The Wilczek-Zee (WZ) holonomy arises in degenerate states while the Uhlmann holonomy characterizes finite-temperature topology. We investigate possible relationships between the Uhlmann phase and the scalar WZ phase, which reflects the Uhlmann and WZ holonomy respectively, in an exemplary four-level model with two doubly degenerate subspaces. Through some solvable exact solutions, we contrast the behavior of the Uhlmann and WZ connections and their associated phases. In the zero-temperature limit, the Uhlmann phase may or may not agree with the scalar WZ phase of the degenerate ground states due to obstructions from the Hamiltonian manifested as Dirac points. This is in stark contrast to nondegenerate systems where the correspondence between the Uhlmann and Berry phases in general holds. Our analyses further show that for the example studied here, the Uhlmann phase catches the singular behavior at the Dirac points while the WZ connection and scalar WZ phase vanish along a zero-field axis. We also briefly discuss possible experimental implications.

The magnetic correlations in double perovskites $\mathrm{L}{\mathrm{a}}_2\mathrm{M}{\mathrm{n}}_{2-x}\mathrm{N}{\mathrm{i}}_x{\mathrm{O}}_6$ ($x=0.5$, 0.75, 1.0, 1.25, and 1.5) have been systematically investigated across macroscopic, mesoscopic, and microscopic length scales using temperature-dependent bulk DC magnetization, neutron depolarization, and neutron powder diffraction measurements, respectively. The magnetic properties evolve from a long-range ferromagnetic (FM) order to a cluster ferromagnetic/spin-glass (FM/SG) behavior as the Ni concentration increases. This evolution is directly linked to changes in the crystal structure, transitioning from pure orthorhombic ($x=0.5$) to mixed orthorhombic and monoclinic ($x=0.75-1.0$), and eventually to mixed trigonal and monoclinic ($x=1.25-1.5$) symmetries. Ni substitution enhances the magnetic ordering temperature from 170 K ($x=0.5$) to 280 K ($x=1.0$), but this is accompanied by a reduction in both magnetization and ordered magnetic moment. Beyond $x=1.0$, any long-range magnetic ordering is absent. Additionally, all compositions exhibit a reentrant spin-glass-like phase at low temperatures (below $\sim 50$ K). Neutron diffraction analysis confirms that long-range FM order occurs only in the orthorhombic phase, while the monoclinic and trigonal phases lack such magnetic ordering. The temperature-dependent magnetic correlations are closely connected to variations in crystal structural parameters, including lattice constants and unit-cell volume. The electrical conductivity behavior, following the variable range hopping (VRH) model, highlights the role of multivalent Mn and Ni ions on the electrical properties. This study elucidates the microscopic mechanisms behind the tunable magnetic and electrical properties of $\mathrm{L}{\mathrm{a}}_2\mathrm{M}{\mathrm{n}}_{2-x}\mathrm{N}{\mathrm{i}}_x{\mathrm{O}}_6$, offering valuable insights for the design of advanced materials for spintronic applications.

The quasiparticle self-consistent $GW$ method is used to study the electronic band structure, optical dielectric function, and exchange interactions in chalcopyrite, $I\overline{4}2d$, structure ${\mathrm{MnGeP}}_2$. The material is found to be an antiferromagnetic semiconductor with a lowest direct gap of 2.44 eV at the $\mathrm{\Gamma }$ point and a lower indirect gap of 1.87 eV from $\mathrm{\Gamma }$ to $M$. The material is an altermagnet because the two magnetic atoms of opposite spin are related by a twofold rotation operation perpendicular to the main fourfold rotation inversion axis. The spin splittings along a low symmetry line like $PN$ is sizable while at k points on the diagonal mirror planes or on the twofold symmetry axes the spin splitting is zero. The exchange interactions are calculated using a linear response approach. The antiferromagnetic exchange interaction between nearest neighbors in the primitive unit cell is dominating and found to be slightly decreasing upon carrier doping but not sufficiently to change the interaction to become ferromagnetic. The bare (noninteracting) and interacting transverse spin susceptibilities, which provide interatomic site exchange interactions after averaging over the muffin-tin spheres, are calculated from the $GW$ band structure and wave functions. From these exchange interactions, the spin wave spectra are obtained along the high symmetry lines and the Néel temperature is calculated using the mean-field and Tyablikov estimations. The dielectric function and the optical absorption spectra are calculated including excitonic effects using the Bethe Salpeter equation. The exchange interactions around ${\mathrm{Mn}}_{\mathrm{Ge}}$ defect sites is also studied. While we find it can generate ferromagnetic interactions with neighboring spins, we did not find direct evidence of producing an overall ferromagnetic phase. First, if Mn antisites are introduced by exchanging Mn with a nearby Ge, the interactions stay largely antiferromagnetic. Second, when we add additional Mn, in other words in Mn-rich stoichiometry, the ${\mathrm{Mn}}_{\mathrm{Ge}}$ antisites produce a strong ferromagnetic interaction primarily with the Mn in the same basal plane but weaker ferromagnetic interaction with adjacent plane Mn. The interactions between regular lattice Mn stay antiferromagnetic as before and thus favor keeping the antiferromagnetic order along the [001] direction. Adding Mn antisites, however, does lead to a metallic band structure.

A novel magnetic class blending ferromagnetism and antiferromagnetism, termed altermagnetism, has gained significant attention for its staggered order in coordinate and momentum spaces, time-reversal symmetry-breaking phenomena, and promising applications in spintronics. Ruthenium dioxide (${\mathrm{RuO}}_2$) has been considered a candidate material for altermagnetism, yet the presence of magnetic moments on Ru atoms remains a subject of debate. In this study, we systematically investigated the magnetic properties of ${\mathrm{RuO}}_2$ powder using nuclear quadrupole resonance (NQR) measurements. The NQR spectra show that there is no internal magnetic field. Furthermore, the temperature independence of spin-lattice relaxation rate, $1/T_{1}T$, proves that there are no magnetic fluctuations. Our results unambiguously demonstrate that Ru atoms in ${\mathrm{RuO}}_2$ possess neither static magnetic moments nor fluctuating magnetic moments, and thus ${\mathrm{RuO}}_2$ does not possess the magnetic characteristics essential for altermagnetism.

We investigate the transverse instability of two-component solitons forming in a planar waveguide operating in the regime of strong light-matter coupling. The instability emerges as a result of the coupling between transverse diffraction of the photonic component and nonlinearity of the material excitations. Solutions of three different forms are addressed which include bright, gray-dark, and gray-gray solitons. In the limit of long-wavelength transverse perturbations, the instability is described with an asymptotic expansion whose predictions agree with the results of numerical simulations. The dynamic development of instability of initially perturbed bright solitons leads to the formation of high-intensity spots in the photonic component. For gray-dark and dark-dark solitons, the transverse instability leads to the spontaneous nucleation of vortex-antivortex pairs which emerge in both fields as transient patterns.

We demonstrate a tunable Dirac-Weyl semimetal phase in two dimensions, realized by introducing in-plane $d$-wave altermagnetism into a Dirac system. This phase hosts both a central Dirac point and momentum-separated Weyl points connected by Fermi line edge states. The Weyl point positions—and thus the edge-state connectivity—can be continuously tuned by rotating the altermagnetic axis. In contrast, out-of-plane altermagnetism gaps part of the bulk spectrum while preserving a single Dirac point accompanied by chiral edge modes, as evidenced by quantized edge polarization. Our findings provide a tunable platform for manipulating Dirac-Weyl physics and topological edge transport in two dimensions.

Single crystals of $R{\mathrm{Rh}}_6{\mathrm{Ge}}_4$ ($R$ = Pr, Nd, Sm, Gd–Er) were synthesized using a Bi flux and their physical properties were characterized by magnetization, resistivity, and specific heat measurements. These compounds crystallize in the noncentrosymmetric ${\mathrm{LiCo}}_6{\mathrm{P}}_4$-type structure (space group $P\overline{6}m2$), where rare-earth atoms form a triangular lattice in the $ab$ plane and chains along the $c$ axis. ${\mathrm{PrRh}}_6{\mathrm{Ge}}_4$ and ${\mathrm{ErRh}}_6{\mathrm{Ge}}_4$ do not exhibit magnetic transitions above 0.4 K. ${\mathrm{NdRh}}_6{\mathrm{Ge}}_4$ and ${\mathrm{SmRh}}_6{\mathrm{Ge}}_4$ are ferromagnets, while ${\mathrm{GdRh}}_6{\mathrm{Ge}}_4$ and ${\mathrm{DyRh}}_6{\mathrm{Ge}}_4$ show antiferromagnetic transitions, whereas ${\mathrm{HoRh}}_6{\mathrm{Ge}}_4$ is a ferrimagnet. In addition, ${\mathrm{DyRh}}_6{\mathrm{Ge}}_4$ shows multiple transitions and magnetization plateaus when a magnetic field is applied along the $c$ axis. In ${\mathrm{SmRh}}_6{\mathrm{Ge}}_4$, like the Ce counterpart, the crystalline-electric field effect leads to an easy plane anisotropy, while in other compounds it gives rise to a pronounced uniaxial anisotropy.

We consider a ladder system where one leg, referred to as the “bath,” is governed by an Aubry-André (AA)-type Hamiltonian, while the other leg, termed the “subsystem,” follows a standard tight-binding Hamiltonian. We investigate the localization properties in the subsystem induced by its coupling to the bath. For the coupling strength larger than a critical value ($t^{\prime }>t_c^{\prime }$), the analysis of the static properties shows that there are three distinct phases as the AA potential strength $V$ is varied: a fully delocalized phase at low $V$, a localized phase at intermediate $V$, and a weakly delocalized (fractal) phase at large $V$. The fractal phase also appears in a narrow region along the boundary between the delocalized and localized phases. An analysis of the projected wave-packet dynamics in the subsystem shows that the delocalized phase exhibits a ballistic behavior, whereas the weakly delocalized phase is subdiffusive. Interestingly, the narrow fractal phase shows a super- to subdiffusive behavior as we go from the delocalized to localized phase. When $t^{\prime }<t_c^{\prime }$, the intermediate localized phase disappears and we find a delocalized (ballistic) phase at low $V$ and a weakly delocalized (subdiffusive) phase at large $V$. Between those two phases, there is also an anomalous crossover regime where the system can be super- or subdiffusive. Beyond the ballistic phase observed at low $V$, we also identify a superdiffusive regime emerging in the limit $t^{\prime }/V\ll 1$, which continuously approaches the ballistic behavior as $t^{\prime }\to 0$. Finally, in some limiting scenario, we also establish a mapping between our ladder system and a well-studied one-dimensional generalized Aubry-André (GAA) model.

Recent experimental evidence suggests the presence of an unconventional, nodal surface-superconducting state in trigonal ${\mathrm{PtBi}}_2$. We construct a Ginzburg-Landau theory for the three superconducting order parameters, which correspond to the three irreducible representations of the point group $C_{3v}$. The irreducible representations $A_1$ and $A_2$ are the most likely. We develop a systematic method to determine the symmetry-allowed terms and apply it to derive all terms up to fourth order in the three order parameters. The Ginzburg-Landau functional also includes coupling to the magnetic field. The functional is employed to determine the effect of an applied uniform magnetic field on the nodal structure for $A_1$ and $A_2$ pairing. The results facilitate clear-cut experimental differentiation between these symmetries. We also predict field-induced helical superconductivity.

High-quality ($Q$) all-dielectric chiral absorbers are crucial for enhancing spin-selective light-matter interactions by enabling differential absorption of left- and right-circularly polarized (LCP and RCP) light. Conventional approaches typically require back reflectors, which cause heat dissipation and reduce out-of-band transparency. We propose an all-dielectric chiral metasurface composed of zigzag-shaped silicon nanoparticles embedded in a uniform silica background. Each nanoparticle, formed by etching two diagonal corners from a square base, supports two bound states in the continuum (BICs) associated with vortex polarization singularities. By breaking the in-plane $C_2$ symmetry through asymmetric corner widths, these BICs evolve into chiral quasi-BICs (QBICs) that couple selectively to LCP light. The resulting orthogonal modes exhibit opposite parity and are dominated by a toroidal dipole (TD) and an electric quadrupole (EQ), respectively. Although each QBIC contributes less than 50% absorption due to critical coupling, spectral degeneracy between them boosts the total absorption to 90.3% at 910.3 nm, with a $Q$ factor of 824 and circular dichroism of 79.3%. The design is extendable to RCP absorption via corner-length asymmetry. This approach provides a thermally efficient, planar platform for high-$Q$ chiral absorption, offering promising applications in photodetection and chiral optoelectronics.

Moiré superlattices constructed by stacking two two-dimensional (2D) materials offer a natural platform for exploring fascinating topological photonics scenarios, owing to the large lattice periodicity and unique electronic structures, which help to overcome the limitations of artificial photonic structures imposed by fabrication techniques. In this study, we demonstrate the potential of the 2D moiré superlattice formed by graphene and hexagonal boron nitride, a promising 2D photonic material, in supporting topological valley plasmons. Our calculations reveal that, by adjusting the Fermi level of the superlattice, interband transitions of electrons can be suppressed, facilitating the emergence of low-loss valley plasmons with wave vectors reaching the corners of the moiré Brillouin zone. These plasmons carry opposite valley Chern numbers in the $K$ and $K^{\prime }$ valleys, displaying scattering-resistant topological protected boundary states. Moreover, the frequency gap of the valley plasmons can be tuned by varying the position of the Fermi level or applying a compressive strain along the out-of-plane direction. Our findings offer a strategy for realizing more miniaturized and tunable topological photonic devices.

Controlling Mott insulator states has been a long-standing topic in condensed matter physics. Among various controlling parameters, two-dimensional (2D) confinement in epitaxial heterostructures has been demonstrated to convert the correlated metallic nature of ${\mathrm{SrVO}}_3$ into a Mott insulator by reducing the quantum well thickness. Here, we fabricate double quantum well (DQW) structures of ${\mathrm{SrVO}}_3$ with a magnetic barrier of ${\mathrm{EuTiO}}_3$ to tune the hybridization of wave functions by a magnetic field. A significant positive magnetoconductance is observed for DQWs with barriers thinner than 2 nm, while DQWs with thicker barriers do not show such large positive magnetoconductance, instead behaving as a parallel circuit of two single QWs. The observed positive magnetoconductance is accounted for in terms of enhanced hybridization of V $3d$ orbitals across the ${\mathrm{EuTiO}}_3$ barrier under a magnetic field, where the barrier height is reduced by the Zeeman splitting of Ti $3d$ bands in forced ferromagnetic ordering of localized $4f$ electrons on $\mathrm{E}{\mathrm{u}}^{2+}$ sites.

We present a comprehensive first-principles study of the magnetoresistance in $\mathrm{ZrSi}X$ $(X= \mathrm{S}, \mathrm{Se}, \mathrm{Te})$ topological nodal-line semimetals. Our study demonstrates that all primary features of the experimentally measured magnetoresistance in these materials are captured by our calculations, including the unusual butterfly-shaped anisotropic magnetoresistance. This anisotropic magnetoresistance can be accurately reproduced using the semiclassical Boltzmann transport theory without introducing any information on the topological nature of bands or the concepts of topological phase transition. Considering the complex structure of the Fermi surface in these topological materials, we develop a theoretical description explaining the features observed in magnetoresistance measurements. Additionally, the atypical Hall resistance can be interpreted using the same semiclassical approach. Our findings establish magnetotransport as a powerful tool for analyzing the geometry of the Fermi surface, complementing angle-resolved photoemission spectroscopy and quantum oscillation measurements. This approach is demonstrated to be particularly useful for determining the role of nontrivial topology in transport properties.

Spin-orbit coupling (SOC) lifts molecular orbital degeneracy, enabling bilevel electronic platforms suitable for next-generation digital devices. However, common light-atom molecular feedstocks exhibit weak SOC due to the absence of heavy elements. To enhance SOC without synthesizing new materials, we leverage interfacial interactions between molecules and transition-element-based solid-state materials. This computational study investigates SOC splitting in metal-phthalocyanine adsorbed on transition metal dichalcogenides (TMDs) using density functional theory (DFT). The enhanced SOC splitting is attributed to strong orbital hybridization at the molecule-substrate interface. Specifically, Zn-phthalocyanine (ZnPC) on monolayer $\mathrm{Mo}{\mathrm{S}}_2$ achieves a notable SOC splitting of $\sim 8$ meV. Furthermore, when ZnPC forms self-assembled chains on $\mathrm{Mo}{\mathrm{S}}_2$, the splitting increases to $\sim 20$ meV, driven by the formation of hybrid bands modulated by molecular periodicity. These findings highlight the role of interfacial and intermolecular interactions in inducing and enhancing SOC in surface-adsorbed molecules, providing a new strategy for molecular spintronic materials without complex synthetic efforts.

We treat the disordered Heisenberg model in one dimension as the standard model of many-body localization (MBL). Two new and independent order parameters stemming solely from the half-chain von Neumann entanglement entropy $S_{\text{vN}}$ are introduced to probe the eigenstate phase transition in this model. From the symmetry-endowed entropy decomposition, they are the probability distribution deviation $\left|d\right(p_n\left)\right|$ and the von Neumann entropy $S_{\text{vN}}^n(D_n=\text{max})$ of the maximally dimensional symmetry subdivision. The finite-size scaling reveals that the probability set $\left\{p_n\right\}$ drives the localization transition, preceded by a thermalization breakdown transition governed by $\left\{S_{\text{vN}}^n\right\}$. For the noninteracting case, these transitions coincide, but in the interacting circumstance, they separate. Such separability creates an intermediate phase regime and discriminates between the Anderson and MBL transitions. One obstacle whose solution eludes the community to date concerns the violation of the Harris criterion in most numerical investigations of MBL. Upon elucidating the mutually independent measures comprising $S_{\text{vN}}$, it becomes clear that the previous studies may lack the resolution to pinpoint, and thus potentially overlook, the crucial internal structure of the transition. We show that after this necessary decomposition, the universal critical exponents for both transitions of $\left|d\right(p_n\left)\right|$ and $S_{\text{vN}}^n(D_n=\text{max})$ fulfill the Harris criterion: $\nu \approx 2(\nu \approx 1.5)$ for quench (quasirandom) disorder. Our work puts forth symmetry combined with entanglement as an organization principle for the generic eigenstate matter and phase transition.

We investigate the collective dynamics of skyrmions in a monoaxial periodic substrate under dc and ac drives, based on the Thiele approach. Despite the repulsive interaction between skyrmions, clustering behavior and a complex-oriented dimers phase emerge when a dc drive is applied along the substrate-periodicity direction, and the phase diagram is depicted. Further, for a dc drive perpendicular to the substrate-periodicity direction, anomalous transport behaviors under an additional perpendicular or parallel ac drive are detected, including negative mobility and negative differential conductivity. The underlying mechanism of these anomalous transports is explored. The skyrmion Hall effect plays a crucial role in all these dynamic behaviors. In this study, we provide understanding of the heterogeneous behaviors of skyrmions which are important both theoretically and experimentally.

Magnetic nanowires (NWs) are critical components in fields such as data storage and spintronics, where precise control of their magnetic properties is essential for device optimization. The behavior of isolated NWs is often different from that of an ensemble, offering an opportunity to explore the role that dipolar and magnetoelastic interactions play in the latter system. Unfortunately, the comparison between a collection of NWs and single ones is often poorly characterized, as measuring individual NWs with weak magnetic signals is a challenging task. In this work, we employ a highly sensitive micromechanical torsional oscillator to measure the magnetic response of a few individual Ni NWs with $(72\pm 5)$ nm average diameter, fabricated by electrodeposition in anodic aluminum oxide templates as an array and subsequently released from this membrane. When comparing the magnetic properties as a function of temperature between single NWs and the array, we show that coercivity values of individual NWs are at least twice as large as for the array in the range 5–200 K. Also, we characterize the differences in the hysteresis loops, which are more squared for isolated NWs, with a high magnetic remanence $\sim 80\%$ of the saturation value. Our results highlight the crucial role of dipolar and mechanical interactions in modifying the magnetic behavior of NW arrays, providing valuable insights for the design and application of NW-based magnetic devices.

We present the results of muon-spin relaxation $\left(\mu \mathrm{SR}\right)$ measurements of the static and dynamic magnetism of $M_{1/3}{\mathrm{NbS}}_2$ $(M=\mathrm{Fe}, \mathrm{V}, \mathrm{Mn})$, three intercalated transition-metal dichalcogenides. Transitions to long-range magnetic order are observed in all three materials, and local magnetic fields at muon sites are compared to dipole field calculations. Measurements on ${\mathrm{Fe}}_{1/3}{\mathrm{NbS}}_2$ capture the evolution of two coexisting magnetic phases. In ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$, we observe a peak in the dynamic response at 9 K, coincident with previous reports of a possible low-temperature phase transition. The observation of high-frequency muon precession in ${\mathrm{Mn}}_{1/3}{\mathrm{NbS}}_2$ suggests the existence of an additional muon site that implies a difference in the electronic energy landscape compared to the other materials in the series. Taken together, this demonstrates that the change in intercalant species drives significant variations in magnetism, highlighting the $M_{1/3}{\mathrm{NbS}}_2$ series as an ideal group of materials for investigating a wide range of magnetic phenomena.