AI for Science

Electric field control of magnetic order in two-dimensional (2D) van der Waals magnets is a central goal for low-power spin-based technologies. In the ambient-stable antiferromagnet CrSBr, strong magnetic anisotropy and robust exciton-spin coupling provide a favorable platform, yet deterministic electric field control of its magnetic phases has not been achieved. Here we demonstrate electric-field-driven reversible switching between antiferromagnetic and ferromagnetic states in dual-gated bilayer CrSBr without intentional carrier doping. In parallel, photoluminescence measurements resolve a tightly bound interlayer exciton with an intrinsic dipole moment of only ~1 e angstrom. The electric field dependence of the magnetic phase transition reveals two coexisting mechanisms: a linear magnetoelectric effect in the antiferromagnetic state and an electric-field-modulated interlayer exchange coupling. Their interplay accounts for the asymmetric evolution of the critical magnetic field. Our results establish bilayer CrSBr as a promising 2D material for electrically controlled spin-optoelectronic functionalities.

This study establishes a route to the Hartree--Fock (HF) limit for molecules and solids within the linearized augmented plane wave (LAPW) framework. We remove current limitations of the standard LAPW approach to nonlocal exchange by constructing radial basis functions and core orbitals consistently with the HF Hamiltonian. The presented method yields total energies of molecules and solids with a precision of a few $μ$Ha, and we use it to provide reference data for 14 semiconductors and insulators. For the systems considered in this study, the standard approach based on (semi)local potentials for constructing radial basis functions and core orbitals remains highly precise for practical relative energies, including molecular and solid-state formation energies and Si self-interstitial defect formation energies. More broadly, the results provide stringent all-electron benchmarks for basis-set and pseudopotential assessment, improve error control in hybrid-functional calculations within LAPW, and open the way to X-ray spectroscopy simulations within LAPW based directly on hybrid-functional core orbitals.

The emergence of non-relativistic spin splitting (NRSS) in altermagnetic systems has introduced a new paradigm in antiferromagnets with vanishing net magnetization. Although sliding-induced valley-polarized phases have recently been demonstrated in two-dimensional altermagnets, the observed valley-polarized state represents only a partial manifestation of altermagnetism, and a comprehensive classification based on spinsplitting characteristics remains lacking. Here, using first-principles calculations, general stacking theory, and spin-Laue symmetry analysis, we propose a coupled quasialtermagnetic state representing a distinct subclass of altermagnetism, in which reversible type-IV NRSS is controlled through interlayer sliding. Accordingly, the sliding-induced phases are classified into two categories: altermagnetic and quasi-altermagnetic states. We establish a direct correspondence between reciprocal-space spin splitting and real-space switching between the two quasi-altermagnetic states. Importantly, the spin-polarized bands in these states remain spin split at Γ point even in the absence of spin-orbit coupling (SOC), distinguishing them within the proposed classification framework. To demonstrate the interplay between altermagnetic and quasi-altermagnetic states, we investigate the two-dimensional Lieb-lattice material Mn2WS4 and its Janus derivative Mn2WS2Se2, analysing how changes in the local environment influence the different magnetic phases. Importantly, the underlying mechanism is broadly applicable to a wide class of twodimensional square-lattice systems. We further investigate the effects of SOC, focusing on spin texture and transport signatures in coupled quasi-altermagnetic states.

Valley polarization in 2D TMDs is promising for low-power valleytronic and spin-valley information processing, but time-reversal symmetry in pristine nonmagnetic TMDs keeps the K+ and K- valleys degenerate, limiting device applications. In this work, we investigated the structural stability, electronic properties, and tunable valley polarization of V-alloyed MoTe2 monolayer, Mo0.75V0.25Te2, using first-principles density functional theory (DFT) calculations. Substitutional alloying of MoTe2 with V introduced magnetic exchange interaction, which, together with spin-orbit coupling (SOC), lifted the valley degeneracy at the unequal valleys. The alloyed structure was found to be energetically and dynamically stable due to the absence of imaginary phonon modes. In pristine MoTe2, SOC produced spin splittings of 34.0 meV and 218.9 meV in the conduction bands and valence bands, respectively, but no valley polarization was observed. In contrast, Mo0.75V0.25Te2 exhibited spontaneous valley polarization of 37.3 meV in the conduction band and 78.2 meV in the valence band. The valley polarization was further enhanced by external electric fields and biaxial strain. A transverse electric field along the crystal c axis produced the maximum valley splitting of 132.8 meV in the valence band, whereas biaxial tensile strain increased the valence band valley splitting up to 160.8 meV. The maximum conduction band valley splitting reached 54.4 meV under 2% biaxial compressive strain. These results demonstrated that V alloying, combined with electric-field and strain engineering, provides an effective strategy for achieving large and tunable valley polarization in MoTe2. Thus, Mo0.75V0.25Te2 can be considered a promising 2D platform for tunable valleytronic device applications, such as transistors and sensors.

The quantum spin Hall effect (QSHE) has attracted widespread attention due to its dissipationless transport, which is protected by non-trivial topological invariants and helical edge states. Because even weak magnetic disorder can destroy the stability of topological quantum states, current research on the QSHE has primarily focused on non-magnetic materials. In this work, we extend the research scope of the QSHE to altermagnets. We establish the relevant symmetry constraints and identify all magnetic point groups that can realize the altermagnetic QSHE. Symmetry analysis reveals that pronounced spin-valley locking or spin-valley-layer locking universally exists in these systems. The concerted interaction between band inversion and spin-valley locking collectively gives rise to the helical edge states. Using first-principles calculations and theoretical models, we demonstrate that monolayer Nb2SeTeO exhibits an altermagnetic QSHE characterized by spin-valley locking, while bilayer Hf3Se3Te2 manifests an altermagnetic QSHE featuring spin-valley-layer locking. This work clarifies the intrinsic symmetry correlation between altermagnetism and quantum spin Hall topological phases, providing a brand-new theoretical perspective and research platform for exploring magnetic topological systems and developing next-generation spintronic devices

Interlayer interactions in layered materials are often assumed to transfer from the bilayer to the bulk, but this assumption can fail when chemically active out-of-plane orbitals participate in bonding. We combine diffusion quantum Monte Carlo (DMC) and density functional theory (DFT) to determine how interlayer coupling evolves in arsenene multilayers. DMC shows that bulk gray arsenic is compact, whereas the corresponding few-layer structures remain at substantially larger interlayer separations despite sharing the same nominal A$_{1}$B$_{-1}$ adjacent-layer registry. Registry alone therefore does not determine the bonding regime; thickness and coordination reshape the interlayer interaction. Among the tested functionals, SCAN+rVV10 most closely reproduces DMC equilibrium separations and stacking energetics. Using the DMC-benchmarked SCAN+rVV10 calculations, we predict a thickness-driven stacking sequence from A$_{1}$A$_{1}$ to A$_{1}$B$_{1}$ and finally bulk-like A$_{1}$B$_{-1}$. The structural crossover coincides with a stacking-dependent DFT band-gap collapse driven by enhanced interlayer As p$_{z}$ hybridization.

Recently, layered corrected kagome metal CsCr3Sb5 have garnered significant attention attributed to its flat bands near the Fermi level (EF) and altermagnetic ground state [ Yi Liu et al., Nature 632, 1032 (2024)]. However, the van Hove singularities (vHSs) in bulk CsCr3Sb5 are far away from the EF, while an effective modulation of VHS toward the EF is essential for exploring intriguing electron transport properties. In this work, using first-principles calculations, we investigate electronic structures of two-dimensional (2D) Cr3Sb5 and CsCr3Sb5 monolayers which may be mechanically exfoliated from bulk materials. Notably, it is revealed that both flat bands and vHSs simultaneously reside in close proximity to the EF in Cr3Sb5 monolayer, signifying enhanced electronic correlations. Importantly, a tensile strain further shifts the incipient flat bands and vHSs of two monolayers simultaneously to the vicinity of the EF, suggesting strain tunable electronic correlations and concomitant quantum effects. Furthermore, altermagnetic ground state is also revealed due to retained mirror symmetry between two sublattices in these two monolayers. Thus, this work advances understanding and modulations of electronic properties of 2D CsCr3Sb5 monolayers, strengthening their great potential for exploring unconventional quantum phenomena and altermagnetism.

We theoretically investigate the optical spin-injection response in different stoichiometric configurations of graphane and fluorographene using density functional theory. Our goal is to determine which configuration yields the strongest degree of spin polarization. The results show that the fluorographene zigzag configuration yields the best degree of spin polarization response (${\cal DSP}^{\mathrm{z}}$), with 98\% spin polarized electrons at the band edge and over a wide range of excitation photon energies. In contrast, other graphane and fluorographene configurations achieve a ${\cal DSP}^{\mathrm{z}}$ of roughly 83--100\%, but only within a limited photon-excitation energy range. In structures with low spin-orbit coupling, the degree of spin polarization is close to 100\% over a wide range of photon energies. For higher spin-orbit coupling, this strong response appears, but only in a narrow photon energy region. Additionally, under the band-resolved decomposition scheme, the contributions of different band-to-band transitions to the ${\cal DSP}^{\mathrm{z}}$ spectrum are identified by summing only the selected valence and conduction bands. Our findings show that almost the entire ${\cal DSP}^{\mathrm{z}}$ spectrum of the fluorographene zigzag configuration comes from transitions that involve only the top valence band, which is a mixture of C--p and F--p states.

Predicting detailed atomistic structures of self-assembling systems remains a challenge for all-atom molecular dynamics simulations. Replica exchange with solute tempering (REST) has been used to study those systems by accelerating all monomers in a global and uniform manner. While such a global approach can in principle predict any morphology of the system, it has computational drawbacks such as inefficient replica traversal due to order-disorder transitions and the growing number of replicas with system size. To address these issues, here we propose an alternative, stepwise construction approach to modeling supramolecular polymers under the assumption of one-dimensional polymerization. Specifically, we generate polymer structures by adding new monomers one by one to the system and applying REST to the new monomers to find their optimal binding positions based on an energy-based scoring function. The monomer addition and enhanced sampling are repeated sequentially until a polymer of desired length is obtained. We test the above procedure using a model supramolecular polymer in explicit solvent, and show that it can generate a polymer structure with characteristic H-bonding patterns at reduced computational costs, while also improving the efficiency of replica traversal significantly. We thus expect that the sequential REST will be useful for modeling supramolecular polymers, particularly for cases where global REST simulations are too demanding computationally.

The work functions of 7Li and 6Li metals have been measured as a function of temperature, by using photoionization of pure isolated metal nanoparticles in a beam. These data reveal a marked isotope effect in the temperature variation of these work functions. Furthermore, for both isotopes the curvature of this temperature variation is found to be significantly larger than may be ascribed purely to a change in the electron gas density. These findings enhance the characterization of lithium as a quantum material in which the interplay between electronic and ionic degrees of freedom is nontrivial, and call for a microscopic understanding beyond simple models. Additionally, the slope of the work function curves was observed to vanish in the low temperature limit, as had been predicted on the basis of the Third Law of thermodynamics.

Brittle materials subjected to thermal shocks experience strong temperature gradients that in turn give rise to mechanical stresses that can be large enough to induce fracture. This work presents a complete model for phase-field fracture for coupled thermo-mechanical problems, wherein the bulk material properties, the material strength, and the fracture toughness are specified independently. The capabilities of the model are assessed across a wide span of scenarios in thermo-mechanical fracture, from the propagation of large pre-existing cracks to crack nucleation under spatially uniform states of stress. In particular, we revisit the controlled quenching of glass plates, and demonstrate how the model captures experimentally observed crack patterns across a range of thermal loads. Ceramic disks subjected to infrared radiation are also examined, with the model reproducing both straight cracks in notched specimens and branching in intact specimens. Finally, ceramic pellets subjected to rapid power pulses are examined, with the model explaining experimental transitions from intact to fractured pellets and the important role of material strength. The results demonstrate that the complete phase-field model unifies the treatment of distinct fracture scenarios under thermal shock, surpassing classical approaches and enabling more reliable prediction of brittle fracture in extreme environments.

Phase transitions are omnipresent in modern condensed matter physics and its applications. In solids, first-order phase transformations typically occur by nucleation and growth under non-equilibrium conditions. Under constant external conditions, $\textit{e.g.}$, constant annealing temperature and pressure, the nucleation and growth dynamics are often thought of as spatially and temporally independent. Here, $\textit{in-situ}$ Bragg X-ray photon correlation spectroscopy (XPCS) reveals nanoscale spatial and dynamical heterogeneity in the perovskite-to-brownmillerite topotactic phase transformation in La$_{0.7}$Sr$_{0.3}$CoO$_3$ thin films annealed under constant reducing conditions over a time span of multiple hours. Specifically, a timescale associated with domain growth remains stable, with a corresponding domain wall speed of $v_d = 6 \pm 0.5 \times10^{-4}$~nm/s ($2 \pm 0.2$~nm/h), while a slower timescale, associated with temperature-driven de-pinning of domains, leads to accelerating dynamics with timescales following an aging power law with exponent -2.2$\pm$0.5. This experiment demonstrates that Bragg XPCS is a powerful tool to study nanoscale dynamics in structural phase transformations, with the ability to extract quantitative average values related to nano-domain motion $\textit{in-situ}$. The results are relevant for phase engineering of phase-change devices, as they show that nanoscale dynamics, linked to domain and domain-wall motion, can continuously evolve and speed up with time, even hours after the initiation of the phase transformation, with potential repercussions on electrical performance.

Phosphatidylcholine liposomes fill a special niche in alleviating osteoarthritis via intra-articular (IA) administration, attributed to their superlubricity at the articular cartilage surface, but their co-utilization as drug delivery vesicles in such therapy remains challenging as they may rupture under mechanical stress. Here, we describe cytoskeleton-inspired, supramolecular, self-assembled nanolipogels (NLGs), encompassing liposome-encased nanogels with a dynamic network formed by hydrogen bonding and cation-pi interactions, as a platform for simultaneous robust drug-delivery and massive reduction of interfacial frictional dissipation. We use a surface force balance to assess such dissipation at the sub-nanometer level, elucidating the mechanism involved, and atomic force microscopy to probe the NLGs structural stability. A useful proxy for the interfacial dissipation is the coefficient of friction, which remains as low as 10-4 at contact pressures at least up to 2 MPa, while under higher pressures exceeding the H-bonding energy density it increases abruptly and irreversibly to the still-low value 10-2. Under sustained sliding above this threshold, however, friction gradually decreases again, indicating recovery of the lubricating interface. Molecular dynamics simulations identify the compressive stress decrease due to hydrogen-bond rupture/rearrangement within the nanogel as a buried supramolecular transition associated with lubrication breakdown and recovery, while cargo release during sliding emphasizes the drug-delivery potential of such NLGs. These findings reveal how supramolecular core-shell reinforcement regulates load-bearing hydration lubrication, and provides a framework for designing adaptive biomimetic lubricants which are at the same time load-bearing intra-articular cargo-delivery vehicles.

We report temperature-dependent charge transport measurements in p-type high-resistivity germanium crystals grown at the University of South Dakota. Hall-effect and four-probe resistivity measurements were performed on five planar samples over the temperature range of 2-300 K. The apparent Hall mobility exceeds 10$^6$ cm$^2$ V$^{-1}$ s${^-1}$ at cryogenic temperatures and decreases systematically with increasing temperature, while the effective Hall carrier concentration exhibits strong carrier freeze-out behavior at low temperatures. The combined evolution of Hall mobility, effective Hall carrier concentration, and resistivity reveals distinct transport regimes associated with carrier freeze-out, extrinsic conduction, and phonon-limited scattering. The transport behavior is interpreted using a Matthiessens-rule-inspired phenomenological mobility model motivated by the combined influence of ionized impurity, neutral impurity, and acoustic phonon scattering. Variations among samples are correlated with differences in effective Hall carrier concentration and transport behavior. These measurements establish a transport baseline for USD-grown high-resistivity germanium crystals and provide guidance for future material optimization toward detector-grade high-purity germanium for low-background rare-event detector applications.

The electronegativity equalization principle provides a simple framework to describe charge redistribution, yet its conventional formulation is limited to a first-order description based on chemical potential equalization. In this work, we introduce 'multi-equalization,' a generalized framework that extends this concept by incorporating higher-order responses within Conceptual Density Functional Theory. This approach represents molecules as sets of flexible electron density partitions, allowing different electronic descriptions (e.g., atomic densities or localized orbitals) to be treated within a unified formalism. We demonstrate that correlations between energy and density derivatives with respect to the number of electrons lead to the simultaneous equalization of multiple descriptors, including chemical hardness and Fukui indices. A constructive algorithm is introduced to determine the optimal density partitions satisfying these multi-equalization conditions. This scheme provides a consistent description of both global charge transfer and local reactivity, overcoming the intrinsic limitations of traditional electronegativity equalization models. Notably, the inclusion of density response functions enables local hardness equalization, introducing spatial resolution into reactivity descriptions. Under multi-equalization, local reactivity descriptors become constrained functionals of the global electron density. This framework establishes a deeper connection between charge equalization models and formal density functional theory, offering a theoretically grounded route toward improved predictions of molecular reactivity.

Voltage-tunable capacitors (varactors) are key to microwave circuits. Tunable dielectric varactors outperform competing technologies in almost every relevant metric but usually suffer from high dielectric loss. In contrast, Ruddlesden-Popper (RPs) dielectric thin films have remarkably low microwave loss. Unfortunately, their crystallographic symmetry has until recently dictated an in-plane device structure, precluding the favorable out-of-plane parallel-plate varactor design for minimized size and maximized electric field in the tunable dielectric. Guided by theory, we report RPs akin to the widely studied tunable microwave dielectric BaxSr1-xTiO3. Assembling these same atoms into the first RP phase with broken out-of-plane symmetry, we achieve a low-loss, out-of-plane tunable dielectric thin film. The highest performing film, (ATiO3)nAO film with A = Ba0.45Sr0.55 and n = 8, unlocks a tenfold improvement in the figure of merit for out-of-plane tunable dielectrics at 10 GHz, paving the way for a new generation of tunable monolithic microwave integrated circuits.

We develop a molecularly motivated description of the nonlinear index (NLI) in oscillatory shear deformation of entangled polymers. The central assumption is that the shear component of the tube-orientation tensor cannot grow without bound. Convective constraint release (CCR), chain stretch, and tube dilation progressively reduce the number and lifetime of orientational constraints, but the maximum shear alignment of a tube segment is geometrically limited by $S_{xy}\leq 1/2$. This motivates a constraint-limited orientation closure in which the NLI first grows approximately with strain amplitude and then approaches the limiting value $\mathrm{NLI}_{\max}=3$ asymptotically rather than through an artificial cutoff. The same framework yields a molecular expression for the characteristic half-saturation strain $γ_s$, defined by $\mathrm{NLI}(γ_s)=3/2$, in terms of the entanglement number, oscillation frequency, and a critical number of remaining orientational constraints. We further derive architecture-dependent expressions for the nonlinear onset strain $γ_c$ for linear, sparsely long-chain-branched, and more regularly branched polymers. The resulting framework provides a compact bridge between Fourier harmonic analysis, CCR-based tube dynamics, and the progressive loss of orientational memory in highly deformed entangled polymer liquids.

Scanning tunnelling microscopy (STM) is a powerful technique for imaging surfaces with atomic resolution, providing insight into physical and chemical processes at the level of single atoms and molecules. A regular task of STM image analysis is the identification and labelling of features of interest against a uniform background. Performing this manually is a labour-intensive task, requiring significant human effort. To reduce this burden, we propose an automated approach to the segmentation of STM images that uses both few-shot learning and unsupervised learning. Our technique offers greater flexibility compared to previous supervised methods; it removes the requirement for large manually annotated datasets and is thus easier to adapt to an unseen surface while still maintaining a high accuracy. We demonstrate the effectiveness of our approach by using it to recognise atomic features on three distinct surfaces: Si(001), Ge(001), and TiO$_2$(110), including adsorbed AsH$_3$ molecules on the silicon and germanium surfaces. Our model exhibits strong generalisation capabilities, and following initial training, can be adapted to unseen surfaces with as few as one additional labelled data point. This work is a significant step towards efficient and material-agnostic, automatic segmentation of STM images.

A comprehensive methodology is developed to extract electron and hole effective masses in degenerate semiconductors through a simultaneous global fit of carrier concentration dependence of bandgap and plasma energy, explicitly incorporating band nonparabolicity. Broadband spectroscopic ellipsometry combined with Hall effect analyses enables accurate determination of the bandgap, plasma energy and carrier concentrations. The dielectric function of sputtered Al-doped ZnO thin films are modeled in the fundamental absorption region using an Elliott based model with overlapping excitonic transitions and Urbach tails, while free carrier absorption is described by a modified sernelius formula. Wide carrier concentrations are achieved via controlled deposition and post-annealing, revealing changes in electron effective masses and deviations from parabolic dispersion. Two nonparabolic models are compared, Pisarkiewicz, assuming spherically symmetric band with a step-function approximation of the Fermi-Dirac distribution and Nilsson, incorporating thermal and impurity effects. The latter is shown to capture accurately band nonparabolicity, yielding effective masses and nonparabolicity parameter consistent with bandgap evolution. This approach quantitatively separates Burstein-Moss shift and bandgap renormalization, reproducing carrier dependent bandgap shifts across a wide concentration range. Neglecting valence band contributions introduces systematic bias. Bandgap renormalization is further evaluated using plasmon pole and random phase approximations, underscoring the importance of many-body screening. This framework also enables determination of the Mott critical concentration and the fundamental absorption edge onset. Collectively, these results establish a reliable methodology for extracting band-structure parameters and bandgap shifts, extendable to other transparent conducting oxides.

Superatomic graphene platforms host a rich portfolio of flat-band-driven exotic quantum properties, yet their experimental realization remains challenging. Here, we report the bottom-up on-surface synthesis of superatomic graphene using phosphorus-doped triangulene as building blocks. Scanning tunneling microscopy and spectroscopy measurements resolve the well-defined honeycomb lattice of as-fabricated superatomic graphene and demonstrate the characteristic Dirac band and flat band electronic structures. Density functional theory calculations reveal that the flat bands originate from the in-plane p$_x,_y$-like frontier orbitals of the phosphorus-doped triangulene units, leading to intrinsic half-metallic behavior. Furthermore, oxygen functionalization of the molecular precursor enables deterministic modulation of the electronic structure and magnetic ordering. This work establishes a general platform for designing correlated quantum materials with tunable flat band properties.

Solution-processed thin films of colloidal lead halide perovskite (LHP) nanocrystals (NCs) show great potential for the implementation into optoelectronic devices such as light-emitting diodes (LEDs), lasers, and solar cells. However, these hybrid LHP NC solids exhibit non-negligible size and shape polydispersity, which introduces both structural and energetic disorder. Here, we resolve the exciton dynamics in space, time, and energy to elucidate the impact of different forms of disorder (structural and energetic) on exciton transport. We show that the disorder depends sensitively on the length of the alkylamine ligand used in the synthesis. While shorter alkyl chain lengths lead to high polydispersity, longer alkyl chains lead to more monodispersed and smaller particles where quantum confinement becomes more pronounced and, consequently, lead to increased energetic disorder. Strikingly, we find that exciton transport is less efficient in NC solids with long alkyl chain ligands, despite having a significantly more monodisperse ensemble. This demonstrates that energetic disorder, rather than structural disorder, is the dominant factor for predicting exciton transport within these materials. These findings reveal the critical role of ligand engineering in designing high-performance optoelectronic devices based on hybrid LHP NCs, providing new insights into energy transport dynamics in disordered systems and highlighting the versatility of these materials for advanced photonic and optoelectronic applications.

High quality crystalline growth of a thin film on sapphire requires sufficient substrate preparation, often achieved via the use of aggressive chemical cleaning. Direct thermal reconstruction of the sapphire substrate via a CO$_2$ laser beam may allow for an alternative way to prepare the substrate for epitaxy without the use of any chemical processing. Within this work, we demonstrate that thermal annealing of sapphire into its ($\sqrt{31}$$\times$$\sqrt{31}$)$R$$\pm$9° reconstruction is a valid alternative preparation technique for sapphire substrates. TiN films grown via plasma-assisted molecular beam epitaxy upon these substrates exhibit greater crystallinity than those grown on chemically cleaned sapphire substrates. Superconducting resonators fabricated from these films exhibit similar performance, with many possessing internal quality factors at single photon levels greater than 10$^6$ for both substrate preparation methods.

Ruthenium dioxide ($\mathrm{RuO_2}$) has been proposed as an altermagnetic candidate, although its magnetic ground state remains controversial. Here, we probe weak interfacial magnetic states at the surface of (001)-oriented $\mathrm{RuO_2}$ films using the magnetic proximity effect (MPE) in a van der Waals heterostructure consisting of monolayer tungsten diselenide ($\mathrm{WSe_2}$) atop $\mathrm{RuO_2}$. Temperature-dependent magneto-optical spectroscopy reveals an anomalous excitonic energy shift and a deviation from conventional Varshni behavior below 55 K that are absent in an encapsulated $\mathrm{WSe_2}$ control sample. The anomalous shift reverses sign upon field cooling with opposite magnetic field polarity, indicating a magnetic origin. Polarization-resolved measurements further show a nearly field-independent and fluctuating valley splitting in $\mathrm{WSe_2 / RuO_2}$ in strong contrast to the conventional linear Zeeman splitting observed in the control bare $\mathrm{WSe_2}$ sample. These results suggest that the valley states are governed predominantly by interfacial exchange fields associated with weak surface magnetic states in $\mathrm{RuO_2}$, which do not produce a conventional linear Zeeman response within the applied magnetic field range. Importantly, this approach enables direct optical probing of emergent surface magnetism without introducing an additional ferromagnetic layer, positioning MPE-based optical probing as a tool for investigating weak surface magnetism and offering new possibilities for studying magnetic materials with controversial magnetic states.

In multiscale modeling of heterogeneous softening materials, boundary conditions (BC) in the fine-scale model strongly influence the strain localization pattern and the macroscopic response. For rectilinear models (e.g., squares or cubes), standard Periodic BCs produce artificially ductile behavior with excessive energy dissipation when the localization band inclination does not match the periodicity directions. Recently proposed Tessellation and Percolation-path-aligned BCs promise to address this by adapting the periodicity frame to align with the evolving localization bands. Alternatively, spherical/circular models provide an orientation independent response by design. Unfortunately, the standard Periodic BCs do not allow development of proper localization band crossing spherical model's boundaries. A recently proposed modification addresses this by adding a displacement jump to the spherical periodic BCs. This study evaluates the applicability of these novel BCs to a mesoscale discrete particle model of concrete. Two-dimensional square and circular models under uniaxial tension with different loading directions are analyzed, with the selected approaches extended to three-dimensional cube models. Results show that Percolation-path-aligned BCs exhibit major shortcomings: they can lead to multiple localization bands due to uneven straining of the two boundary sections and their weakly constrained section can be prone to spurious strain localization. In contrast, Tessellation BCs consistently yield a well-defined localization band, whose length is determined solely by the model geometry, making it straightforward to account for in post-processing. Periodic boundary conditions augmented with a displacement jump applied to a circular model sometimes incorrect produce crack patterns similar to those under the standard Periodic BCs.