Topological Density Research Articles

Chern Fermi pocket, topological pair density wave, and charge-4e and charge-6e superconductivity in kagomé superconductors

The recent discovery of novel charge density wave (CDW) and pair density wave (PDW) in kagomé lattice superconductors AV3Sb5 (A = K, Rb, Cs) hints at unexpected time-reversal symmetry breaking correlated and topological states whose physical origin and broader implications are not understood. Here, we make conceptual advances toward a mechanism behind the striking observations and new predictions for novel macroscopic phase coherent quantum states. We show that the metallic CDW state with circulating loop currents is a doped orbital Chern insulator near van Hove filling. The emergent Chern Fermi pockets (CFPs) carry concentrated Berry curvature and orbital magnetic moment. We find that the pairing of electrons on the CFPs leads to a superconducting state with an emergent vortex-antivortex lattice and the formation of a complex triple-Q PDW. A plethora of correlated and topological states emerge, including a never-before-encountered chiral topological PDW superconductor, a loop-current pseudogap phase, and vestigial charge-4e and charge-6e superconductivity in staged melting of the vortex-antivortex lattice and hexatic liquid crystal. Our findings reveal previously unknown nature of the superconducting state of a current-carrying Chern metal, with broad implications for correlated and topological materials.

Prediction of physical parameters of Jatropha biodiesel-ethanol dual fuel based on topological indices

A new topological index method was used to construct a quantitative structure–property relationship (QSPR) prediction model for elucidating the performance indicators of the Jatropha biodiesel-ethanol (JB-E) dual fuel. This model effectively solves the problem of these physical parameters being difficult to measure. On the one hand, the QSPR prediction model has been established based on the topological indices, calorific value, density, kinematic viscosity, and solidifying point of JB-E, while the internal and external tests of the prediction model are analyzed. On the other hand, a correlation model is established between the topological indices and critical parameters of dual fuels. The results show that the exponential decay model is more effective in reflecting the relationship between the topological indices and kinematic viscosity, while the linear model is more suitable for elucidating the relationship between the topological indices, calorific value, and density. The correlation coefficients of the three models are all greater than 0.999. Moreover, the correlation model between the topological index and critical parameters Tcm, Pcm, Vcm, and Zcm is established to accurately predict the critical parameters of dual fuels. Overall, this study has laid a strong foundation for theoretical calculations and applications of dual fuels.

Isotropic energy absorption of topology optimized lattice structure

Lightweight lattice structures received much attention recently because of their high specific mechanical properties and usefulness in biomedical, heat dissipation, and energy absorption applications. However, most of the investigated lattice structures are anisotropic, which leads to variations in performance depending on the direction of deployment. For example, in many energy absorption applications, direction-independent energy absorption may be an advantage. This paper investigates the energy absorption of a 3D printed titanium-based isotropic topology optimized lattice structure under quasi-static compression. Simple cubic and body-centered-cubic lattices were also investigated for comparison. Finite element analysis (FEA) was used to evaluate the compressive behavior of the lattice structures, while laser powder bed fusion was used to manufacture selected lattice structures and validate the FEA model via experimental testing. The effects of lattice topology and relative density on the mechanical behavior were investigated both numerically and experimentally. Lattices were loaded at different orientations to evaluate the energy absorption isotropy. The results showed that the topology optimized lattice exhibits a mixed stretching and bending deformation mode. Moreover, the topology optimized structures showed higher or comparable relative energy absorption than triply periodic minimal surfaces. The topology optimized lattice also showed nearly perfect SEA isotropy, which may be beneficial in energy absorption applications.

Effective compressive behavior of functionally graded TPMS titanium implants with ingrown cortical or trabecular bone

This work investigates numerically the effect of gradient coefficient, partial ingrowth length of bone, topology, loading direction, and average relative density on the yield strength (YS) and effective stiffness of functionally graded (FG) triply periodic minimal surface (TPMS)-based titanium implant topologically interconnected with ingrown bone subjected to uniaxial compression. The partially or fully topologic interconnection of two bi-continuous phases including titanium TPMS and bone forms a partially or fully interpenetrating phase composites (IPCs), for which their effective mechanical response is determined by means of finite element analysis and computational homogenization. The numerical framework used for this purpose is conceptually validated against the experimental characterization of the effective mechanical properties of additively manufactured two-phase FG IPC samples consisting of a white Polylactic Acid (PLA)-based reinforcement phase and white porous Polyvinyl Alcohol Natural (PVA)-based matrix phase under the same conditions such as the topology, dimensions, boundary conditions, and material property. The results show that the effective yield strength of the titanium-bone IPC increases with the decreased absolute value of the gradient coefficient regardless of the loading direction. Comparison between homogenization results obtained using titanium implant TPMS architectures with gyroid, primitive, diamond, and IWP shows that IWP exhibits the highest effective yield strength for a given porosity level. Moreover, the effective yield strength of the bone-implant FG IPCs increases with a rise of partial ingrowth length of bone and higher average relative density of the implant. The effective yield strength is also found to be substantially dependent on the direction of the applied load.

DUEL: Dempster Uncertainty-Based Enhanced- Trust Level Scheme for VANET

This work presents an uncertainty-based Trust Model (TM). It uses Dempster Shafer Theory (DST) to cater to uncertainty arising due to information scarcity in Vehicular Adhoc Networks (VANETs). DST combines direct and indirect trust values of vehicles sending messages to build its new trust opinion. Malicious vehicles, albeit authenticated, may alter or drop messages. The solution is to establish trust. Trust establishment assumes that vehicle behaviour is predictable, and its past transactions are useful for anticipating its future response. The high vehicular mobility, dynamic topology, and low neighbourhood density in VANETs cause a lack of credible information for establishing trust. The work also presents the introduction of the penalty function, forgetting function, rewarding factor, and the uncertainty-based importance factor during the combination of direct and indirect trust values using DST. Apart from this, the forgiving factor deals with a situation when a distrusted vehicle starts behaving ideally. Additionally, we present trust contexts based on types of messages altered or dropped by them. Four different trust levels and uncertainty in DUEL aids the receiver make correct decisions during an attack. DUEL is applied and tested on the real-time data of vehicle trajectory. Results show that DUEL can capture both false message attacks and message suppression attacks even in rapidly changing neighbourhoods and performs well in terms of high values of TPR and low values of FPR.

Nematic order condensation and topological defects in inertial active nematics.

Living materials at different length scales manifest active nematic features such as orientational order, nematic topological defects, and active nematic turbulence. Using numerical simulations we investigate the impact of fluid inertia on the collective pattern formation in active nematics. We show that an incremental increase in inertial effects due to reduced viscosity results in gradual melting of nematic order with an increase in topological defect density before a discontinuous transition to a vortex-condensate state. The emergent vortex-condensate state at low enough viscosities coincides with nematic order condensation within the giant vortices and the drop in the density of topological defects. We further show flow field around topological defects is substantially affected by inertial effects. Moreover, we demonstrate the strong dependence of the kinetic energy spectrum on the inertial effects, recover the Kolmogorov scaling within the vortex-condensate phase, but find no evidence of universal scaling at higher viscosities. The findings reveal complexities in active nematic turbulence and emphasize the important cross-talk between active and inertial effects in setting flow and orientational organization of active particles.

Kibble-Zurek mechanism for nonequilibrium phase transitions in driven systems with quenched disorder

We show that the Kibble-Zurek mechanism applies to nonequilibrium phase transitions found in driven assemblies of superconducting vortices and colloids moving over quenched disorder where a transition occurs from a plastic disordered flowing state to a moving anisotropic crystal. We measure the density of topological defects as a function of quench rate through the nonequilibrium phase transition, and find that on the ordered side of the transition, the topological defect density ρd scales as a power law, {rho }_{{{{{{{{rm{d}}}}}}}}}propto 1/{t}_{{{{{{{{rm{q}}}}}}}}}^{beta }, where tq is the quench time duration, consistent with the Kibble-Zurek mechanism. We show that scaling with the same exponent holds for varied strengths of quenched disorder and that the exponents fall in the directed percolation universality class. Our results suggest that the Kibble-Zurek mechanism can be applied to the broader class of systems that exhibit absorbing phase transitions.

Torsional anomaly in Kerr black hole and quantization in Einstein–Cartan gravity

Recently, presence of gravitational and axial anomalies in Riemann–Cartan (RC) spacetime [Garcia de Andrade, Class. Quantum Gravity 38 (2021)] indicates that topological densities expressed in terms of torsion may be very useful in understanding the physics involved. Pontryagin and Euler density may be presented in terms of torsion in teleparallelism. In this paper, computation of these topological torsional densities in Kerr black holes is given. The geometric quantisation of torsion is also discussed in terms of the teleparallel metric. Actually, the recent work of Del Grosso and Poplawski [arXiv: 2107.06112] showed that the torsion quantization appears when torsion is the generator of momentum quantum mechanical commutator. Moreover, Poplawski et al. showed that use of quantum torsion in quantum electrodynamic (QED) may avoid the divergences in Feynmann integrals, process called, a torsion regularization. Here, we compute the momenta components in terms of teleparallel Kerr black hole torsion generator, like a Casimir tensor. The quantum generator, while not yet related by torsion, is seen to be naturally associated to axial torsion skew-symmetric in the teleparallel geometry. An important fact is that from torsion quantization, torsion chirality appears naturally in the Einstein–Cartan spin-torsion analogy, where now spin-angular momentum of the black hole is connected to torsion. Torsional chiral anomalies are shown to diverge at black hole singularity, and then they cannot be canceled at singularity.

Chaos and Shadowing in General Systems

In this paper we describe some basic notions of topological dynamical systems for maps of type f : X × X → X named general systems. This is proved that every uniformly expansive general system has the shadowing property and every uniformly contractive general system has the (asymptotic) average shadowing and shadowing properties. In the rest, Devaney chaos for general systems is considered. Also, we show that topological transitivity and density of periodic points of a general systems imply topological ergodicity. We also obtain some results on the topological mixing and sensitivity for general systems.

Growth forms of grid tilings.

Growth forms of tilings are an interesting invariant of tilings. They are fully understood in the periodic case but there are very few examples in the quasiperiodic case. Here this problem is studied for quasiperiodic tilings obtained by the grid method. It is proven that such tilings have polygonal/polyhedral growth forms that can be obtained as projections of central sections of orthoplexes. Furthermore, properties of the obtained growth forms in 2D and 3D cases are studied. This work contributes to a wider understanding of growth forms which can be used to study coordination numbers of grid tilings and in the calculation of topological densities.

Phase driven topological states in correlated Haldane model on a honeycomb lattice

Using mean field method and random phase approximation, we studied the phase driven topological exotic states in correlated Haldane model on a honeycomb lattice. It is found that topological spin density waves emerge with the phase change of next-nearest-neighbor hopping. We also investigated the topological properties of these spin density waves, including Chern number, edge state and Hall conductivity. Our work provides a new insight for topological phase transitions in correlated quantum anomalous Hall insulators.

Uncovering the crystal defects within aragonite CaCO3

Knowledge of deformation mechanisms in aragonite, one of the three crystalline polymorphs of CaCO3, is essential to understand the overall excellent mechanical performance of nacres. Dislocation slip and deformation twinning were claimed previously as plasticity carriers in aragonite, but crystallographic features of dislocations and twins have been poorly understood. Here, utilizing various transmission electron microscopy techniques, we reveal the atomic structures of twins, partial dislocations, and associated stacking faults. Combining a topological model and density functional theory calculations, we identify complete twin elements, characters of twinning disconnection, and the corresponding twin shear angle (∼8.8°) and rationalize unique partial dislocations as well. Additionally, we reveal an unreported potential energy dissipation mode within aragonite, namely, the formation of nanograins via the pile-up of partial dislocations. Based on the microstructural comparisons of biogenic and abiotic aragonite, we find that the crystallographic features of twins are the same. However, the twin density is much lower in abiotic aragonite due to the vastly different crystallization conditions, which in turn are likely due to the absence of organics, high temperature and pressure differences, the variation in inorganic impurities, or a combination thereof. Our findings enrich the knowledge of intrinsic crystal defects that accommodate plastic deformation in aragonite and provide insights into designing bioengineering materials with better strength and toughness.

Synthesis, cytotoxic activity, crystal structure, DFT, molecular docking study of some heterocyclic compounds incorporating benzo[f]chromene moieties

The β-enaminonitrile (1) interacted with 1,1,1-triethoxymethane in the presence or absence of acetic anhydride under reflux resulted in the formation of an imidate (2a,b) bearing a 1H-benzo[f]chromene moiety. The synthesized imidate derivatives were characterized by spectral data, and compound 2a was confirmed via X-ray diffraction. The cytotoxic activities of 2a,b were studied in four different human cancer cell lines (MCF-7, HCT-116, HepG-2 and A549) and compared with the positive controls (Colchicine and Vinblastine) using the MTT cell viability technique. The obtained results confirmed that compound 2a revealed strong and selective cytotoxic activities against the four cancer cell lines. The SAR studies of compounds 2a and 2b revealed that compound 2a (9-acetoxy) was more potent against HCT-116, HepG-2, and A549 cell lines than compound 2b (9-hydroxy) compared to Colchicine. To explore the molecular features of compounds 2a and 2b, DFT simulation was performed using the B3LYP/ 6-311++G(d, p) level, which agrees with the X-ray structure data. The intermolecular-interactions were studied with the topological electron density (r), QTAIM, and NCI methods. The ADMET profile of the studied compounds showed good oral-bioavailability properties. The molecular docking analysis showed a strong interaction with DNA methyltransferase1.

Astrophysical chiral dynamos and strain-torsioned Weyl materials

Our goal in this paper is two-fold: First we show that in the absence of four-fermion interactions, from Einstein–Cartan–Maxwell (ECM) anisotropy cosmology, one may derive instabilities in chiral dynamo equations from magnetic perturbations. They are obtained from a model, where the spinning-fluid does not couple directly to the Einstein–Maxwell model. Instead spin fluid enter into the evolution equation of density perturbations. Chiral dynamo equation is obtained from magnetic perturbations in the particular case where the perturbations in the chiral magnetized plasma can be neglected in second order of perturbations. The vanishing of the Nieh–Yan (NY) topological density in this Bianchi type-I model is also investigated. In the second example, use of the magnetic and torsion perturbations are given by the technique of encoding the magnetic perturbations in the metric constrained by teleparallelism. We consider non-uniform chiral chemical potential in the chiral flipping equation in order to obtain the magnetic field dynamo amplification. Dynamo effects are obtained from current perturbations expressed in terms of chiral chemical potential when number density of left-handed chiral particles is approximately zero. The damping found in magnetic field by the end of inflation, may help to explain why so weak galactic dynamo seeds are found at present universe. Furthermore, damping depends upon the strain–torsion relation of the Weyl topological materials. Though in general, torsion does not couple to electromagnetic fields, it influences the magnetic field through strain–torsion pseudo-magnetic potential.

Realization of Coexisting Charge Density Wave and Quantum Spin/Anomalous Hall State in Monolayer NbTe2

AbstractThe combination of nontrivial topology and charge density wave (CDW) has been proposed as a powerful resource for realizing novel quantum phenomena such as axion electrodynamics and the anomalous Hall effect. Hence, topological materials with CDW states attract great interest, yet they are still very rare, particularly in the 2D limit. Here, it is predicted that monolayer NbTe2 in its high‐symmetry 1T phase stabilized by anharmonicity at room temperature exhibits nontrivial topology sensitive to electronic interactions: it changes from a quantum spin Hall (QSH) state to a quantum anomalous Hall (QAH) state when the Hubbard potential U exceeds a critical value. At low temperature, a 4 × 4 CDW order emerges and coexists with the nontrivial topology. Meanwhile, the critical U increases because CDW reduces density of states at Fermi level. More interestingly, in contrast to the high‐symmetry structure that actually is a topologically nontrivial metal, the CDW structure shows an insulating nontrivial gap either in the QSH or the QAH phase, indicating CDW is an effective means to modulate the topological state for developing new functions and devices. These discoveries establish NbTe2 as a promising candidate to explore exotic quantum states at the confluence of nontrivial topology, electronic correlation, and CDW.

A Newly Synthesized β-amino-α, β-unsaturated Ketone Derivative of β-himachalene: Structural, NBO, NLO, and Molecular Docking Studies

In the current study, a new β-amino-α,β-unsaturated ketone-based himachalene ((1S,3R,8R)-9-amino-2,2-dichloro-3,7,7,10-tetramethyltricyclo[6.4.0.01,3]dodec-9-en-11-one) (4) was synthesized from β-himachalene (1) extracted from essential oil of Atlas Cedar. The β-amino-α, β-unsaturated ketone product (4) was characterized by 1D NMR (1H, 13C) and 2D NMR (HSQC, COSY, NOESY), FTIR analysis, and single-crystal X-ray diffraction. The title compound, C16H23Cl2NO, crystallizes with two molecules in the asymmetric unit with similar conformations. One of the two molecules is characterized by chlorine and one-methyl position disorder. In the crystal, intermolecular N—H…O hydrogen bonds lead to forming a three-dimensional framework. In addition, the molecular structure of the title compound was examined by Hirshfeld topology analysis and Density Functional Theory (DFT) using B3LYP calculations at 6-311+G(d,p) level. The optimized structure parameters were compared with the experimental result, an excellent correlation between theoretical structures parameters and experimental values was found. The natural bond orbitals (NBO) analysis and the first-order hyperpolarizability were also performed. Moreover, two biological activities were examined for product 4 against Acetylcholinesterase and Cytochrome P450 3A4, which bind to similar fragments with molecular docking. We find good scores and binding affinity of our molecule to link to these two proteins.

Effective Stiffness of Fused Deposition Modeling Infill Lattice Patterns Made of PLA-Wood Material

Fused deposition modeling (FDM) uses lattice arrangements, known as infill, within the fabricated part. The mechanical properties of parts fabricated via FDM are dependent on these infill patterns, which make their study of great relevance. One of the advantages of FDM is the wide range of materials that can be employed using this technology. Among these, polylactic acid (PLA)-wood has been recently gaining attention as it has become commercially available. In this work, the stiffness of two different lattice structures fabricated from PLA-wood material using FDM are studied: hexagonal and star. Rectangular samples with four different infill densities made of PLA-wood material were fabricated via FDM. Samples were subjected to 3-point bending to characterize the effective stiffness and their sensitivity to shear deformation. Lattice beams proved to be more sensitive to shear deformations, as including the contribution of shear in the apparent stiffness of these arrangements leads to more accurate results. This was evaluated by comparing the effective Young’s modulus characterized from 3-point bending using equations with and without shear inclusion. A longer separation between supports yielded closer results between both models (~41% for the longest separation tested). The effective stiffness as a function of the infill density of both topologies showed similar trends. However, the maximum difference obtained at low densities was the hexagonal topology that was ~60% stiffer, while the lowest difference was obtained at higher densities (star topology being stiffer by ~20%). Results for stiffness of PLA-wood samples were scattered. This was attributed to the defects at the lattice element level inherent to the material employed in this study, confirmed via micro-characterization.

Density Problem Some of the Functional Spaces for Studying Dynamic Equations on Time Scales

In this paper we study some topological density properties of certain functional spaces on the time scales and its relationships to Lebesgue spaces in the sense of ∇-integrals on time scales. Our results are provided with applications

Scaling theory of the Kosterlitz-Thouless phase transition

We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. Relaxation times of both a normal power-law and an anomalous power-law with a logarithmic factor are studied. Finite-size and finite-entanglement scaling forms somehow similar to but different from a frequently employed ansatz are presented. The Kibble-Zurek scaling of topological defect density for a linear driving across the KT transition point is investigated in detail. An implicit equation for a rate exponent in the theory is derived, and the exponent varies with the distance from the critical point and the driving rate consistent with relevant experiments. To verify the theories, we utilize the KT phase transition of a one-dimensional Bose-Hubbard model. The infinite time-evolving-block-decimation algorithm is employed to solve numerically the model for finite bond dimensions. Both a correlation length and an entanglement entropy in imaginary time and only the entanglement entropy in real-time driving are computed. Both the short-time critical dynamics in imaginary time and the finite-time scaling in real-time driving, both including the finite bond dimension, for the measured quantities are found to describe the numerical results quite well via surface collapses. The critical point is also estimated and confirmed to be 0.302(1) at the infinite bond dimension on the basis of the scaling theories.

QCD θ-vacuum in a uniform magnetic field

We study the θ-vacuum of QCD using two-flavor chiral perturbation theory (χPT) in the presence of a uniform, background magnetic field calculating the magnetic field-dependent free energy density, the topological density, the topological susceptibility and the fourth cumulant at one-loop order. We find that the topological susceptibility is enhanced by the magnetic field while the fourth topological cumulant is diminished at weak fields and enhanced at larger fields when θ=0. However, in the QCD vacuum with θ≠0, the topological susceptibility can be either monotonically enhanced or diminished relative to their θ-vacuum values. The fourth cumulant also exhibits monotonic enhancement or suppression except for regions of θ near 0 and 2π, where it is both diminished and enhanced. Finally, the topological density is enhanced for all magnetic fields with its relative shift being identical to the relative shift of the up and down quark condensates in the θ-vacuum.