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Article
Physical Sciences
Condensed Matter Physics

Andrezza França Batista

,

Everton Crestani Rambo

,

Júlio Goulart dos Santos

,

Hugo Campos Loureiro

,

Romildo Jerônimo Ramos

,

Edson Ferreira Chagas

,

Eralci Moreira Therézio

Abstract: Combining thiophene derivatives offers a route to improve film morphology while retaining electronic properties relevant to optoelectronic applications. This work investigates electrochemically synthesized poly(3-methylthiophene-co-3-hexylthiophene) (P3MT:P3HT) films in comparison with poly(3-methylthiophene) (P3MT) and poly(3-hexylthiophene) (P3HT) prepared under the same deposition conditions. Films were deposited on fluorine-doped tin oxide (FTO) by galvanostatic electropolymerization with charge control and characterized using electron and atomic force microscopy, Kelvin probe force microscopy, optical spectroscopy, and cyclic voltammetry. The copolymer exhibited a more homogeneous surface than P3MT and an intermediate thickness of 410 ± 45 nm. Its average surface potential was 0.44 V, close to P3MT (0.39 V) and lower than P3HT (0.70 V). An oxidation onset of 0.50 V versus Ag/AgCl and an optical gap of 2.05 eV provided estimated HOMO and LUMO energies of -4.93 and -2.88 eV, respectively. Photoluminescence analysis revealed changes in the relative emission contributions, while the separation between absorption and excitation maxima decreased from 30 nm for P3MT to 11 nm for the copolymer. These results demonstrate that electrochemical copolymerization improves film uniformity while preserving surface potential and oxidation characteristics close to P3MT, combining complementary morphological, optical, and electronic properties for optoelectronic applications.

Review
Physical Sciences
Condensed Matter Physics

Cleber A. Amorim

,

Adenilson J. Chiquito

Abstract: This review examines the development of SnO2 nanowires from synthesis and structural control to surface engineering, device integration, and manufacturing-related considerations. A total of 210 studies published between 2001 and 2026 were included. Vapor-based methods, particularly thermal evaporation, vapor–liquid–solid growth, and chemical vapor deposition, were the most frequently reported synthesis routes, while hydrothermal, template-assisted, physical vapor deposition, and atomic layer deposition approaches contributed to specific architectures and integration strategies. The literature shows a progressive shift from isolated nanowires toward networks, aligned arrays, branched structures, and core–shell heterostructures, accompanied by increasing use of catalytic decoration, doping, and defect engineering. Gas sensing was the dominant application, followed by photodetection and photonics, energy storage, biosensing, and photocatalytic systems. Across these applications, device performance was strongly influenced by nanowire dimensions, surface depletion, interwire junctions, heterointerfaces, and metal contacts. Stability was more frequently evaluated than reproducibility, and systematic comparison across independently fabricated devices or synthesis runs remained less common. Although large-scale and on-chip growth have been demonstrated, the transition to manufacturing still depends on controlling morphology, interfaces, process uniformity, device yield, and fabrication complexity. Overall, SnO2 nanowire research has evolved from synthesis-centered studies toward increasingly integrated and application-oriented systems, with reproducibility and scalable fabrication remaining central challenges for broader technological implementation.

Article
Physical Sciences
Condensed Matter Physics

Sergey G. Fedosin

Abstract: In vector field theory, calculating the energy of a rotating body requires using components of four-potentials and field tensors. In this connection, the scalar potentials and strengths of electromagnetic and gravitational fields, acceleration fields and pressure fields are calculated for the case of the relativistic uniform spherical system consisting of charged particles rotating with a constant angular velocity. The calculation method is based on the use of spherical vector polynomials associated with Legendre polynomials. It is shown that in a rotating system the same relation holds between field coefficients as in a stationary system. The rotation leads to new relativistic effects, in which directions of force lines of field strengths begin to deviate from the purely radial directions of rotating sphere. In addition, the scalar potentials of electromagnetic and gravitational fields in the center of the sphere and beyond the sphere increase in absolute value, as do the scalar potentials of acceleration field and pressure field in the center of the sphere. The Lorentz factor of particles moving in the center of the sphere also increases. The indicated effects were discovered due to the fact that the calculation method allows achieving high accuracy.

Article
Physical Sciences
Condensed Matter Physics

Sergei Mukhin

Abstract: The Q-ball mechanism of high-Tc superconductivity in cuprates, recently proposed by the author, is farther explored. Euclidean Q-balls are Bose condensed spin/charge density wave fluctuations (SDW/CDW) with zero static mean that arise simultaneously with Cooper/local pairs superconducting condensate for which they serve as the ’pairing glue’. Bose condensates of SDW/CDW fields possess wave-vectors connecting ’nested’ parts of the Fermi surface near van Hove singularities causing pairing of the fermionic states into superconducting Bose condensates. Self-consistency equations for quantum orders periodic in the imaginary Matsubara time fields signify a new development beyond Landau static mean-field order parameter approach. Cooper/local pairs condensation lowers Q-balls total energy relative to not condensed thermal SDW/CDW fluctuations in the same volume. Q-balls’ superconducting condensates cause spectral gap on the nested parts of the Fermi surface in the ’pseudogap’ phase of high-Tc cuprates, where the Q-ball scenario was supported by micro X-ray diffraction data in HgBa2CuO4+y. Scattering on the Q-balls causes: T-linear growth of electrical resistivity, splitting of in-plane phonon brunches into softened and hardened ones and "hourglass" dispersion of spin-wave excitations close to CDW and SDW wave vectors respectively. Diamagnetic response of Q-balls’ gas above Tc is in qualitative accord with experimental data in high-Tc cuprates.

Article
Physical Sciences
Condensed Matter Physics

Susy Exists

,

Sougata Mardanya

,

Vineet Kumar Sharma

,

Matthew Matzelle

,

Arun Bansil

,

William Ratcliff

,

Sugata Chowdhury

Abstract: Altermagnetism has emerged as the third fundamental magnetic phase alongside ferromagnetism and antiferromagnetism, generating a rapidly growing literature that is increasingly difficult to curate by hand. Here we present a physics-grounded knowledge-base pipeline for altermagnetic materials that combines symmetry-based material seeding, layout-aware document reading, LLM-assisted extraction, auditing, and vector-database retrieval within a distributed inference stack. The workflow begins from crystallographically screened candidate materials, harvests relevant literature from arXiv, transforms papers into structure-preserving text representations, and finally builds validated records through either single-agent or crew-based extraction paths before serving grounded question answers over our knowledge base. Across benchmark tests at two model scales, our structured single and crew pipelines greatly outperform the bare LLM baseline in recovering paper-grounded values, with the smaller model remaining consistently faster. Our analysis shows that scientifically useful performance is driven primarily by structured retrieval and high-fidelity document reading, with agentic complexity acting as a secondary design choice rather than the central source of accuracy gains.

Article
Physical Sciences
Condensed Matter Physics

Jiahao Wang

,

Wei Wu

,

Shilin Zhu

,

Yanmin Zhang

,

Lei Qin

,

Jianlin Luo

Abstract: Layered transition-metal dichalcogenides provide an ideal platform to explore the competition between charge-density-wave (CDW) order and superconductivity. The 3R-stacked TaSe2 hosts intrinsic CDW and superconductivity without chemical doping, yet systematic high-pressure experimental evidence remains lacking. Here we report on systematic studies of pressure phase diagrams up to 2 GPa in high-quality single crystals of 3R-TaSe2. At ambient pressure, a CDW transition emerges near 100 K, and bulk superconductivity onset occurs at Tc ≈ 2.8 K. Upon hydrostatic compression, the CDW transition temperature is monotonically suppressed, while Tc increases to ~3.1 K at 2 GPa, clearly revealing an antagonistic relationship between these two quantum phases. Hall and thermopower measurements suggest CDW-driven Fermi-surface reconstruction and single-band carrier behaviour. From pressure-dependent transport we construct the P(T) phase diagram, and anisotropic upper-critical-field data demonstrate quasi-two-dimensional superconductivity in bulk 3R-TaSe2. This work offers key experimental insights into competing correlated states in van der Waals layered materials.

Article
Physical Sciences
Condensed Matter Physics

Aleksei Novgorodtsev

Abstract: Scalar magnetic descriptors are useful only when omitted information does not change the selected response beyond the required accuracy. We combine a literature audit with one-dimensional and three-dimensional tests. In an eight-material historical ledger, room-temperature labels coincide with magnetic-order eligibility, preventing identification of an additional descriptor effect. A published boundary benchmark resolves size dependence at fixed material descriptor. In a finite chiral-spin model with complete dipolar interactions, four near-matched-radius pairs at the same initial field and pairwise equal thickness have different field-step responses. First-order source-state susceptibility fails its declared twofold-improvement criterion. A disclosed second-order extension, derived from equilibrium response, is tested on eight new settings. Its root-mean-square radius error is 0.000259 lattice spacings, compared with 0.006649 for the best tested scalar normalization and 0.002221 for a multivariable baseline. Independent dipole calculations, stationarity refinement, contour checks and isolated prediction replay establish the numerical scope. The method requires the complete source configuration and Hamiltonian derivatives. The results demonstrate a target-specific audit and mechanistic restoration within declared finite geometries; they do not establish a low-cost material-only descriptor, calibrated lifetime or universal material optimum.

Article
Physical Sciences
Condensed Matter Physics

Jian Zhou

,

Juan Wang

,

Yewen Yao

,

Yongliang Wang

,

Man Wang

,

Wei Peng

Abstract: The critical current (Ic) of a Josephson junction (JJ) is a significant physical parameter that plays a crucial role in the design of subsequent devices and circuits, as well as in the preparation of manufacturing processes. To ensure accurate measurement values, it is necessary to conduct tests in an ideal shielding room. However, due to limitations in laboratory conditions, the actual tests are often conducted in unshielded environments, which are inevitably influenced by various environmental noises. This introduces significant uncertainty in the measurement results of the critical current of the JJ and thus impacts the design of superconducting circuits that follow. We examines the impact of conductive, radiated, and flux noise on the repeatability of the Ic value in an unshielded environment, and setup an empirical formula for predicting Ic values in shielded environments from unshielded environment data.The deviation of empirical value of Ic and the experimentally measured value is less than 1%, verifying the effectiveness of the empirical formula.This approach offers a relatively accurate and cost-effective method for testing the critical current (Ic) of Josephson junctions (JJ) under unshielded conditions.

Article
Physical Sciences
Condensed Matter Physics

Ming Yin

,

Lei Wang

,

Smita Speer

,

Hsin Wang

,

Congyuan Zeng

,

Shengmin Guo

,

Silu Huang

,

Rongying Jin

,

Timir Datta

Abstract: We report on our experimental study of polycrystalline Ge2Sb2Te5 including crystal structure (through x-ray diffraction and Raman spectroscopy), electrical resistivity ρ(T) (with applied magnetic field up to 35 Tesla), thermal conductivity κ(T), Seebeck coefficient S(T), and magnetic susceptibility in a wide temperature range. We find a residual resistivity ratio ρ(300 K)/ρ(1.8 K) of approximately 1.2 and a power-law, ρ(T) ∝ Tⁿ temperature dependent metallic behavior; where n ≈ 2 for1.8 K ≤ T ≤ 50 K and n ≈ 1.22 for 50 K < T ≤ 400 K. These results indicate that electron-phonon scattering dominates charge transport above 50 K, whereas electron-electron scattering becomes significant at lower temperatures. In applied magnetic fields B (up to 35 T) magnetoresistance is positive with an approximately linear √B dependence. Although at room temperature, thermal conductivity κ(T) is relatively low, about 2.5 W m⁻¹ K⁻¹ the Seebeck coefficient S(T) is also small. The implications of these findings are discussed.

Article
Physical Sciences
Condensed Matter Physics

Valery Volodin

,

Yuriy Tuleushev

,

Yeldar Zhakanbayev

,

Bakytzhan Tynyshbay

Abstract: By averaging the sizes of metal nanoparticles capable of merging at different concentrations of elements in the alloy, the size dependence of ultrafine particles on the melting point of the corresponding bulk elements was determined: dMe = 2RMe = 1.46 − 7.3 × 10−5T0. It was found that the particle size is the predominant factor in the formation of alloys from nanosized particles at low temperatures, regardless of their physical properties and crystal structure. Based on the Thomson equation and the average sizes of metal nanoparticles, the values of interfacial tension at the crystal–melt interface for like metals were derived and found to satisfactorily follow a linear dependence. An approximate calculation of the interfacial tension for nanoparticles of like elements in the range of (100 − dMe) nm revealed no dependence on cluster size in this range. The study of size-dependent properties of dissimilar nanoparticles during the formation of solid solutions requires separate investigation. The obtained results can be used to produce new alloys from other elements not considered in this study.

Article
Physical Sciences
Condensed Matter Physics

Yeldar Zhakanbaev

,

Bakytzhan Tynyshbay

Abstract: The aim of this study was to develop a technology for the magnetron synthesis of hafnium carbonitride coatings and to develop a method for determining the melting temperature of the synthesized coating material that correlates with the melting temperatures of the corresponding bulk materials. Using magnetron sputtering, a coating with a composition of 53 at.% Hf, 27 at.% C, and 20 at.% N was obtained. X-ray diffraction and electron microscopy studies were performed to characterize the synthesized coatings. The results demonstrated the feasibility of magnetron synthesis of hafnium carbonitride coatings with a specified stoichiometric composition. The nitrogen concentration in the plasma-forming gas required for the onset of Hf–C–N compound formation was determined. A method for determining the melting temperature of thin-film coatings was developed, providing an approach for determining the melting temperatures of new materials in thin-film form.

Article
Physical Sciences
Condensed Matter Physics

E.I. Kats

Abstract: The discovery of the twist-bend nematic phase in liquid crystals composed of bent-core and dimeric molecules has revealed an unexpected mechanism for the spontaneous formation of nanoscale periodic structures in soft condensed matter. Unlike conventional liquid-crystalline phases, the twist-bend phase (NTB) exhibits a nanoscale heliconical modulation despite the absence of molecular chirality. In this note, dedicated to the late R. Meyer, we discuss a Landau phenomenological interpretation of this phenomenon. The central idea is that a short-range orientational order parameter undergoes condensation, giving rise to a heliconical structure characterized by a finite wave vector. We emphasize that the conventional nematic order is already long-ranged, whereas the additional order parameter describes local orientational correlations hidden within the nematic state. The resulting phase transition bears a close analogy to the de Gennes theory of the nematic–smectic-A transition. Fluctuation effects are expected to drive the transition weakly first order. The theory also predicts a new Goldstone mode associated with the spontaneously broken continuous symmetry of the heliconical state.

Article
Physical Sciences
Condensed Matter Physics

Jundong Guo

Abstract: Artificial spin ice systems have provided powerful platforms for exploring frustrated magnetism and emergent phenomena. However, nanoscale fabrication constraints limit the direct manipulation and real-time visualization of individual magnetic elements for square ice model. Macroscopic mechanical analogues overcome these limitations by enabling direct observation and flexible control of local interactions. Nevertheless, how geometry-tuned intra-unit interactions regulate global ordering in frustrated systems remains poorly understood. Here, we construct a “macroscopic square ice” experimental platform to investigate this problem, using the unit gap l as a tunable geometric parameter while fixing the vertex gap d at 1.1 mm. By directly monitoring magnetic domain evolution and vertex-type distributions, we reveal a non-monotonic order–disorder–order transition driven by the competition between intra-unit and inter-vertex interactions. This work provides direct experimental insight into the role of geometry-controlled local interactions in governing collective ordering and offers a visible approach for studying emergent behaviors in frustrated systems.

Article
Physical Sciences
Condensed Matter Physics

Evgeny F. Talantsev

Abstract: Temperature-dependent electrical resistivity ρ(T) in cuprate, iron-based, and nickelate superconductors represents one of unresolved problems in modern solid-state physics, because of the high absolute value of ρ(T), which, in many cases, exceeds the Ioffe-Rigel criterion, and a large difference in the ρ(T) shape for samples with different doping. Here I show that the nearest neighbours parallel resistivity model (arXiv: 2607.23484) can well describe the in-plane resistivity ρab(T) in iron-based superconductors (IBS) of type 11, 111, 122, 1111, 1144 and 42214 in which the spin density wave phase or nematic order is suppressed by doping. The model is based on the postulate that ρab(T) is a sum of two parallel conduction channels, where one channel is described by the Bloch-Grüneisen equation and the other by the Arrhenius hopping equation. Consequently, the variety of ρab(T) in the IBS is explained as a variation of the Debye temperature ΘD and the hopping activation energy Ea. The derived Debye temperatures were used to estimate the electron-phonon coupling constant in the studied IBS.

Article
Physical Sciences
Condensed Matter Physics

Cristian E. Patiño

,

Daniel E. Nuñez

,

Y. Porras Ramírez

,

Jorge A. Calderón

,

Heiddy P. Quiroz

,

A. Dussan

Abstract: TiO₂ nanotubes and ZnO thin films were investigated as oxide-based memristive systems for resistive switching and state-retention applications under variable environmental conditions. TiO₂ nanotubes were synthesized by electrochemical anodization, while ZnO thin films were deposited on Ti substrates by DC magnetron sputtering. Structural, chemical, and morphological properties were examined by Raman spectroscopy, X-ray diffraction, X-ray photoelectron spectroscopy, and scanning electron microscopy. TiO₂ exhibited a vertically aligned nanotubular morphology, whereas ZnO showed a granular thin-film surface. Electrical characterization was performed using Au top electrodes and Ti as the bottom electrode under atmospheric pressure and high-vacuum conditions, with temperature varied from 353 K down to 77 K. Both materials exhibited hysteretic current–voltage behavior associated with resistive switching, although their response was strongly influenced by morphology, defect distribution, and environmental conditions. TiO₂ nanotubes showed stable high- and low-resistance states, with an ON/OFF ratio of approximately 4.65, indicating robust state retention. The observed behavior was attributed to oxygen-vacancy-mediated transport, filament stabilization, and interface effects. These results highlight the relevance of comparing TiO₂ and ZnO nanostructures for identifying oxide systems capable of maintaining resistive states under temperature and pressure variations, supporting their potential for low-power non-volatile memory applications.

Article
Physical Sciences
Condensed Matter Physics

Y. Porras Ramírez

,

D. Laverde Lizarazo

,

Heiddy P. Quiroz

,

Jorge A. Calderón

,

A. Dussan

Abstract:

In this work, TiO2 and TiO2:Co nanotubes were fabricated via electrochemical anodization, using Ti (99.99% purity) and Ti/Co foils as the anode and cathode. Cobalt was deposited onto the Ti foils using the DC magnetron sputtering technique under a working pressure of 2.5×10⁻² Torr. The resulting nanotubes exhibited wall nodes and an average length of ~300 nm. The synthesized structures were characterized by X-ray diffraction (XRD), identifying anatase as the predominant phase, accompanied by an amorphous halo. Two types of MSM devices were fabricated to study bulk and surface conduction: a transverse configuration (TE/(TiO2, TiO2:Co)/Ti), with top electrodes (TE) Al or Au, and a coplanar configuration (Al/TiO2/Al). Topographic study was analyzed using Atomic Force Microscopy (AFM) and Kelvin Probe Force Microscopy (KPFM) in tapping mode. The device behavior is mainly governed by the TE/ TiO2 junction due to the absence of an energy barrier at the TiO2/Ti interface. All samples exhibit asymmetric I-V behavior with higher conduction under positive bias. The Au/ TiO2/Ti device showed the lowest resistance among Ti BE structures, displaying Schottky behavior with low reverse current leakage and a shift in the zero-current crossing depending on the scan direction. Barrier heights near the zero-current crossing, calculated via the thermionic emission model, were 0.91 eV and 0.70 eV for reverse and forward directions, respectively. Ideality factors and series resistance exceeded 6.8 and 40 kΩ, suggesting additional transport mechanisms. In addition, magnetization as a function of the applied field was realized to TiO2:Co nanotubes evidencing the ferromagnetic-like behavior.

Article
Physical Sciences
Condensed Matter Physics

Ahmed Ali

Abstract: Decoherence is the operative crisis of quantum computing——every architecture confronts it, and every proposed remedy carries a hidden cost in overhead, gap requirement, or temperature constraint. This paper derives, in full algebraic detail and without unexplained transitions, a holographic decoherence-suppression mechanism rooted in the AdS$_3$/CFT$_2$ correspondence, showing that the bulk--boundary geometry of three-dimensional anti-de Sitter space acts as a geometric filter that exponentially screens environmental noise from qubit degrees of freedom encoded in the helical edge modes of topological insulators and in trapped-ion chains. Starting from the chiral Luttinger liquid Hamiltonian of a quantum spin Hall edge, we derive the Virasoro algebra with central charge \(c\), identify the bosonic density fluctuation \(\delta\rho(x,t)\) as the boundary trace of a bulk dilaton field \(\phi(z,x,t)\), solve the dilaton equation of motion step by step to obtain the bulk-to-boundary propagator, and couple it to the Lindblad master equation to derive the modified decoherence rate:\[ \gamma_{\text{holo}} = \gamma_{\text{std}} \exp\!\left(-\frac{2\pi \Delta_n}{c}\frac{l}{\xi}\right), \qquad \frac{T_{\text{std}}^{\text{holo}}}{T_{\text{std}}^{\text{std}}} = \exp\!\left(\frac{\xi}{6}\ln\frac{l}{\xi}\right). \]. Every intermediate numerical estimate in the paper is anchored to independently measured material parameters: Fermi velocity \(v_{\mathrm{F}}\), bulk gap \(\Delta_{\mathrm{gap}}\), and coherence length \(\xi = \hbar v_{\mathrm{F}} / \Delta_{\mathrm{gap}}\). We derive explicit density--density correlation functions, dynamical structure factors, and out-of-time-order correlators (OTOCs), each carrying logarithmic holographic corrections testable by scanning tunneling microscopy, angle-resolved photoemission spectroscopy (ARPES), and Ramsey interferometry. Gate fidelities exceeding \(99.9\%\) are shown to be achievable for Majorana-based qubits when the geometric ratio satisfies \[L/\xi \gtrsim 15 \quad \text{with} \quad c \geq 2. \] Three experimental platforms are analyzed quantitatively: \(\mathrm{Bi}_2\mathrm{Se}_3\) topological insulator edges, \(\mathrm{HgTe}/\mathrm{CdTe}\) quantum wells, and \(^{171}\mathrm{Yb}^+\) trapped-ion chains, with detailed measurement protocols for each.

Article
Physical Sciences
Condensed Matter Physics

Zhangyong Chang

,

Yuxia Zhang

,

Zhigang Xiao

,

Ming Cheng

,

Zhenhua Chen

,

Cuiling Hou

Abstract: Whether the plasticity of silicon at high temperatures originates from dislocation slip or solid-state phase transition remains difficult to investigate directly through experimental observation due to its microscopic nature. Using molecular dynamics simulations, we investigated the deformation behavior of silicon crystals along four typical crystallographic directions at a reduced temperature of T/Tm = 0.88. The results indicate that prior to yielding, compressive stress induces uniform amorphization throughout the crystal. Once the critical stress is exceeded, Shockley partial dislocations nucleate on the {111} crystal planes, initiating plastic flow, while the amorphous phase undergoes recrystallization during the stress relaxation. These findings demonstrate that at high temperatures, the plasticity of silicon involves both stress-assisted amorphization and dislocation-mediated plasticity, which occur sequentially rather than competing with one another. This study provides atomic-scale guidance for suppressing dislocation defects in the directional solidification growth of polycrystalline silicon.

Article
Physical Sciences
Condensed Matter Physics

Miao Zhongzheng

Abstract: The physical properties of hydrogen-bonded systems spanning zero to three dimensions—covering low-dimensional ices, bulk liquid water and biological hydration layers—are characterized by disjoint theoretical formalisms, without a consistent quantitative analytical toolkit. This work constructs an axiomatic Topological Relational Field Theory (TRFT) rooted in the core axiom that relational connections precede discrete material entities. Geometric dimension \(d∈[0,3]\) is defined as a continuously adjustable control parameter. A three-term dimension-scaling free-energy functional is formulated, the physical quantity of dimensional-confinement generalized force is introduced, and manifold compactification regularization is adopted to eliminate mathematical divergences at the d→0 limit. The theory derives universal global thermodynamic stability conditions and constructs piecewise kinetic functionals. Rigorous mathematical proof verifies d_(c,ph)=2 as the critical dimension of phonon softening, which marks the boundary of a second-order topological phase transition. This work clearly distinguishes topological soft modes from intrinsically unstable imaginary phonon frequencies, thereby revising the oversimplified single stability criterion in conventional lattice dynamics. Dimensional lifting-reduction operator algebra is established, and a linking-number conservation theorem is proven for all d≤1 closed-loop manifolds undergoing smooth deformation without hydrogen-bond cleavage. A spatiotemporal duality theorem is further proposed, which unifies the spatial boundary confinement of solid ice and finite temporal observation restriction of liquid water into an identical topological constraint mechanism. The “topological constraint” introduced herein for liquid water specifically refers to the dynamic geometric confinement imposed by the finite observation window τ_obs<∞. Numerous transient closed-loop geometries do exist within liquid water; however, their topological validity is bounded by the observation window. Closed loops act as effective carriers of topological constraints and participate in thermodynamic statistics only when τ_obs≲τ_esc, and their statistical weights are collectively governed by the hydrogen-bond breaking probability peff(T). This “transient-topology” effect differs fundamentally from the “permanent geometric topology” found in solid ice—with respect to the temporal persistence of constraints and statistical weighting. The triple-helix interlocked closed loop (Lk = ± 3), the optimal space-filling configuration identified in the fourth DFT study, is employed in the present work merely as a numerical illustration of transient topology, rather than serving as the definitional prerequisite for topological constraints in liquid water. The resultant universal equation of state takes solid-state DFT outputs as primary inputs, with only one single calibration point at atmospheric-pressure water density maximum to fix the effective hydrogen-bond energy. Homogeneous quantitative interpretations are simultaneously obtained for six century-long puzzles: the 4 °C liquid water density maximum (T_max=277.15 K), the 228 K critical singularity of supercooled water, abnormally high static dielectric permittivity under ambient conditions, freestanding thermodynamic stability of substrate-free low-dimensional ice, systematic misjudgment induced by imaginary-frequency phonon diagnostics, and Pauling residual entropy for nanoconfined hydrogen networks. The framework achieves closed theoretical coverage of solid, liquid and gaseous phases at the zero-density gas limit. All derivations are based on pure mathematical deduction, with no empirical fitting parameters extracted from liquid experimental data; all characteristic transition temperatures of the system can be solved a priori solely via topological parameters of solid hydrogen-bond lattices. The mathematical architecture of TRFT exhibits formal isomorphism with the phase diagrams of cuprate high-temperature superconductors and percolation equations describing cosmic large-scale matter distributions, indicating broad cross-disciplinary application prospects and laying a conceptual foundation for subsequent theoretical and experimental research.

Article
Physical Sciences
Condensed Matter Physics

Chengtian Liang

,

Xuanting Hong

Abstract: Hinge states are a characteristic boundary manifestation of three-dimensional higherorder topological phases, but identifying them in realistic Wannier tight-binding models requires a sequence of choices that is rarely automated: selection of a target bulk gap, construction of multiple mixed-boundary geometries, sparse solution of large wire Hamiltonians, and discrimination of corner-localized spectral weight from surface and bulk weight. We present HingeStateDetector, a computational method that performs this sequence using a wannier90_hr.dat Hamiltonian and a POSCAR as its mandatory inputs. The program parses and validates the real-space hopping model, estimates sampled global bulk gaps, constructs wires that are finite along two lattice directions and periodic along the third, and uses shift--invert sparse diagonalization near the selected gap. For every eigenstate it reports corner-, edge-, and interior-cell probabilities and builds an energy- and cell-resolved local density of states (LDOS). An automatic mode screens all three lattice axes, while machinereadable JSON and NPZ outputs retain the parameters and numerical evidence needed for convergence studies. We verify the implementation with the chiral hinge model of Benalcazar, Bernevig, and Hughes: only the expected periodic direction is classified as positive, four corner-localized branches traverse the bulk gap, and the interior weight falls below one percent for converged cross sections. A 30-orbital spinful Bi$_2$Se$_3$ Hamiltonian distributed with WannierTools provides a realistic stress test. In addition, a 128-orbital spinful Hamiltonian for the experimentally established higher-order topological insulator \(\alpha\)-Bi$_4$Br$_4$ supplies a real-material positive control. The detector selects the quasi-one-dimensional chain direction and retains corner-dominated in-gap candidates as the cross section grows from $3\times3$ to $5\times5$. These results establish an axis-resolved, quantitative route from Wannier interpolation to finite-boundary evidence, while showing explicitly why hinge localization alone is not a bulk topological invariant

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