strong dissipation. Finally, we show that while the choice of coherent dynamics is very flexible, exact solvability strongly constrains the allowed form of dissipation. Our work establishes an analytically tractable framework to explore nonequilibrium quantum phases of matter and the relaxation mechanisms toward them.