We propose a planar tunneling setup to probe vacancy-bound Majorana modes in the chiral Kitaev spin liquid. In this geometry, the inelastic tunneling conductance can be expressed directly in terms of real-space spin correlations, establishing a link between measurable spectra and the underlying fractionalized excitations. We show that spin vacancies host localized Majorana states that generate sharp near-zero-bias features, well separated from the continuum of bulk spin excitations. Compared to local STM measurements, the planar configuration naturally enhances the signal by coherently summing over multiple vacancies, reducing spatial resolution requirements. Our results demonstrate a realistic and scalable route to detect Majorana excitations in Kitaev materials.

A modified spin-orbital superexchange theory is developed to derive the effective spin Hamiltonian ${\mathcal{H}}_S$ governing the exchange interactions between pseudospins-$1/2$ on a square lattice, as occurs, for instance, in planar iridium oxide ${\mathrm{Ba}}_2{\mathrm{IrO}}_4$. The procedure begins with the underlying three-orbital Hubbard model for the $t_{2g}$ orbital manifold, which is first unitarily transformed to account for the strong spin-orbit interaction in all orders of the coupling constant $\lambda$, and then an explicit perturbative expansion with respect to the transformed hopping integrals and the Hund's interaction is used. To place this novel analytical approach into a general context, a brief outline is given for the computational superexchange formalism based on the post-Hartree-Fock calculations in the framework of the cluster quantum chemistry methods. A complementary computational approach, based on the density functional theory with strong spin-orbit coupling and aimed at the extraction of a single-bond exchange parameter of the corresponding pseudospin model, is also discussed in some detail.

We present a systematic investigation of all 16 marginally relevant fermion-fermion interactions in two-dimensional (2D) time-reversal symmetry-breaking kagome semimetals hosting a quadratic band crossing point (QBCP). Employing a momentum-shell renormalization-group approach that treats every interaction on an equal footing, we derive energy-dependent flow equations that capture the hierarchical evolutions of interaction parameters. Our analysis begins by tracking the energy-dependent flows of fermion-fermion interactions. The interaction couplings evolve towards divergence at a critical energy scale, signaling quantum critical behavior governed by a certain fixed point (FP). The character of this FP depends intimately on structural parameters $d_{0,1,2,3}$ which classify the microscopic model into rotationally symmetric and asymmetric cases. Then, we identify two stable FPs in the rotationally symmetric case and nine additional FPs in the asymmetric case dubbed ${\mathrm{FP}}_{1-10}$. Their boundary conditions are approximately demarcated and established by linear and plane-fitting techniques in the structural parameter space. Furthermore, we examine distinct interaction-driven instabilities near these FPs by incorporating the relevant external source terms and computing their susceptibilities. It indicates that the charge density wave and superconductivity become dominant at ${\mathrm{FP}}_{2,4,5,6,8}$ and ${\mathrm{FP}}_{1,9,10}$, while the $x$-current and bond density prevail at ${\mathrm{FP}}_3$ and ${\mathrm{FP}}_7$, respectively. In addition to these leading states, several underlying subordinate instabilities are presented as well. These results would be helpful to further study the low-energy critical behavior in a 2D kagome QBCP and related materials.

To understand the origin of muon spin relaxation and frequency shift in water with temperature, we performed weak transverse-field muon spin rotation and relaxation ($\mu \mathrm{SR}$) measurements over a temperature range of 220 K to 300 K. Using a conventional model with a phenomenological relaxation term, the spin relaxation of diamagnetic muons in frozen water (0.2473 $\pm$ 0.0061 MHz at 270 K) was found to be significantly higher than that in liquid water (0.0 $\pm$ 0.0020 MHz at 300 K). Furthermore, this conventional model reveals a non-negligible frequency shift below the freezing point. We propose a model that incorporates spin-dipole interactions between the muon in $\mathrm{MuOH}$ and the nearest-neighboring (first- and second-shell) protons of ${\mathrm{H}}_2\mathrm{O}$. This model reproduced the spectra well without the need for a phenomenological relaxation term. The validity of this model and quantitative information about spin-dependent interactions were tested using $\mathrm{MuOD}$ in ${\mathrm{D}}_2\mathrm{O}$ under identical field and temperature conditions. We also estimated the fractions of muons precessing with the Zeeman field versus those influenced by combined spin-dipole and Zeeman interactions in ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$. This study provides deeper insights into $\mu \mathrm{SR}$ behavior in condensed matter, including water, hydrated samples, and aqueous solutions.

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.