Recently, higher-order topological phases have been extended from Euclidean lattices to non-Euclidean hyperbolic lattices. Though higher-order topological type-I hyperbolic lattices have been extensively studied, their counterpart, higher-order topological type-II hyperbolic lattices, have never yet been reported. Here, by mapping the celebrated Bernevig-Hughes-Zhang model onto a type-II hyperbolic lattice, we present a theoretical exploration of the first-order topological edge states and second-order topological corner states in a type-II hyperbolic lattice. Compared with the higher-order topological type-I hyperbolic lattices, we discover two unique topological phenomena that stem from the nontrivial geometrical topology of the type-II hyperbolic lattice. First, topological edge and corner states exist on both inner and outer boundaries of the type-II hyperbolic lattice and exhibit higher degeneracy than those in the type-I hyperbolic lattice with only an outer boundary. Second, the degeneracy of type-II hyperbolic corner states can be arbitrarily tuned by changing the characteristic (or inner) radius, in contrast to its type-I counterpart, which is determined by the number of sides of the tessellated polygons. Our work explores topological states in more complex hyperbolic lattices, significantly expanding the research scope of hyperbolic topological physics.

The Lucas sequences are integers defined by a homogeneous recurrence relation. They include the well-known Fibonacci numbers, which appear abundantly in nature. The complementary Lucas numbers, defined by the same recurrence relation, are less well-known. In this work, we show that such complementary Lucas sequences can be observed simultaneously on the same physical platform, using zero modes in one-dimensional system(s) coupled to a non-Hermitian reservoir. When the latter consists solely of gain and loss modulated non-Hermiticity, the two Lucas sequences can manifest as a linearly localized edge state and a constant-intensity mode, respectively. When the reservoir features asymmetric couplings as well, more general Lucas sequences can be realized either directly on one sublattice in the reservoir or by reconstructing the wave function on both sublattices. Finally, if we allow, in addition, an alternate frequency detuning in the reservoir, all Lucas sequences can be observed in principle, including the Fibonacci and Lucas numbers.

Hydrogen, carbon, and nitrogen are amongst the most important light elements in the composition of the solar system. They form the organic molecules and atmospheric components of many outer planets. Under the extreme conditions within planets, exploring the H-C-N chemical space is central to understanding the abiotic chemistry and interior structure of icy planets and moons. Here, based on effective crystal structure searches and ab initio calculations, we report the ground state phase diagram of the H-C-N system at pressures up to 500 GPa. Two thermodynamically stable ternary compounds ${\mathrm{CH}}_2{\mathrm{N}}_2$ and ${\mathrm{C}}_2{\mathrm{HN}}_3$ are predicted to maintain their stability up to the pressure of the mantle-core boundary of Neptune. Upon compression, both ${\mathrm{CH}}_2{\mathrm{N}}_2$ and ${\mathrm{C}}_2{\mathrm{HN}}_3$ benefit from the formation of a dense tetrahedrally connected network formed from $s{p}^3$ hybridized carbon and nitrogen, supported by hydrogen bonding. The simplest possible compound, hydrogen cyanide HCN, is found to be metastable. Amongst methane-ammonia mixtures, we identify five metastable compounds: (${\mathrm{CH}}_4{)}_2{\mathrm{NH}}_3, {\mathrm{CH}}_4{\mathrm{NH}}_3, {\mathrm{CH}}_4$(${\mathrm{NH}}_3{)}_2, {\mathrm{CH}}_4$(${\mathrm{NH}}_3{)}_3$, and ${\mathrm{CH}}_4$(${\mathrm{NH}}_3{)}_4$. Potential synthesis pathways for the metastable compounds are provided for further discussion on the formation of mixtures based on simple molecules.

Understanding superconductivity emerging from repulsive fermions remains a major challenge in condensed matter physics. In this paper, we investigate the pairing tendencies in a one-dimensional, three-component repulsive Hubbard model, using the density matrix renormalization group method. At half filling, the system exhibits density wave ground state due to strong Hubbard repulsions. Upon doping, Cooper pairs can emerge in the system, whose long-range fluctuations predominate the low-energy physics across a broad parameter range. The effective attractions between Cooper pairs are mediated by the particle-hole fluctuations in the third nonpairing component, resembling an excitoniclike mechanism of superconductivity. The coexistence of density waves and superconductivity at different fermion fillings is explored. We also present an analytical study of the pairing mechanism in both weak and strong coupling limits. Our results provide a new perspective for understanding and exploring unconventional superconductivities in strongly correlated fermionic systems.

The extension of single-site coherent potential approximation (CPA) to multiorbital Hubbard models with full Hund's coupling has remained challenging due to the difficulty of constructing an appropriate alloy-analogy model. Here, we decompose the exact Green's functions of the atomic-limit two-orbital Hubbard model with full Hund's coupling into pole expansions, enabling the construction of the alloy-analogy model and thus facilitating the development of an extended two-orbital CPA that incorporates spin-flip and pair-hopping terms beyond previous treatments. Applying this method to the two-orbital Hubbard model on square lattice, we reveal a metallic phase stabilized around $U^{\prime }=U/2$, which is absent in earlier studies, and identify a rapid growth in the on-site interorbital doublon-holon correlation for $U^{\prime }>U/2$. This phase and the evolution of the doublon-holon state are elucidated through the exact atomic-limit Green's function solution. The effect of distinct Hund's coupling components is also examined.

We study charge transport across a junction between a normal metal and a Rashba metal in the presence of a Zeeman field applied to the spin-orbit coupled region. While an out-of-plane Zeeman field does not generate a transverse response in a homogeneous Rashba system, we show that such a junction exhibits a finite transverse conductivity that is inherently nonreciprocal, i.e., it depends on the direction of the applied bias. We demonstrate that this effect originates from the breaking of the $k_y\to -k_y$ symmetry of the Hamiltonian in the presence of the Zeeman field, which prevents cancellation of transverse current contributions from opposite transverse momenta. We further show that evanescent modes in the spin-orbit coupled region play a crucial role by carrying a finite spin polarization that gives rise to a transverse current localized near the junction. The transverse conductivity exhibits a peak at an energy scale set by the Zeeman field, displays distinct behavior for opposite bias directions, and shows spatial dependence governed by the nature of the contributing modes. We also identify bound states at the junction for attractive barrier strengths, which enhance conductivity when their energies lie near the transport window. Our results reveal a mechanism for nonreciprocal transverse charge transport in Rashba systems without requiring in-plane magnetic fields or ferromagnetic contacts, and should be experimentally accessible in semiconductor heterostructures.

The atomistic Hubbard interaction $U$, representing the on-site Coulomb repulsion, serves as a pivotal parameter in theoretical models describing correlated systems, yet its precise experimental determination, especially in moiré systems, remains challenging. Scanning tunneling microscopy (STM) provides real-space images of the local density of states (LDOS), offering rich datasets that reflect the unique electronic structure of the material. Here, we introduce a systematic methodology for extracting the Hubbard $U$ parameter directly from these LDOS images through the application of machine learning in the case of twisted bilayer graphene in the flat-band regime. Accurate regression of $U$ is achieved despite the extremely high visual similarity between Fourier transform-LDOS (FT-LDOS) images corresponding to different interaction strengths. Subsequent data analysis further suggests a gradual interaction-dependent redistribution of spectral weight, with a possible crossover scale of order $U/t\sim 1$. To assess robustness beyond idealized simulations, we introduce physically motivated perturbations that emulate experimental STM imperfections and demonstrate that augmentation-based training substantially improves generalization to noisy and symmetry-broken FT-LDOS images.

CoPt alloy thin films as ferromagnetic metal materials have attracted widespread attention for magneto-optical (MO) applications due to their high perpendicular magnetic anisotropy (PMA) and strong MO effect. However, quantitative determination of the off-diagonal dielectric permittivity tensor ${\varepsilon }_{ij}\left(i\ne j\right)$, which governs the MO effect, remains challenging in ultrathin multilayer films. In this study, we adopt an analytical approach combining experimental polar magneto-optical Kerr effect (P-MOKE) measurements with an inverse MO Fresnel transfer matrix method (TMM) to quantitatively extract ${\varepsilon }_{ij}\left(i\ne j\right)$ of the CoPt alloy thin films embedded in CoPt/AlN periodic multilayer structures. Beyond parameter extraction, the introduction of dielectric AlN spacer layers enables pronounced optical interference effects, leading to a substantial enhancement of the polar Kerr rotation through structural engineering. CoPt/AlN multilayers with varying stacking numbers ($N=1–10$) are fabricated via DC magnetron sputtering and ex situ postannealing to achieve high-quality interfaces between CoPt and AlN layers. Crystallographic and surface morphology characterizations confirm that annealing treatment leads to improved crystallinity and enhanced texturing. Magnetic characterizations done by vibrating sample magnetometer (VSM) further demonstrate that annealing treatment effectively increases both the coercivity and saturation magnetization. UV–Vis spectroscopy is employed to experimentally validate the optical parameters of the individual constituent layers. P-MOKE measurements reveal nonmonotonic Kerr rotation due to optical interference in the multilayer structures. Theoretical modeling based on MO Fresnel TMM show excellent agreement with experimental results. Furthermore, simulations comparing bulk-like thick films and multilayer stacked thin films elucidate the underlying mechanism of Kerr rotation reversal. Based on the experimental and simulation results, the extraction of ${\varepsilon }_{ij}\left(i\ne j\right)$ in ferromagnetic CoPt layers, which is critical for designing interference-enhanced MO devices, is realized.

We consider the SU(2) gauge theory for spin fluctuations in the two-dimensional Hubbard model, where the electron field is fractionalized in terms of spinons and chargons. In this theory, spinons are described by a nonlinear sigma model, while chargons are treated as fermions at a mean-field level. We investigate the instability to a superconducting state (SC*), arising from a fractionalized Fermi liquid (FL*) where pairing between chargons occurs. Consistent with previous studies, our analysis reveals a coexisting phase characterized by both magnetic and superconducting order for the chargons. The central contribution of this work is the calculation of the feedback of superconductivity on spatial and temporal spin stiffnesses, thereby quantifying its impact on spin fluctuations. Our key finding is that superconductivity significantly suppresses these spin stiffnesses, enhancing quantum spin fluctuations. This enhancement suggests that superconductivity can play a crucial role in stabilizing quantum disorder against long-range magnetic ordering.

The anomalous Hall effect (AHE) serves as a pivotal transport phenomenon for deciphering the interplay between magnetic spin textures and topological bands in magnetic materials, with its origin attributed to intrinsic (momentum-space Berry curvature linked to Weyl or Dirac point) and extrinsic (spin-dependent scattering, i.e., skew scattering and side-jump) mechanisms. The complex magnetic structure and strong spin-orbit coupling effect of rare-earth magnetic materials make them an important platform for studying AHE. Here, we report a disordered ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ single crystal and investigate its magnetic and transport properties. In this single crystal, Ho-Au mixed occupancy on the $2c$ site and vacancies on the Si $2b$ sublattice give rise to pronounced chemical disorder. ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ belongs to the rare-earth ferromagnetic material with a magnetic ordering temperature of 8 K ( $T_c$ ) and easy magnetization along the $c$ axis. The magnetoresistance (MR) of ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ exhibits different behaviors at high and low temperatures in the $H\parallel ab$ and $I\parallel c$ configurations. At 3 K ($T<T_c$), the MR is initially positive and becomes negative with the magnetic field further increasing. This is due to the gradual disappearance of magnetic domain-wall scattering as the magnetization process approaches saturation. At 100 K ($T>T_c$), the MR remains negative as a result of the suppression of the scattering from spin fluctuations. With regard to the AHE, considering the scaling behavior between the anomalous Hall resistivity ${\rho }_{xz}^A$ and the longitudinal resistivity ${\rho }_{zz}$, the origin of the AHE in ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ can be described by the skew scattering mechanism. The dominance of skew scattering is likely driven by the structural disorder present in ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$: the Ho-Au mixed occupancy and Si vacancies create a random potential landscape and break local chemical periodicity, which are expected to enhance asymmetric carrier scattering. The anomalous Hall angle Θ${}_{AH}$ and anomalous Hall factor $S_H$ of ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ are 0.49% and 0.03 ${\mathrm{V}}^{-1}$, respectively, at 3 K, and both decrease as the temperature rises. The small Θ${}_{AH}$ and $S_H$ are attributed to the finite $s\text{−}f$ exchange coupling in this $4f$ localized-moment ferromagnet and to the enhanced scattering environment associated with Ho-Au mixed occupancy and Si vacancies. This work establishes disordered ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ as a platform for studying the role of structural disorder in skew-scatter-dominated AHE in rare-earth localized-moment ferromagnets.

In photoluminescence experiments of hole-doped ${\mathrm{WSe}}_2$ monolayer, a counterintuitive phenomenon is observed: the emission from the lower-energy dark positive trion (${\mathrm{D}}^{+}$) anomalously diminishes at high hole densities, while the signal from the higher-energy bright positive trion (${\mathrm{X}}^{+}$) becomes dominant. In this work, we propose a nonradiative Auger recombination as the mechanism responsible for this paradoxical observation. We performed first-principles calculations based on density functional theory (DFT) to obtain the electronic band structure and Bloch wave functions of ${\mathrm{WSe}}_2$ monolayer. To accurately capture the many-body correlation within the trion complex, we utilized the stochastic variational method (SVM). Using this combined framework, we have quantified the density-dependent Auger recombination rates by applying Fermi's golden rule. Our theoretical analysis reveals that as the hole density increases, the Auger recombination rate for dark trions increases dramatically. Specifically, at a critical hole density of a few times ${10}^{12}{\mathrm{cm}}^{-2}$, our calculations show that the Auger lifetime drops below the nanosecond-scale measured lifetime of the dark positive trion at residual hole density. This nonradiative Auger process becomes the dominant pathway, effectively quenching the emission from $D^{+}$, and leading to the experimentally observed dominance of bright trions. This study provides a comprehensive theoretical framework for understanding the nonradiative interaction that governs trion dynamics in hole-doped ${\mathrm{WSe}}_2$ monolayer.

The interplay between real-space topology such as magnetic skyrmions and momentum-space topology characterized by topological surface states (TSSs) is predicted to realize novel phenomena and functionalities, yet materials hosting both topologies are scarce. Skyrmion-hosting helimagnet family ${\mathrm{EuGa}}_2{\mathrm{Al}}_2$ and ${\mathrm{EuAl}}_4$ has been a prime candidate for such a dual-topology system, but conclusive evidence for its momentum-space topology has remained elusive. We provide this evidence by directly observing TSSs that stem from bulk Dirac nodal lines using high-resolution angle-resolved photoemission spectroscopy. These TSSs are exceptionally robust against various perturbations such as a $2\times 1$ surface reconstruction, a chemical change in the termination of the crystal surface, and the onset of helical antiferromagnetic order. Crucially, below the Néel temperature, we observe replica bands driven by the magnetic ordering. Moreover, we demonstrate clear surface-termination dependence of this magnetotopological coupling. Our findings establish $\mathrm{Eu}{\left({\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\right)}_4$ as a dual-topology material and offer a rare platform to explore and control the interaction between the two fundamental topological realms.

Spontaneous spin polarization in quasi-one-dimensional (1D) electron systems is inherently fragile, often masked by structural disorder or potential anharmonicity. Here we report the deterministic stabilization of an exchange-driven spin gap, manifesting as a robust $0.5(2e^2/h)$ conductance plateau at zero magnetic field in a mesoscopic bilayer cavity. We demonstrate that this many-body phase is governed by a dual-parity protection mechanism. The spectral isolation of the tunnel-coupled bilayer energetically protects the ground state, while the symmetric harmonicity of the lateral cavity geometry shields the 1D van Hove singularity against transverse mode mixing. Breaking this spatial parity via asymmetric gating or localized central-gate screening violates the Stoner criterion for 1D ferromagnetism, quenching the $0.5(2e^2/h)$ state and restoring spin-degenerate transport. Our findings establish electrostatic spatial parity as a macroscopic, tunable lever for engineering correlated quantum phases in mesoscopic architectures.

We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two successive Wolff clusters reflects critical behavior and can be used as an order parameter for the algorithm's dynamics. In the case of the Swendsen-Wang algorithm, similar behavior is demonstrated by the variance of the overlap of two consecutive lattice configurations, which behaves like an order parameter. Nothing similar is observed for the Metropolis algorithm, where the dynamics in the critical region are determined by the spin-flip frequency, which is equivalent to the acceptance rate. Thus, the critical behavior of the Wolff cluster overlap and of the variance of the configuration overlap in the Swendsen-Wang algorithm are naturally related to the critical behavior of geometric objects—Fortuin-Kasteleyn clusters. Interestingly, in all cases the geometric quantity—the configuration overlap or its variance—reflects the thermodynamics of the phase transition.

Hafnium dioxide ($\mathrm{Hf}{\mathrm{O}}_2$), commonly known as hafnia, serves as a critical high-$k$ gate dielectric material in complementary metal-oxide-semiconductor (CMOS) devices and is also widely utilized in dynamic random-access memory (DRAM) capacitors. To gain better understanding of their physical properties, crystalline structures and dielectric constants of the three orthorhombic phases (OI-Pbca, OII-Pnma, OIII-$Pca{2}_1$) of $\mathrm{Hf}{\mathrm{O}}_2$ under mechanical strain have been investigated by first-principles calculations. Strain modifies both the mode effective charges and the frequencies of infrared-active (IR-active) phonon modes. The dielectric constant is directly proportional to the former and inversely proportional to the latter. Moreover, lattice-dynamics simulations revealed that large biaxial/triaxial tensile strains induce a phase transition from the ferroelectric phase (OIII-$Pca{2}_1$) to antipolar phase (OVIII-Pbcn), which arises from the coordination number change in half of the oxygen atoms. These results demonstrate strain engineering as a powerful means to control and modulate the dielectric properties and phase stabilities of $\mathrm{Hf}{\mathrm{O}}_2$.

An excess of low-frequency vibrational states beyond the Debye prediction—known as the boson peak—is a universal feature of disordered materials, yet its microscopic origin and connection to atomic-scale structural disorder remain unresolved. Here we study the microscopic origin and real time evolution of the boson peak during crystallization of amorphous Ge-Sb-Te by carrying out large-scale molecular dynamics simulations using machine learning interatomic potentials. The boson peak frequency is found to match with the transverse Ioffe-Regel crossover frequency throughout crystallization. As crystallization proceeds, the boson peak shifts to higher frequencies and its intensity progressively weakens, while the macroscopic shear modulus increases concurrently. The square-root scaling of the boson peak frequency with the shear modulus is more pronounced in mechanically soft and interfacial regions than in stiff regions. Atom-resolved vibrational anomaly highlights the population of quasilocalized low-frequency modes in the mechanically soft regions. The anticorrelation between the shear modulus and the boson peak intensity persists even at atomic scales in both amorphous and partially crystalline phases. Our large-scale atomistic simulations of structural ordering provide a microscopic perspective on the interplay between structural ordering, local elastic rigidity, and vibrational anomalies in real materials.

We investigate a novel class of topological superconducting phases protected by exact fermion-parity symmetry and average crystalline symmetries. These phases belong to the broader class of average crystalline symmetry-protected topological (ACSPT) states and include numerous examples of intrinsic ACSPTs—topological phases that arise only in the presence of disorder or decoherence. Unlike conventional symmetry-protected topological (SPT) phases, which require exact symmetry protection, average SPT (ASPT) phases remain robust as long as the symmetry is restored on average across disorder realizations or mixed-state ensembles. To classify these phases, we extend the real-space block state construction framework to account for average crystalline symmetries. In this generalized setting, lower-dimensional cells are decorated with ASPT phases, and the obstruction-free conditions are reformulated to incorporate the constraints imposed by average symmetry at block intersections. This provides a physically transparent and systematic method for classifying ASPTs with spatial symmetries that are only preserved statistically. We further validate our classification using a generalized spectral sequence analysis, which serves as an independent consistency check. Our results demonstrate that many crystalline topological superconductors remain well defined under realistic imperfections, and they uncover a rich landscape of intrinsically average-symmetry-protected phases that have no analog in clean systems.

We investigate the dissipative spectral form factor (DSFF)—a widely used probe of non-Hermitian quantum chaos—in the elliptic Ginibre unitary ensemble (eGinUE), which interpolates between the non-Hermitian Ginibre unitary ensemble (GinUE) and the Hermitian Gaussian unitary ensemble (GUE) via a symmetry breaking parameter. We derive exact finite-dimensional results and large-dimensional approximations for the DSFF, revealing a scaling relationship that connects the DSFF of eGinUE to that of GinUE and the spectral form factor of GUE. This relation explains the distinct timescales underlying the characteristic dip-ramp-plateau structure across GinUE, GUE, and crossover regimes. Additionally, we refine estimates of dip-ramp and ramp-plateau transition times for different symmetry regimes. We validate our results with Monte Carlo simulations and demonstrate applications to paradigmatic quantum-chaotic systems: the crossover Sachdev-Ye-Kitaev model and the crossover power-law banded random matrices. We highlight an analogy between eGinUE eigenvalues and the positions of a rotating fermionic gas in a two-dimensional anisotropic trap.

Short midinfrared laser pulses efficiently facilitate ultrafast manipulation of ferroic order parameters, including the full reversal of magnetization or ferroelectric polarization, with the invoked mechanisms relating to the properties of polar phonons in ionic crystals. Much less is known, however, about the behavior of such order parameters in response to an excitation in the far-infrared range, where phonons have larger oscillator strengths and are more damped. Here we investigate transient crystallographic strains and polarization switching in ferroelectric barium titanate ($\mathrm{BaTi}{\mathrm{O}}_3$) driven by an excitation in the frequency range of 5–8 THz, or wavelengths of 35–60 µm. We find that switching persists in a large part of this range, but is governed primarily by optical absorption rather than by the longitudinal optical phonons or epsilon-near-zero conditions that dominate in the mid-infrared regime.