The van der Waals magnets ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ and ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$, chemically similar yet magnetically distinct, provide an ideal platform for probing how structural complexity governs emergent magnetic order, anisotropy, and topological textures. ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ does not host skyrmions, whereas ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$ does, raising fundamental questions about the roles of inversion symmetry, frustration, and exchange interactions. Through comprehensive magnetization, susceptibility, and critical exponent analysis, we demonstrate that magnetic frustration, absent in ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, is crucial in ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$. The extra ${\mathrm{Fe}}^{+}$ sublattice in ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$ breaks inversion symmetry, introduces competing exchange, and yields a significant frustration parameter $f\approx$ 3.8. Critical exponent analysis reveals field-driven crossover from a mean field to a 2D-Heisenberg class with increasing field in ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, whereas field-driven crossover from a frustrated 3D-Heisenberg class ($\beta =0.348,\gamma =1.32$) at low fields reveals a conventional 3D-Heisenberg class ($\beta =0.368,\gamma =1.368$) at high fields in ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$. Our results establish magnetic frustration, rather than the Dzyaloshinskii-Moriya interaction alone, as the key ingredient stabilizing skyrmionic phases, offering a design principle for topological spin textures in layered van der Waals magnets. We show here that an extra sublattice in ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$ is essentially responsible for most of the differences in magnetic properties between ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ and ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$.

Two-dimensional magnetic materials have emerged as a frontier in condensed matter physics, offering a versatile platform for investigating unprecedented quantum phenomena under extreme conditions. This work focuses on $\mathrm{Mn}\mathrm{P}{\mathrm{S}}_3$, a prototypical Heisenberg antiferromagnet with a Néel temperature ($T_{\mathrm{N}}$) of around 78 K. By combining high-pressure Raman spectroscopy and density functional theory (DFT) calculations, we systematically investigate its phononic and magnetic evolution under compression. Our results reveal a significant pressure-induced enhancement of $T_{\mathrm{N}}$, which rises to 240 K at 20.2 GPa, indicating a substantial strengthening of magnetic coupling. This enhancement is also consistent with the notable blueshift of a possible two-magnon-related magnetic Raman feature. DFT results show that this magnetic evolution is intrinsically linked to a pressure-induced layer-sliding transition occurring near 5 GPa, which triggers a magnetic reconfiguration from interlayer ferromagnetic to interlayer antiferromagnetic coupling. These insights underscore the profound impact of pressure on the structural and magnetic properties of $\mathrm{Mn}\mathrm{P}{\mathrm{S}}_3$, providing critical insights into 2D magnetic systems under extreme conditions and opening new avenues for manipulating the emergent phenomena in low-dimensional magnetic materials via precise pressure control.

Driven by quantum geometric effects, nontrivial superfluid weight in flat-band superconductors has recently attracted considerable attention. In this paper, we show that for multigap superconductors, in which each band possesses a distinct gap function, the second-order correction to the gap function is essential for the geometric superfluid weight. Within the mean-field approximation, we derive a formula for the geometric superfluid weight of multigap superconductors that maintains the same form as in the isolated band limit. Beyond the isolated band limit, our formula establishes lower and upper bounds for the geometric superfluid weight. Comparison with recent experimental results on magic-angle twisted bilayer graphene reveals that our predicted upper bound is in good agreement with the experimental data.

Structure-property relations of the recently discovered germanium allotrope $\mathit{oP}32$-Ge are examined using a variety of experimental high-pressure techniques and compared with the results of density functional theory (DFT) calculations. High-pressure single-crystal x-ray diffraction shows that the unit-cell parameters and atomic positions of $\mathit{oP}32$-Ge change continuously up to 6 GPa, while peak shape and diffuse-scattering features remain essentially unchanged. X-ray diffraction reveals a sluggish transformation of $\mathit{oP}32$-Ge to the $\beta$-Sn Ge-II polymorph, i.e., the transition begins around 8 GPa and is complete by 12 GPa. The reconstructive transition is associated with the breakdown of $\mathit{oP}32$-Ge crystals into polycrystalline aggregates, which were examined up to 32 GPa. Synchrotron infrared absorption measurements indicate an increase in the band gap of $\mathit{oP}32$-Ge prior to the transition at 8 GPa to the higher-pressure metallic phase, which is characterized by high optical reflectivity. The DFT calculations of the structural and electronic properties are in good agreement with the measurements. Our experimental work conclusively shows that, under room-temperature quasihydrostatic compression, $\mathit{oP}32$-Ge remains in its semiconducting phase up to approximately 8 GPa, transforming into the Ge-II structure only by 12 GPa, a stability interval comparable to that of diamond-structured Ge (Ge-I). Crucially, we observe no anomalous structural or bonding changes over the range of conditions explored, indicating that the previously reported low-pressure superconductivity (near 2 GPa) must stem from subtle structural or stress-induced modifications accessible under the nonhydrostatic, low-temperature conditions of those experiments.

We develop a theoretical framework for time-modulated acoustic metasurfaces comprising a line array of modulated cavities, and show that bound acoustic surface waves can undergo temporal diffraction from bound states localized at an interface into bulk waves. The dispersion relation is derived via an operator formalism that captures the spatiotemporal coupling between Floquet sidebands. We show that under periodic modulation of the cavity length sidebands spaced by the modulation frequency are produced (diffraction in time), enabling the coupling of bound surface acoustic waves with bulk radiation, i.e., from a bound state $\mathit{to}$ the continuum. We observe the negative-frequency spectra as spatial reflections along the array via time-domain finite element simulations. Spectral $k$-gaps are observed at band crossings, with the width of the gap proportional to the modulation amplitude. The modulation enters solely through a time-dependent reflection phase, such that the framework applies generally to metasurfaces with programmable boundary conditions, beyond purely mechanical modulation.

We investigate the nematic phase transition in the Heisenberg $J_1\text{−}{J}_2$ model on square and triangular lattices, accounting for finite lattice compressibility and bond-length-dependent magnetic exchange. Using Nematic Bond Theory, a diagrammatic self-consistent method, we study the nematostriction that happens when the onset of nematic order in the spin-system drives a concomitant structural phase transition. We analyze the mechanisms by which the magnetoelastic couplings renormalize the critical temperature and modify the phonon spectrum. The magnetoelastic feedback can also alter fundamentally the nature of the phase transition. Specifically, on the square lattice, the transition shifts from continuous to weakly first-order (discontinuous) beyond a critical magnetoelastic coupling threshold. Conversely, on the triangular lattice, the transition remains discontinuous regardless of coupling strength.

We present a real-space spectral method for computing the orbital magnetization of crystals. Starting from the commutator form of the orbital magnetization operator, we formulate an energy-resolved spectral function that is amenable to exacting Chebyshev polynomial expansions and yields the total magnetization upon integration up to the Fermi level. This avoids the need for computing eigenstates and ground-state projects, providing an efficient numerical framework that is applicable to very large systems even in the presence of disorder and finite temperature. Our approach is benchmarked on the Haldane model, finding results that are in excellent agreement with the modern $k$-space formulation of orbital magnetization. Leveraging this technique, we extend our study to systems with uncorrelated disorder and point defects, and further show that the bulk Chern number can be directly obtained from the magnetization spectral density. These results open a promising route to investigate orbital responses and topological transitions in real-space models of quantum materials with realistic complexity.

We investigate the properties of ${\mathrm{CuVOF}}_4{\left({\mathrm{H}}_2\mathrm{O}\right)}_6·{\mathrm{H}}_2\mathrm{O}$, in which two different spin species, Cu(II) and V(IV), form antiferromagnetic spin-1/2 dimers with weak interdimer coupling provided via hydrogen bonding. Using radio-frequency susceptometry and electron-spin resonance (ESR), we show how the temperature-magnetic field spin-dimer phase diagram evolves as a function of applied hydrostatic pressure and correlate this with pressure-induced changes to the crystal structure. These results, coupled with pressure-tuned DFT calculations, confirm the prior prediction that the primary exchange interaction is mediated via an unusual mechanism in which the V(IV) ions provide considerable spin density to the oxygen that joins the two spins in each dimer and which lies along the Jahn-Teller axis of the Cu(II) ion. In addition, the dissimilarity in the spins that make up each dimer unit leads to a nonlinear field dependence of the electronic energy levels as detected in the ESR measurements.

Antiferromagnets on the Shastry-Sutherland lattice have attracted lots of research interest due to the possible existence of deconfined criticality. In the present work, we study the $J_1\text{−}{J}_2\text{−}{J}_r$ model using variational Monte Carlo (VMC) method, where $J_1, J_2$, and $J_r$ stand for the nearest-neighbor, next-nearest-neighbor, and ring exchange interactions, respectively. An empty plaquette (EP) phase with spontaneous mirror symmetry breaking is reproduced. However, the EP phase in the VMC approach is $Z_2$ deconfined and have Majorana-type gapless spinon excitations, which is qualitatively different from the EP phase in literature. The central observation of the present study is the gapless $Z_2$ Quantum spin liquid phase resulting from the competition between the EP phase, the full plaquette (FP) phase and the antiferromagnetic Néel phase. While the phase transition from the $Z_2$ QSL phase to the EP phase is likely of Landau-Ginzburg type, the continuous transitions to the confined FP and Néel phases are exotic and need to be further explored.

We investigate the energetics, interactions, and ordering tendencies of bimerons (cholesteric fingers of the second type, CF-2) and hopfions in thin films of chiral magnets and chiral liquid crystals hosting a conical background state. Although isolated bimerons possess positive eigenenergy with respect to the conical phase, they develop an attractive interaction mediated by the restructuring and partial overlap of their positive-energy shells—intermediate regions formed relative to the conical state. This attraction promotes the formation of bound pairs and extended bimeron chains, even in parameter regimes where a periodic bimeron lattice is no longer thermodynamically stable. Extending the analysis to three dimensions, we show that circularization of bimerons into hopfions renders their energy finite and gives rise to a well-defined metastability window closely linked to the stability range of cholesteric fingers. Isolated hopfions likewise exhibit an attractive interaction within the conical phase, leading to the formation of hexagonally ordered clusters. The attraction originates from the competition between favorable and unfavorable twist regions and from the energetic cost of the shell structures imposed by the conical background. Despite the presence of attractive pair potentials and cluster formation, we demonstrate that hexagonal hopfion lattices do not exhibit an equilibrium lattice period. Instead, the system evolves toward states in which the conical spiral or the CF-1 phase (cholesteric fingers of the first type) progressively invade the intersoliton regions, thereby preventing crystallization. Our results reveal a regime of attraction without stable long-range order and clarify the interplay between topology, confinement, and conical-phase frustration in chiral-magnet and liquid-crystal thin films.

The superconductor $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$ is well known for its inconsistent experimental indications of single versus multiple superconducting (SC) gaps, while simultaneously being considered a promising candidate for topological superconductivity. To clarify its SC behavior, we investigate the SC gap, the quasiparticle density of states (DOS), and $T_c$ in the frameworks of superconducting density functional theory and density functional perturbation theory. We explicitly consider the $\mathbf{k}$-dependent dynamical screened Coulomb pseudopotential, spin-fluctuation, and electron-phonon coupling in a fully first-principles way by incorporating the relativistic spin-orbit coupling (SOC). The strong SOC increases the electronic DOS near the Fermi level and enhances the electron-phonon coupling strength, which in turn leads to a larger SC gap and $T_c$ values that more closely match with recent experiments. The Fermi surface (FS) size of the $\alpha$ band, which is linked to the ${\mathrm{\Gamma }}_6^{-}$ irreducible representation and originates from Bi $p_{1/2}$-orbitals, is notably reduced with the SOC. This FS size reduction leads to isotropic and strong pairing strength, primarily driven by the coupling between the $\alpha$ band and $A_{1g}$ phonons. As a result, distinct SC gaps emerge that are characterized by the SOC-splitted Bi $p_{1/2}$ and $p_{3/2}$ states. This is further consistent with observed kinks in the quasiparticle DOS spectra, agreeing with the recently observed experimental multigap behavior. The average gap values of $\sim 0.75\mathrm{meV}$ and $T_c\sim 4.2\mathrm{K}$ are both consistent with experimental reports. Additionally, our calculated heat capacity jump ratio $\mathrm{\Delta }C/{\gamma }_n{T}_c\simeq 1.9$ suggests that $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$ is a strongly coupled superconductor.

In recent years, charge-channel order in strongly correlated metals has attracted much attention. Representative examples include electronic nematic order in cuprates and iron-based superconductors, and Star-of-David order in kagome metals. Critical phenomena and unconventional superconductivity arising from fluctuations of such charge-channel orders are central issues today; however, the essential role is played by many-body effects (vertex corrections) beyond the mean-field approximation, and their origin and computational methods have not been established. In this study, we propose the Bethe-Salpeter equation method to evaluate electron-electron interactions in two-dimensional Hubbard models beyond the mean-field approximation. Based on the Baym-Kadanoff conserving approximation, we find that an attractive interaction in the charge channel emerges from the Aslamazov-Larkin vertex corrections that describe the interference processes among spin fluctuations. Applying this method to the square-lattice Hubbard model shows that the cooperation of attractive charge fluctuations and repulsive spin fluctuations yields high-$T_c d$-wave superconductivity together with enhanced effective mass. These results provide a natural explanation for the phase diagram of cuprate superconductors, in which $d$-wave superconductivity is strongly enhanced near the charge-order critical point. The theory can also be applied to iron-based and nickelate superconductors, suggesting broad potential for future applications.

Integrable Trotterization provides a method to evolve a continuous-time integrable many-body system in discrete time, such that it retains its conserved quantities. Here, we explicitly show that the first-order Trotterization of the critical transverse-field Ising model is integrable. The discrete-time conserved quantities are obtained from an inhomogeneous transfer matrix constructed using the quantum inverse scattering method. The inhomogeneity parameter determines the discrete-time step. We then focus on the noninvertible Kramers-Wannier duality symmetry for the Trotterized evolution. We find that the discretization of both space and time leads to a doubling of these duality operators. They account for discrete translations in both space and time. As an interesting application, we find that these operators also provide maps between Trotterizations of different orders. This helps us extend our results beyond the Trotterization scheme and investigate the Kramers–Wannier duality symmetry for finite-time Floquet evolution of the critical transverse-field Ising chain. Finally, we investigate how these noninvertible operators shape the phase diagram of the discrete-time evolution. This question is particularly interesting in the Floquet setting, which is known to host a richer phase structure than its undriven counterpart. We systematically construct the necessary operators, which relate different phases away from criticality for both Trotterized and Floquet evolutions.

Magnetic proximity effects in $\text{Co}\text{/}\text{hBN}\text{/}\text{graphene}$ heterostructures are systematically analyzed via first-principles calculations, demonstrating a pronounced localized spatial variation of the induced spin polarization of graphene's Dirac states. The proximity-induced exchange coupling, magnetic moments, and tunneling spin polarization (TSP) are shown to depend sensitively on the atomic registry at the interfaces. We analyze more than 20 distinct stackings—including high- and low-symmetry configurations—and reveal that the spin splittings of graphene's Dirac bands span a wide range from 1 to 100 meV, depending on the local hybridization of Co $d_{z^2}$, hBN $p_z$, and graphene $p_z$ orbitals. The strongest proximity effects emerge at geometric resonances, or “proximity hot spots”, where the three orbital states overlap maximally. The local spin polarization also depends sensitively on energy: Dirac states aligned with resonant Co orbitals experience the most pronounced exchange interaction. At these energies, the pseudospin Hamiltonian description of magnetic proximity effects breaks down. Outside these resonances, the pseudospin picture is restored. Our findings highlight the intrinsically local nature of proximity effects, governed by the spectral resonance and interlayer wave function overlap. We further quantify how additional hBN layers, interlayer twist, and multilayer graphene modify the proximity exchange and TSP, offering microscopic insight for designing spintronic van der Waals heterostructures with engineered interfaces and optimized spin transport.

Low-dimensional quantum systems host a variety of exotic states, such as symmetry-protected topological ground states in spin-1 Haldane chains. Real-world realizations of such states could serve as practical quantum simulators for quantum phases if the interactions can be controlled. However, many proposed models, such as the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, require unconventional forms of spin interactions beyond standard Heisenberg terms, which do not naturally emerge from microscopic (Coulomb) interactions. Here, we demonstrate a general strategy to induce a biquadratic term between two spin-1 sites and to tune its strength $\beta$ by placing pairs of spin-1/2 spacers in between them. $\beta$ is controlled by the ratio of the Heisenberg couplings between the spin-1 sites and the spacer spins, and between the spacer spins themselves. Detailed atomistic calculations reveal that chains of nanographene flakes with 22 and 13 atoms, respectively, which could be realized by state-of-the-art bottom-up growth technology, yield precisely the couplings required to approach the AKLT state. These findings deliver a blueprint for engineering unconventional interactions in bottom-up synthesized quantum simulators.

The altermagnet (AM), a recently identified class of collinear magnet, has garnered significant attention due to its unique combination of zero net magnetization and spin-split energy bands, leading to a variety of novel physical phenomena. Using numerically exact lattice Monte Carlo simulations, we investigate AM-like phases within the Ising-Kondo lattice model (the anisotropic easy-axis limit of the Kondo lattice model), which is commonly employed to describe heavy-fermion materials. By incorporating an alternating next-nearest-neighbor hopping (NNNH) term, which arises from the influence of nonmagnetic atoms in altermagnetic candidate materials, our results reveal key signatures of AM-like states, including spin-splitting quasiparticle bands and spectral functions, and demonstrate that a $d$-wave AM remains stable across a broad range of interaction strengths, electron concentrations, NNNH amplitudes, and temperatures, highlighting its robustness. Furthermore, through an analysis of non-magnetic impurity effects, we further confirm the $d$-wave symmetry of the AM phase. These findings establish a solid theoretical foundation for exploring AM-like phases in $f$-electron compounds, paving the way for future investigations into their exotic magnetic and electronic properties.

Moiré materials with opposite nonzero minibands Chern numbers in time-reversal-partner valleys are two-dimensional topological insulators at band filling $\nu =2$. We explore the possibility that in this class of moiré materials intervalley coherence can sometimes be present in interaction-induced insulators at band filling $\nu =1$, using Landau levels with opposite signs of the magnetic field as a convenient generic model. In the absence of intravalley interactions the mean-field ground state at filling factor $\nu =1$ is a gapless intervalley coherent state that maps under a particle-hole transformation of one valley to a strong-field superconducting vortex-lattice state that has been studied previously. When the ratio $\lambda$ of intravalley to intervalley exchange interactions is increased, gapped states appear, one with broken time-reversal symmetry and a quantized Hall effect but no valley polarization and one with broken parity symmetry and zero Hall conductivity. We discuss the possibility that the latter state could be related to the fractional quantum spin Hall effect recently observed at an odd filling factor in a moiré topological insulator and comment on related systems in which correlations between electrons in bands with opposite Chern numbers might play a key role.