Papers

We introduce a systematic analysis of density functional approximation errors in solids by separating functional-driven from density-driven contributions using quantum Monte Carlo densities of silicon, sodium chloride, and copper as reference. Typically, functional errors dominate, but we identify important exceptions where density-driven errors exceed functional errors by factors of 2-3, notably for SOGGA11 and {\tau}-HCTH in the semiconductor and the insulator. Material dependence is striking: 63% of functionals show error cancellation in silicon versus 18% in copper, and only five functionals surpass LDA accuracy for metallic copper even with exact densities. For silicon and sodium chloride, GILL or BECKE exchange combined with PBE, PW91, or P86 correlation achieves near-exact xc energies on QMC densities, while copper requires specialized functionals like PBEsol or PBELYP. High-quality densities consistently reduce density-driven errors across all systems. Historical analysis reveals that 1990s GGA functionals outperform many modern meta-GGAs, contradicting expectations of systematic improvement along Jacob's ladder. These results provide practical guidance for functional selection and highlight implications for machine learning potential development, where material-dependent error cancellation may compromise transferability.

Altermagnets have attracted intense interest because they have the advantages of both ferromagnets and antiferromagnets. However, their experimental identification remains challenging, in particular for the A-type altermagnets that account for a large group of material candidates. Here, we discover a kind of anisotropic surface spin waves in A-type altermagnets, which is absent in ferromagnets and conventional antiferromagnets. The anisotropic surface spin waves arise directly from the nature of altermagnets, i.e., the spin-opposite sublattices cannot be related by translation or inversion, which breaks the combined spatial-inversion and time-reversal symmetry, leading to the anisotropic surface spin waves with two properties, the chirality-dependent top-bottom positions and chiral split constant frequency contours. We further show that these two properties can be measured experimentally from the stray field and by resonance absorption spectrum, respectively. Our results provide a signature for detecting altermagnets and will inspire spin-based logic and information-storage devices.

We investigate the weakly nonlinear dynamics of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. Building on our previous linear stability analysis, we derive Stuart-Landau amplitude equations governing the emergence and saturation of oscillations near the Hopf bifurcation. The Landau coefficients are expressed in terms of the critical eigenmode, its adjoint, and quadratic correction fields arising from the asymptotic expansion. The reduced theory predicts the criticality of the Hopf bifurcations, the saturated oscillation amplitude, and the nonlinear frequency correction, in quantitative agreement with direct numerical simulations for representative material parameter regimes. Applying the theory to both stability boundaries of the finite oscillatory window, we find that the lower Hopf bifurcations are supercritical, whereas the upper restabilization threshold is subcritical. These results provide a normal-form description of follower-force-driven oscillations in geometrically exact Cosserat rods and a reduced framework for studying nonconservative elastohydrodynamic instabilities in soft robotic structures and active filaments.

Nitrogen-vacancy (NV) centers in diamond are a leading platform for solid-state quantum sensing and quantum information processing. While most optical studies rely on the visible fluorescence associated with the triplet transitions, the infrared singlet transition near $1042$ nm, which is typically considered dark within the singlet manifold of the NV optical cycle, provides an alternative optical channel. Here, we report wavelength-resolved optically detected magnetic resonance (ODMR) measurements of this infrared emission. We directly observe ODMR contrast in the $1042$ nm emission and analyze its dependence on the magnetic field. The field-dependent spectral dispersion of the ODMR signal demonstrates that the spin-state information encoded in the NV center is transcribed to the infrared singlet emission through the spin-selective intersystem crossing, in close analogy to the visible fluorescence readout. These results establish infrared ODMR as a high-fidelity optical readout pathway. Crucially, by extending spin-state transcription directly into the $1300-1600$ nm range, this work demonstrates a direct, conversion-free interface between diamond spin-qubits and standard telecommunication infrastructure, bypassing the efficiency bottlenecks of active frequency conversion and benefiting from the already well-developed technologies in this range of the electromagnetic spectrum.

Modern implementations of path integral molecular dynamics (PIMD) simulations of distinguishable particles frequently make use of high order factorization schemes for the Boltzmann operator to expedite convergence of equilibrium averages. Among these methods is the generalized Suzuki-Chin factorization (GSF), which is accurate up to fourth order in the imaginary-time step. In this work, we show that the GSF decomposition of the Boltzmann operator is applicable to bosonic PIMD, and results in an improved convergence of estimators. In particular, we show that the recently developed quadratic scaling bosonic PIMD need not change when using the GSF. The GSF scheme is implemented as a re-weighting factor for observables, without affecting the sampling generated by the standard, second-order, primitive factorization. We study the effect of this factorization for bosons in a harmonic trap and a sinusoidal potential. We also assess the effectiveness of GSF in calculating fermionic expectation values for harmonically-trapped atoms. In all these cases, we find that the GSF speeds up convergence with the Trotter number by a factor of $\sim 2-4$ across a wide temperature range, at only a modest computational cost.

In physical systems, whenever a continuous symmetry is spontaneously broken, the system possesses excitations called Goldstone modes, which allow coherent information propagation over long distances and times. In this work, we study deep neural networks whose internal layers are equivariant under a continuous symmetry and may therefore support analogous Goldstone-like degrees of freedom. We demonstrate, both analytically and empirically, that these degrees of freedom enable coherent signal propagation across depth and recurrent iterations, providing a mechanism for stable information flow without relying on architectural stabilizers such as residual connections or normalization. In feedforward networks, this results in improved trainability and representational diversity across layers. In recurrent settings, we demonstrate the same mechanism is valuable for long-term memory by propagating information over recurrent iterations, thereby improving performance of RNNs and GRUs on long-sequence modeling tasks.

Focused electron beam induced deposition (FEBID) is an additive manufacturing technique uniquely suited for fabricating functional 3D nanostructures for a range of applications, including spintronic devices. However, the variation of growth dynamics associated with lateral movement of the electron beam results in structures with non-uniform composition when fabricating intricate 3D geometries. Herein, we measure changes in atomic composition and corresponding changes in magnetic induction in 3D ferromagnetic nanostructures with overhanging elements, e.g. bridges or arches. To investigate the effects of electron beam lateral movement, we fabricated Co and Fe nanowire (NW) structures with growth angle relative to the optic axis varying from 0{\deg} to 90{\deg}. The (scanning) transmission electron microscopy techniques of electron energy loss spectroscopy and off-axis electron holography were performed to map the NW elemental composition and magnetic induction as a function of NW growth angle. Comparison of the results reveals a reduction in metal content with increased growth angle in FEBID NWs. The magnitude of metal content reduction can be tuned by controlling electron beam parameters, and ferromagnetic NWs with approximately equal metal content at growth angles from 0{\deg} to 60{\deg} were fabricated by using the lowest viable electron beam voltage and the highest viable beam current to reduce the interaction volume and increase the metal content, respectively.

Autoresearch offers a flexible paradigm for automating scientific tasks, in which an AI agent proposes, implements, evaluates, and refines candidate solutions against a quantitative objective. Here, we use composition-based materials-property prediction to test whether such agents can perform a task beyond model selection and hyperparameter optimization: the design of input descriptors. We introduce Automat, an autoresearch framework where a coding agent based on a large language model generates composition-only descriptors for chemical compounds and evaluates them using a random forest workflow. The agent is restricted to information derivable from chemical formulas and iteratively proposes, implements, and tests chemically motivated descriptor strategies. We apply Automat, with OpenAI Codex using GPT-5.5 as the coding agent, to the prediction of experimental band gaps in inorganic materials and Curie temperatures in ferromagnetic compounds. In both tasks, Automat improves over fractional-composition, Magpie, and combined fractional-composition/Magpie baselines, while producing descriptor families that are chemically interpretable. These results provide a demonstration that autoresearch agents can generate competitive, task-specific materials descriptors without manual feature engineering during the run. They also reveal current limitations, including descriptor redundancy, sensitivity to greedy feature expansion, and the need for explicit complexity control, descriptor pruning, and more sophisticated search strategies.

Hydrogen (H2) is a promising carbon-neutral energy carrier. However, its deployment is limited by the lack of lightweight, reversible storage media that operate under practical conditions. Here, we establish nitrogen-doped graphdiyne (N-GDY) as a programmable two-dimensional platform for stabilizing dispersed light-metal dopants and enabling high-capacity physisorption of molecular H2. The computational package involves density functional theory (DFT) combined with ab initio molecular dynamics (AIMD) and Langmuir-based statistical thermodynamic modeling. The results revealed that N-sites of N-GDY bind up to five Li, Na, K, and Ca atoms per primitive cell with binding energies of -2.27, -1.57, -1.80, and -2.13 eV, respectively, exceeding their respective bulk cohesive energies. AIMD simulations at 400 K further confirm the structural robustness of the decorated frameworks and the absence of metal aggregation. The polarised metal centres activate reversible H2 adsorption through electrostatic and dispersion interactions, with average adsorption energies falling within the optimal window (-0.15 to -0.35 eV per H2). Sequential adsorption analysis reveals uptake of up to 25 H2 molecules per primitive cell, achieving intrinsic gravimetric capacities of 13.08, 10.82, 9.23, and 9.15 wt% for Li-, Na-, K-, and Ca-functionalized systems, respectively. Thermodynamic analysis indicates favorable adsorption-desorption behavior under near-ambient conditions, with Li- and Ca-functionalized systems exceeding the 6.5 wt% U.S. Department of Energy's ultimate system-level target when considering intrinsic material capacity. These results identify N-GDY as a chemically tunable scaffold for dispersing lightweight metals and provide a mechanistic design strategy for achieving high-capacity, reversible hydrogen storage in porous two-dimensional materials.

We investigate localization and spectral topology in a non Hermitian quasiperiodic Su Schrieffer Heeger lattice with Rashba spin orbit coupling and spin-dependent hopping. By analyzing the inverse participation ratio, complex energy spectrum, and spectral winding numbers, we demonstrate the emergence of a re-entrant transition from extended to localized and back to extended phases as the non-Hermitian parameter increases. The localization transition is accompanied by a simultaneous real-complex-real spectral transition in the complex-energy plane. In the absence of spin dependent hopping, the spectrum forms two nearly spin-degenerate loops characterized by winding numbers w = 2. Upon introducing finite spin-dependent hopping, each loop splits into two independent spin-resolved spectral branches, resulting in four disconnected spectral contours carrying distinct winding sectors. Our results reveal a direct correspondence between localization, spectral topology, and spin-resolved spectral splitting in non-Hermitian quasiperiodic systems.

The electronic structure of Samarium (Sm) was calculated using the density functional theory combined with the single-site dynamical mean-field theory. In this work, we investigated the electronic properties of {\alpha}, e̱ta} and {\gamma} phases at ambient pressure, including the band structures, density of states, self-energy functions and valence state histograms. Our results agree with the experimental data.The calculation shows that the 4f electrons in all these phases are well localized, the Kondo peaks are suppressed and the hybridization between the 4f electrons and conduction electrons are quite weak. Our results also show the strong correlation effect is significant in Sm metal.

Nanoscale quantum light sources are essential building blocks for integrated quantum photonic systems. Here, we report a wavelength-scale entangled-photon source based on van der Waals-engineered NbOBr$_2$, and benchmark its performance for telecom-wavelength quantum light generation. By exploiting the material's second-order nonlinearity, we generate quantum-correlated photon pairs via spontaneous parametric down-conversion. We then use a 90$^{\circ}$ twisted stacking to induce quantum interference in photon-pair generation, yielding polarization-entangled photons. This approach enables tunability of the quantum optical state via control of the excitation laser polarization. We experimentally obtain entanglement fidelities exceeding 95% for Bell states, along with a high coincidence-to-accidental ratio of $\sim$335, and a brightness approximately one order of magnitude higher than recently reported telecom sources based on transition metal dichalcogenide (TMD) 2D materials. These results establish twisted van der Waals engineering as a powerful platform for highly tunable, high-brightness quantum light sources at telecom wavelengths.

We propose a superconducting circuit hosting $d$ low-lying states, well separated from the rest of the spectrum, that naturally realizes a qudit system protected from leakage errors. The system represents a generalization of the fluxonium and the low-energy states are constituted by fractional fluxon states, that we call fraxons, localized in the minima of a suitably designed Josephson potential. The latter is tailored through a Fourier engineering approach, that employs multi-harmonic Josephson building block elements composed by a Josephson junction and an inductance connected in series. We present the spectrum of a $d=4$ and a $d=5$ qudit system and study in detail the qutrit case. We analyze the dipole matrix elements for coupling to radiation and propose a non-Abelian, stimulated Raman adiabatic passage (STIRAP) protocol for single-qutrit gates, that is particularly suited for the present system. The proposed platform opens novel perspectives in circuit engineering and quantum computing beyond the qubit paradigm.

The thermoresponsive behavior of Pluronic F127 solutions is governed by temperature-dependent micellization and complex self-assembly of these micelles. This study investigates the effect of thermal stimuli on the kinetics of phase transition of Pluronic systems during heating and cooling cycles. We employ Differential Scanning Calorimetry measurements to investigate the dependence of the micellization temperature on thermal stimuli, revealing that both the micellization temperature and the peak intensity vary systematically with the applied thermal ramp rate. Furthermore, we employ rheological characterization which reveals a sharp sol to soft-solid transition upon heating. Interestingly, we observe a novel multi-step transition during the cooling phase, indicating a more complex reorganization pathway with intermediate metastable states than typically assumed for reversible micellization. Our findings indicate that the characteristic multi-step cooling transition is transient, gradually weakening with successive thermal cycles. We also present a comprehensive mathematical model which accurately captures the kinetics and multiple step transition in viscoelastic parameters. Significantly, the distinct peaks in Small-Angle X-ray Scattering (SAXS) measurements clearly reveal the evolution from a disordered unimers/micelles state at low temperatures to a highly ordered lattice with long-range spatial correlation at elevated temperatures. We also present a comprehensive phase diagram highlighting the critical role of thermal stimuli and pathways in defining the phase behavior of Pluronic system. This work, therefore, offers essential experimental and theoretical insights into the thermally driven self-assembly, transition kinetics, and microstructural evolution of thermoreversible Pluronic solution.

DNA methylation is usually treated as an epigenetic memory mark: transcriptional history is written into regulatory DNA and later stabilizes a chosen cell identity. This picture explains persistence, but it makes memory passive. Here we show that the same promoter-level coupling required for methylation memory can instead turn methylation into an internal control variable for regulatory dynamics. Transcription-factor occupancy protects regulatory DNA from methylation, while methylation shifts later transcription-factor binding thresholds. Under time-scale separation, this reciprocal loop separates into fast expression dynamics conditioned on methylation and a slow methylation flow written by expression. Minimal promoter, self-activation, and fate-toggle models show that this feedback does more than preserve a past state: it autonomously reshapes the expression landscape. In a methylation-coupled toggle, the preferred expression state can move continuously through single-well drift, allowing commitment without first entering a multiwell regime. Stochastic simulations further show that evolving methylation reduces fate reversals relative to a frozen landscape, making weak early expression bias more predictive of later fate. These results recast DNA methylation from a downstream stabilizer of cell identity into a slow dynamical coordinate that can help determine how regulatory states are chosen.

Dirac-Weyl semimetals host both Dirac and Weyl fermions and the exploration of material candidates with tunable topological properties is essential to realize topological spintronic devices. In this work, we propose CaAgBi as a Dirac-Weyl semimetal with tunable type-I and type-II Weyl points based on first-principle calculations. In addition to the three pairs of Dirac points located along the rotational axis as previously reported, our calculations reveal 18 additional pairs of dual-type Weyl points distributed across three distinct planes: type-I in the $k_z=0$ plane and type-II in the $k_z= \pm 0.0698\,\frac{2\pi}{c}$ planes. The topological features are further confirmed through chirality of the Weyl points as well as the existence of surface Fermi arcs. Moreover, we find that the position and annihilation of Dirac and Weyl points are tunable by the alloy engineering and external strains. The alloy engineering is employed to modulate the positions of Weyl points, revealing different annihilation concentrations for type-I and type-II Weyl points, potentially offering novel experimental strategies for Weyl point manipulation. Under tensile biaxial strain, the Weyl points in the $k_{z}=0$ plane annihilate along the $\Gamma$–$\mathrm{M}$ path at $2.1\%$ strain, whereas the Weyl points in the $k_{z}\neq 0$ planes remain robust within $6\%$ strain. This work provides a versatile platform for manipulating Dirac/Weyl interactions, with spin-orbit coupling (SOC) driven alloy control and strain-selective engineering opening avenues for topological electronics.

This work explores the static and dynamic magnetic properties of weakly antiferromagnetically coupled Fe/Ti superlattices, emphasizing the link between magnetic behavior and structural characteristics. HRTEM and XRD analyses confirm alternating Fe and Ti layers with rough interfaces, especially in upper layers. Magnetic measurements reveal two-step hysteresis loops and a temperature and thickness-dependent interlayer exchange coupling (IEC). A macrospin model incorporating bilinear and biquadratic coupling reproduces the experimental data and supports a phase diagram analysis identifying non-collinear configurations. The results underscore the impact of structural imperfections and highlight the crucial role of biquadratic exchange in Fe/Ti/Fe multilayers.

Methane hydrate nucleation under nanoconfinement remains poorly understood due to the complex interplay between geometric restriction and molecular ordering. Here, we investigate the structural organization of water-methane systems confined between silica planar slit pores with widths ranging from 1 to 5 nm and temperatures between 250 and 295 K. Three-dimensional radial distribution functions reveal a clear suppression of hydrate-like ordering at strong confinement (below 2 nm), indicating frustrated nucleation. In contrast, projected two-dimensional correlations exhibit pronounced in-plane structural organization, evidencing a confinement-induced reduction in the dimensionality of molecular order.

Developing machine learning interatomic potentials (MLIPs) for complex materials systems remains challenging because it requires expertise in atomistic simulations, machine learning, and workflow design, as well as iterative active learning procedures. Existing automated pipelines typically assume a fixed sequence of stages or depend on domain experts, which limits their adaptability to heterogeneous materials systems where the optimal curriculum is not known in advance. To lower the barrier to developing MLIPs for non-experts, we propose Lang2MLIP, a multi-agent framework that takes natural-language input and formulates end-to-end MLIP development as a sequential decision-making problem solved by large language models (LLMs). At each step, a decision-making agent observes the current dataset, model, evaluation results, and execution log, and then automatically selects an appropriate action to improve the model. This removes the need for a predefined pipeline and enables the agent to self-correct by revisiting earlier subsystems when new failures arise. We evaluate this approach on a solid electrolyte interphase (SEI) system with multiple components and interfaces. These results suggest that LLM-based multi-agent systems are a promising direction for automating MLIP development and making it more accessible to non-experts.

Computation of observables in discrete stochastic, possibly conditioned, dynamics over large sparse networks is fundamental for a myriad of applications. The Matrix-Product Belief Propagation method allows a semi-analytical estimation of such observables in tree-like networks with a controlled error that depends on the bond dimension, that is the dimension of the employed square matrices. Its computational cost is linear in the time horizon and the network size for a large family of models with discrete degrees of freedom. Here, a generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is presented, using a tunable expansion in a Hilbert function basis. For a wide class of models, the computational cost of the method is linear in the network size with a prefactor that depends on the basis size and the bond dimension. The method's efficacy is demonstrated by employing a Fourier basis for a mixed continuous/discrete representation of the Kinetic Ising dynamics with real-valued random couplings, where intermediate "local fields" are treated as continuous. The accuracy of the method is verified via comparison with Monte Carlo simulations. For this model, we calculate time auto-correlations, time evolution of energy and magnetization, and finally we estimate the large deviation function of the magnetization at a given future time.

In living cells, proteins involved in specialized biochemical functions are often spatially organized within biomolecular condensates. Increasing evidence suggests that some of these condensates, including DNA repair condensates, emerge through liquid-liquid phase separation (LLPS). In the nucleus, however, condensates form within a highly heterogeneous environment composed of chromatin fibers, RNA, and additional protein scaffolds such as PAR chains, all of which may interact with phase-separating proteins. Moreover, condensate formation is frequently associated with specific chromatin conformations; for instance, loop extrusion has been proposed as a mechanism promoting DNA repair condensates. Here, we investigate how the surrounding fibrous environment controls the morphology and spatial organization of phase-separated condensates. Using Brownian dynamics simulations of minimal models combining Lennard-Jones particles with fixed fibrous substrates, we examine the respective roles of local fiber geometry and large-scale network organization, reflecting the multiscale architecture of chromatin. We show that protein-fiber interactions strongly influence droplet positioning relative to the substrate, in a manner analogous to wetting transitions in soft condensed matter systems. Both local geometric constraints and global network organization markedly affect droplet size, morphology, and multiplicity. In addition, large-scale asymmetries in fiber organization can induce robust spatial localization of the dense phase. Our results thus highlight how multiscale structural heterogeneity of the nuclear environment can regulate the emergence and organization of biomolecular condensates.

Chiral crystals exhibit enantiomer-dependent transport phenomena that generate pure spin or orbital currents, while the handedness sensitivity of spin and orbital Hall conductivities (SHC/OHC) remains insufficiently understood. Using first-principles calculations, we demonstrate that trigonal selenium and tellurium – prototypical chiral semiconductors – exhibit opposite signs of the SHC/OHC tensor elements $\sigma_{yx}^{S_y}$ and $\sigma_{yx}^{L_y}$ between their left- and right-handed enantiomers. This behavior originates from the mirror operation relating the two structures, described by space groups $P3_221$ (left-handed) and $P3_121$ (right-handed). Although both enantiomers share identical band structures and four nonzero SHC/OHC tensor components, $\sigma_{yx}^{S_y}$ and $\sigma_{yx}^{L_y}$ reverse sign due to the antisymmetric transformation of the spin/orbital Berry curvature under the $M_{xy}$ mirror operation. More generally, for mirror-related enantiomorphic structures, selected SHC/OHC tensor components can exhibit symmetry-governed sign reversal. For trigonal Se and Te, the calculated signs of these components can be directly correlated with the left- and right-handed structures under the chosen coordinate convention. These results clarify the symmetry origin of handedness-dependent SHC/OHC and suggest a possible route for correlating measurable SHC/OHC signals with structural handedness in specific chiral materials.

The standard Hamiltonian of a coupled electron-phonon system is based on second-order perturbation theory. The EPI contribution in the standard Hamiltonian consists of two terms, the EPI contribution to the band-structure energy and the partial-Fan-Migdal (FM)-occupied contribution. Within the non-adiabatic approximation, we derive a new expression for the partial-FM-occ contribution and show that it has the structure of a higher-order term, and not a second-order term. Along similar lines, we derive new expressions for the computation of the partial-FM-occ term. The new expressions for the partial-FM-occ term must be preferred over the standard expressions, in theoretical and computational studies, because they incorporate the complete physics underlying this term. Unlike the EPI contribution to individual eigenstates, the EPI contribution to the total energy must be computed in the non-adiabatic approximation for all materials, Infra-red (IR) active and IR-inactive. We report the computation of the standard Hamiltonian, for the first time, for Carbon polymorphs (diamond and hexagonal lonsdaleite) by including the EPI contribution to the total energy. This is the most accurate ab initio total energy reported till date. The present work also opens the way to compute the ab initio free-energy more accurately at finite temperatures by including the EPI contribution.

High-pressure research is a productive route to new structures and emergent properties. However, crucial high-pressure structural information remains highly fragmented across individual publications and heterogeneous computational repositories. This fragmentation creates a major bottleneck for data-driven materials design. To bridge this gap, we introduce the High-Pressure Crystal Structure Database (HPCSD), a traceable, pressure-resolved repository that integrates experimental and theoretical high-pressure structures. HPCSD is constructed from two complementary data streams: elemental high-pressure phases and a searchable configuration space of stable and metastable phases generated via CALYPSO crystal structure prediction. To ensure rigorous comparability, all retained structures underwent re-optimization under a unified density functional theory (DFT) framework , with continuous enthalpy curves systematically generated specifically for the elemental phases across their stability fields. The initial release encompasses 77,346 consistently evaluated structural entries spanning 89 elements. An analysis reveals that pressure-induced polymorphism is ubiquitous and exhibits pronounced family-dependent trends. Structural diversity is strongly influenced by an element's electronic adaptability , with the greatest structural complexity emerging at intermediate rather than highest pressures. By providing standardized, reusable, and rigorously evaluated high-pressure structural data, HPCSD establishes a robust infrastructure to accelerate experimental phase identification, facilitate cross-study thermodynamic comparisons, and support the development of machine-learning interatomic potentials and generative models for high-pressure systems.

We derive a way to diagnose band topology for graphene with triangular and/or honeycomb array of nanoholes directly from the lattice constant of superstructure $m\sqrt{3}\times m\sqrt{3}$ with integer $m$. Taking into account the $C_{6v}$ crystalline symmetry respected by nanoholes and their array, we demonstrate that nontrivial topology appears periodically with $m$ with period two (six) for triangular (honeycomb) array. These behaviors are verified by Wyckoff positions of Wannier centers and parity index of valence bands at high-symmetry points in Brillouin zone. The results provide a convenient guide for material design of topological electronic states based on graphene derivatives.

Maximally localized Wannier functions (MLWFs) are conventionally constructed by iteratively minimizing a spread functional over a high-dimensional gauge landscape. In this work, we present a non-variational constructive algorithm that unifies gauge smoothing and the eigenvalue problem of the projected position operator into a single deterministic framework. We demonstrate that discrete adiabatic transport across band degeneracies emerges naturally as an integral part of the solution procedure for the position eigenvectors. In this transport-aligned gauge, the Bloch overlaps exhibit an approximately linear phase dependence, allowing the Wannier centers to be extracted via deterministic fixed-point iterations and self-consistent updates rather than spread-functional minimization. Benchmark calculations for one- and two-dimensional systems yield spreads and orbital shapes in good agreement with standard minimization schemes. Furthermore, this analytical approach transparently isolates the physical origin of the $\mathcal{O}(L)$ mesh-dependent spread scaling ($L$ being the boundary seam resolution) observed in graphene, demonstrating that it is an intrinsic geometric manifestation of non-commuting projected position operators forcing finite gauge defects to accumulate along a one-dimensional boundary seam.

First-principles density functional theory (DFT) is employed to evaluate the structural, electronic, optical, thermoelectric, and electrocatalytic properties of monolayer CrSi2N4. Its symmetric N-Si-N-Cr-N-Si-N septuple-layer structure exhibits dynamic, thermal (300 K), and mechanical stability, supported by a -8.76 eV/atom cohesive energy. PBE and HSE06 functionals reveal an indirect bandgap of 0.58 eV and 2.16 eV, respectively, driven by localized Cr-3d and N-2p states. The monolayer features 15.57 static dielectric constant and maximum absorption coefficients of 0.9 X 10^6 cm-1 (visible) and 1.4 X 10^6 cm-1 (deep-UV). Semiclassical Boltzmann calculations predict an outstanding room-temperature n-type thermoelectric power factor of 3.5 x mW/mK2. For hydrogen evolution (HER), the basal plane yields a baseline hydrogen adsorption free energy ({\Delta}GH) of 1.05 eV at the N-site. Applying +5% expansive biaxial strain improves HER kinetics, reducing {\Delta}GH to 0.46 eV. Thus, CrSi2N4 is a resilient, tuneable candidate for waste-heat recovery, photodetectors, and sustainable electrocatalysis.

Altermagnetic spin splitting alone does not define Chern matter. The relevant object is the exchange mass projected onto Hall-active surface, valley, orbital or interface sectors. We formulate this projected-mass criterion for compensated magnetic topology. The resulting two-channel $(C,\mathcal{A})$ diagnostic separates hidden compensated Hall responses from additive altermagnetic quantum anomalous Hall phases in a global insulating gap. It also guides interface, thickness and materials design strategies.

Nanoscale fabrication inevitably produces local stochasticity that is commonly treated as a defect, but can instead be harnessed as a material resource for information security. Here we report a chiroptical platform for ternary entropy harvesting based on stochastic Au nanopatterns formed by block copolymer self-assembly. By transducing fabrication-induced stochastic microstates into handedness-dependent optical responses through chiroptical mapping, our platform enables native ternary digitization rather than conventional binary encoding, allowing physically harvested ternary random sequences to be used for key generation. This raises the information density to log2(3) = 1.585 bits per trit, approximately 58.5% higher than the binary limit, enabling more entropy to be harvested from a limited physical footprint. The harvested outputs exhibit near-balanced symbol populations, negligible spatial and inter-sample correlations, Shannon entropy approaching the ternary ideal, and resistance to statistical and machine-learning-based prediction. These results establish self-assembled chiroptical nanostructures as a scalable platform for cryptographic key generation, secure edge devices, and distributed Internet-of-Things platforms.

Amorphous solids represent the extreme limit of broken translational symmetry, in which the absence of long-range order removes well-defined crystal momenta and invalidates the Bloch description of electronic states. Monolayer amorphous carbon (MAC) has emerged as a unique realization of a strictly two-dimensional (2D) amorphous lattice defined by a structurally contiguous but topologically disordered $sp^2$-bonded random network devoid of any defined long-range crystal symmetry. From atomic-resolution measurements of multifractal wavefunctions, we show that disorder in MAC effectively localizes the low-energy part of the electronic spectrum but retains an extended critical-like state near the band centre ($E\sim 0$). We conjecture that this state is protected from topological disorder by remnant chiral symmetry surviving within the continuous random network, described by a Wess-Zumino-Witten (WZW) topological term. Near criticality, we verify the multifractal scaling relation $\eta = -\Delta_2$, providing quantitative agreement between independently measured spatial correlation decay and multifractal scaling exponents. Our results are confirmed by atomistic tight-binding calculations that closely mirror the multifractal scaling near $E\sim 0$. Our results establish MAC as the first strictly 2D amorphous electronic system to exhibit Anderson criticality driven purely by topological disorder