Trivial State Research Articles

Thermal generation of droplet soliton in chiral magnet

Controlled creation of localized magnetic textures beyond conventional $\ensuremath{\pi}$-skyrmions is an important problem in the field of magnetism. Here, by means of spin dynamics simulations, Monte Carlo simulations, and harmonic transition state theory we demonstrate that an elementary chiral magnetic soliton with zero topological charge---the chiral droplet---can be created by thermal fluctuations in the presence of the tilted magnetic field. The proposed protocol relies on an unusual kinetics combining the effects of the entropic stabilization and low-energy barrier for the nucleation of a topologically trivial state. Following this protocol by varying temperature and the tilt of the external magnetic field, one can selectively generate chiral droplets or $\ensuremath{\pi}$-skyrmions in a single system. The coexistence of two distinct magnetic solitons establishes a basis for a rich magnetization dynamics and opens up the possibility for the construction of more complex magnetic textures such as skyrmion bags and skyrmions with chiral kinks.

Robust topological superconductivity in weakly coupled nanowire-superconductor hybrid structures

The emergence of topological superconductivity and Majorana bound states in superconductor nanowire structures relies on a large induced topological gap, usually assumed to require strong coupling between superconductor and nanowire. However, strong coupling also brings detrimental effects such as the need for large critical Zeeman fields and the emergence of trivial zero-energy states. This work demonstrates that the aforementioned problems can be drastically mitigated in the weak-coupling regime, while retaining the robust properties of topological superconductivity including large topological gaps.

Trivial and Topological Bound States in Bilayer Graphene Quantum Dots and Rings

Herein, two different types of confinement in bilayer graphene by top and bottom gating with symmetrical microelectrodes are discussed and compared. Trivial confinement corresponds to the same polarity of all top gates, which is opposed to that of all bottom ones. Topological confinement requires the polarity of part of the top–bottom pairs of gates to be reversed. It is shown that the main qualitative difference between trivial and topological bound states manifests itself in the magnetic field dependence. The finding is illustrated with an explicit calculation of the energy spectrum for quantum dots and rings. Trivial confinement shows bunching of levels into degenerate Landau bands, with a non‐centered gap, while topological confinement shows no field‐induced gap and a sequence of state branches always crossing zero energy.

Scanning tunneling microscopy and spectroscopy of NiTe2

Nickel ditelluride is an unusual member of the transition metal dichalcogenide family which has garnered interest due to potential valley spin-polarized surface states near the Fermi level and the presence of Dirac nodes in its electronic band structure. In this work, exfoliation of bulk nickel ditelluride is performed under ultra-high vacuum in order to generate a clean surface for scanning tunneling microscopy and spectroscopy at 4.8 K. Multiple features in the observed electronic density of states are observed in the vicinity of the Fermi level and compared to calculated band structures to elucidate their origins. Our results are consistent with the presence of the spin-polarized surface states, yet indicate trivial states, which are close to the Fermi level, can interfere with their potential utility in spintronic applications.

Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies

A mathematical model of the dynamic instability of a three-layer conical shells with honeycomb structure made using additive technologies has been obtained. Dynamic instability is recognized as the interaction of the shell with a supersonic gas flow. The middle layer of the structure is a honeycomb that is homogenized into an orthotropic homogeneous medium. The top and bottom layers of the shell are made of carbon fiber. The vibrations of the structure are described by fifteen unknowns. Each layer of the structure is described by five unknowns: three projections of displacements of the layer middle surface and two rotation angles of the normal of the layer middle surface. The high-order shear theory is used to describe the deformation state of the structure. The relation between stresses and strains is expressed by a power expansion in the transverse coordinate up to its cubic terms. To obtain a system of ordinary differential equations describing dynamic instability, the method of given forms is used. To assess the dynamic instability, characteristic indicators are calculated by solving the generalized problem of eigenvalues. The natural vibrations of the structure are studied by the Rayleigh-Ritz method. The minimum natural frequency in the cantilevered shell is observed when the number of waves in the circumferential direction is 6. It is also observed in the shell clamped on both sides when the number of waves in the circumferential direction is 1. The dynamic instability properties of the trivial equilibrium state of the structure are studied using numerical simulation. Shells that are cantilevered and clamped on both sides are analyzed. It is shown that the minimum critical pressure is observed when the number of waves in the circumferential direction is 1. The dependence of the critical pressure on the Mach number and angle of attack is studied. It has been established that with an increase in the Mach number and angle of attack, the critical pressure decreases.

Quasiparticle interference observation of the topologically nontrivial drumhead surface state in ZrSiTe

Drumhead surface states that link together loops of nodal lines arise in Dirac nodal-line semimetals as a consequence of the topologically non-trivial band crossings. We used low-temperature scanning tunneling microscopy and Fourier-transformed scanning tunneling spectroscopy to investigate the quasiparticle interference (QPI) properties of ZrSiTe. Our results show two scattering signals across the drumhead state resolving the energy-momentum relationship through the occupied and unoccupied energy ranges it is predicted to span. Observation of this drumhead state is in contrast to previous studies on ZrSiS and ZrSiSe, where the QPI was dominated by topologically trivial bulk bands and surface states. Furthermore, we observe a near $\mathbf{k} \rightarrow -\mathbf{k}$ scattering process across the $\Gamma$-point, enabled by scattering between the spin-split drumhead bands in this material.

Experimental Demonstration of Bulk-Hinge Correspondence in a Three-Dimensional Topological Dirac Acoustic Crystal.

Three-dimensional topological Dirac semimetal (DSM) is a vital state to explore topological phases and phase transitions. However, its bulk-boundary correspondence is elusive. Here, we experimentally investigate the higher-order hinge states in an acoustic DSM. Not only removable trivial surface states but also robust nontrivial hinge arcs are observed, attributed to the direct correspondence between bulk polarization and hinge charge. We further reveal that a pair of zigzag and bearded hinges possess arcs located in complementary momentum regions. Our work provides solid proof of the bulk-hinge correspondence in DSM and sheds light on the study of topological hierarchy across dimensions.

Fuzzy Delay Tumor Growth with Quiescence Cells: Stability of Steady States

This paper presents a system of delay tumor growth that describes an interaction between the proliferating and quiescent cells tumor. This system is fuzzified by parametric form of α-cut representation of symmetric triangular fuzzy number. The steady state and linear stability of fuzzy tumor growth system with quiescence and without quiescence cells are determined and analyzed. Here, we show that the trivial steady state of the system with quiescence is stable for τ =0 by Routh Hurwitz conditions. For increasing delay the steady state is unstable by using Strum theorem.

Stabilization of An Unstable Interaction Between T Cells, HIV, and ARD in A Dynamic System

This research involves mathematical formulation to investigate the stabilization of an unstable interaction between Tcells, HIV and ARD in a dynamic system. The models were solved analytically where the steady state solutions were obtained. After abtaining the various steady solutions, we did linearization analytically, and the steady solution was found to be unstable. Hence, we introduced a control on some of the pertinent parameters and obtained the new set of eigen values that contains some other parameters. Thereafter, numerical simulation was done using Matlab, by varying the constant supply of the drug to study the effect of the system as well as the HIV. The study showed that the control introduced was effective in stabilising the trivial steady state solution of the dynamic system.

Evaluation of behavior components in the elevated plus maze after the action of external and internal factors

To optimize the treatment of diseases which are accompanied by disorders of the psycho-emotional sphere, it is necessary to identify differences and expose the pathogenesis of these changes appearance depending on the primary pathology. During the study, changes in the components of behavior in the elevated plus maze were studied in rats with a developed explosion-induced neurotrauma (EINT), hyper- and hypothyroidism. The experiment conduc­ted on 33 Wistar rats, of which 12 sexually mature rats were divided into control and expe­rimental (with an established EINT) group, 21 young rats were divided into 3 groups – with hyperthyroidism, hypothyroidism and a control group. All animals were kept in standard conditions of the vivarium of the DSMU, the studies were carried out in accordance with the requirements of bioethics. Analysis of the results showed that under the action of various pathological factors, different behavioral profiles are formed, which indicate the development of a trivial state during stress-like reactions after neurotrauma or with an altered hormonal state. The behavioral profile of rats after reproduction of the EINT in comparison with the control group indicates the development of stress-like conditions (statistically significant (p≤0.05) increase in upright stands by 62%, an increase in the number of bowel movements by 50%. Hyperthyroidism is characterized by sympathetic nervous system activation, as evidenced by a significant (p≤0.05) increase in both the number of measures in the open sleeves by 70% and a significant (p≤0.05) increase in the time spent in light sleeves by 51%. In hypothyroidism, there is a suppression of the emotional component of the rats behavior, as evidenced by a significant (p≤0.05) reduction of measures by 63% and time spent in light sleeves by 86%, grooming duration by 71%, hanging from the edges of open sleeves by 80% and the number of bolus defecation by 100%. Keywords: thyroid gland, antigen, staphylococcal toxoid, mast cells, experiment, rats.

Stability of the Discrete Time-Crystalline Order in Spin-Optomechanical and Open Cavity QED Systems

Discrete time crystals (DTC) have been demonstrated experimentally in several different quantum systems in the past few years. Spin couplings and cavity losses have been shown to play crucial roles for realizing DTC order in open many-body systems out of equilibrium. Recently, it has been proposed that eternal and transient DTC can be present with an open Floquet setup in the thermodynamic limit and in the deep quantum regime with few qubits, respectively. In this work, we consider the effects of spin damping and spin dephasing on the DTC order in spin-optomechanical and open cavity systems in which the spins can be all-to-all coupled. In the thermodynamic limit, it is shown that the existence of dephasing can destroy the coherence of the system and finally lead the system to its trivial steady state. Without dephasing, eternal DTC is displayed in the weak damping regime, which may be destroyed by increasing the all-to-all spin coupling or the spin damping. By contrast, the all-to-all coupling is constructive to the DTC in the moderate damping regime. We also focus on a model which can be experimentally realized by a suspended hexagonal boron nitride (hBN) membrane with a few spin color centers under microwave drive and Floquet magnetic field. Signatures of transient DTC behavior are demonstrated in both weak and moderate dissipation regimes without spin dephasing. Relevant experimental parameters are also discussed for realizing transient DTC order in such an hBN optomechanical system.

Observation of Coexisting Weak Localization and Superconducting Fluctuations in Strained Sn1-xInxTe Thin Films.

Topological superconductors have attracted tremendous excitement as they are predicted to host Majorana zero modes that can be utilized for topological quantum computing. Candidate topological superconductor Sn1-xInxTe thin films (0 < x < 0.3) grown by molecular beam epitaxy and strained in the (111) plane are shown to host quantum interference effects in the conductivity coexisting with superconducting fluctuations above the critical temperature Tc. An analysis of the normal state magnetoresistance reveals these effects. A crossover from weak antilocalization to localization is consistently observed in superconducting samples, indicating that superconductivity originates dominantly from charge carriers occupying trivial states that may be strongly spin-orbit split. A large enhancement of the conductivity is observed above Tc, indicating the presence of superconducting fluctuations. Our results motivate a re-examination of the debated pairing symmetry of this material when subjected to quantum confinement and lattice strain.

Topological phonons and electronic structure of Li2BaSi class of semimetals

Extension of the topological concepts to the bosonic systems has led to the prediction of topological phonons in materials. Here we discuss the topological phonons and electronic structure of Li2BaX (X = Si, Ge, Sn, and Pb) materials using first-principles theoretical modelling. A careful analysis of the phonon spectrum of Li2BaX reveals an optical mode inversion with the formation of nodal line states in the Brillouin zone. Our electronic structure results reveal a double band inversion at the Γ point with the formation of inner nodal-chain states in the absence of spin–orbit coupling (SOC). Inclusion of the SOC opens a materials-dependent gap at the band crossing points and transitions the system into a trivial insulator state. We also discuss the lattice thermal conductivity and transport properties of Li2BaX materials. Our results show that coexisting phonon and electron nontrivial topology with robust transport properties would make Li2BaX materials appealing for device applications.

Topologically valley-polarized edge states in elastic phononic plates yielded by lattice defects

Lattice defects (including disclinations and dislocations) which commonly exist in various materials, have shown a fantastic ability to produce excellent mechanical and physical properties of matters. In this paper, lattice defects are introduced into valley-polarized elastic phononic plates. Deformations of lattices yield interfaces expressing as topologically protected waveguides, due to the valley-polarized phase transition of phononic crystals (PnCs) across interfaces. The topological interface states immunize against the finite sizes and the moderate disturbances of plates, essentially differing from the trivial lattice defect states. The discovery of topologically valley-polarized edge states yielded by lattice defects unveils a new horizon in topological mechanics and physics. It provides a novel platform to implement elastic devices with robust topological waveguides.

Distribution function of nuclei from e± scattering in the presence of a strong primordial magnetic field

The amplitude of the primordial magnetic field (PMF) is constrained from observational limits on primordial nuclear abundances. Within this constraint, it is possible that nuclear motion is regulated by Coulomb scattering with electrons and positrons ($e^\pm$'s), while $e^\pm$'s are affected by a PMF rather than collisions. For example, at a temperature of $10^9$ K, thermal nuclei typically experience $\sim 10^{21}$ scatterings per second that are dominated by very small angle scattering leading to minuscule changes in the nuclear kinetic energy of order $\mathcal{O}$(1) eV. In this paper the upper limit on the effects of a possible discretization of the $e^\pm$ momenta by the PMF on the nuclear momentum distribution is estimated under the extreme assumptions that the momentum of the $e^\pm$ is relaxed before and after Coulomb scattering to Landau levels, and that during Coulomb scattering the PMF is neglected. This assumption explicitly breaks the time reversal invariance of Coulomb scattering, and the Maxwell-Boltzmann distribution is not a trivial steady state solution of the Boltzmann equation under these assumptions. We numerically evaluate the collision terms in the Boltzmann equation, and show that the introduction of a special direction in the $e^\pm$ distribution by the PMF generates no directional dependence of the collisional destruction term of nuclei. Large anisotropies in the nuclear distribution function are then constrained from big bang nucleosynthesis. Ultimately, we conclude that a PMF does not significantly affect the isotropy or BBN.

Fractional Chern insulators in magic-angle twisted bilayer graphene

Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue towards manipulating non-Abelian excitations. Early theoretical studies1–7 have predicted their existence in systems with flat Chern bands and highlighted the critical role of a particular quantum geometry. However, FCI states have been observed only in Bernal-stacked bilayer graphene (BLG) aligned with hexagonal boron nitride (hBN)8, in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field. By contrast, magic-angle twisted BLG9–12 supports flat Chern bands at zero magnetic field13–17, and therefore offers a promising route towards stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in magic-angle twisted BLG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically trivial charge density wave states. We demonstrate that, unlike the case of the BLG/hBN platform, the principal role of the weak magnetic field is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum geometry favourable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in flat moiré Chern bands.

Amorphous Bi2Se3 structural, electronic, and topological nature from first principles

Crystalline ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is one of the most explored three-dimensional (3D) topological insulators with a $0.3\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ energy gap making it promising for applications. Its amorphous counterpart could bring to light new possibilities for large scale synthesis and applications. Using ab initio molecular dynamics simulations, we have studied realistic amorphous ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ phases generated by different processes of melting, quenching, and annealing. Extensive structural and electronic characterizations show that the melting process induces an energy gap decrease ruled by growth of the defective local environments. This behavior dictates a weak stability of the topological phase to disorder, characterized by the spin Bott index. Interestingly, we identify the occurrence of topologically trivial surface states in amorphous ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ that show a strong resemblance to standard helical topological states. Our results and methods advance the search of topological phases in 3D amorphous solids.

Spectral stability of pattern-forming fronts in the complex Ginzburg–Landau equation with a quenching mechanism

We consider pattern-forming fronts in the complex Ginzburg–Landau equation with a traveling spatial heterogeneity which destabilises, or quenches, the trivial ground state while progressing through the domain. We consider the regime where the heterogeneity propagates with speed c just below the linear invasion speed of the pattern-forming front in the associated homogeneous system. In this situation, the front locks to the interface of the heterogeneity leaving a long intermediate state lying near the unstable ground state, possibly allowing for growth of perturbations. This manifests itself in the spectrum of the linearisation about the front through the accumulation of eigenvalues onto the absolute spectrum associated with the unstable ground state. As the quench speed c increases towards the linear invasion speed, the absolute spectrum stabilises with the same rate at which eigenvalues accumulate onto it allowing us to rigorously establish spectral stability of the front in . The presence of unstable absolute spectrum poses a technical challenge as spatial eigenvalues along the intermediate state no longer admit a hyperbolic splitting and standard tools such as exponential dichotomies are unavailable. Instead, we projectivise the linear flow, and use Riemann surface unfolding in combination with a superposition principle to study the evolution of subspaces as solutions to the associated matrix Riccati differential equation on the Grassmannian manifold. Eigenvalues can then be identified as the roots of the meromorphic Riccati–Evans function, and can be located using winding number and parity arguments.

Electron transport probing the electrically tunable topological phase transition in a Dirac semimetal

Electron transport in a Dirac semimetal (DSM) quantum wire without/with an external electric field is investigated by using the Green-function-based Landauer-B\"uttiker formula. Normal-topological phase transition is certificated by the different characteristics between the DSM quantum wire without and with the electric field, including the orbital decomposition for the energy bands, transversally local charge and spin polarization density distributions, topological Chern number, transport behaviors, and disorder effects. Topologically trivial surface states are found in the former system and their transport can be localized by disorders. However, topologically nontrivial surface states are generated in the latter one and their transport is robust against strong disorders when the electric field strength is larger than a critical value. In addition, switching effect of the electron transport in the DSM quantum wire can be achieved by varying the electric field strength. Further studies indicate that the switching effect shows a strong robustness against disorder, displaying the feasibility of designing a topological field effect transistor based on the considered system.

Nontrivial amplitude death in coupled parity-time-symmetric Liénard oscillators.

We unravel the collective dynamics exhibited by two coupled nonlinearly damped Liénard oscillators exhibiting parity and time symmetry, which is a classical example of the position-dependent damped systems. The coupled system facilitates the onset of limit-cycle and aperiodic oscillations in addition to large-amplitude oscillations. In particular, a nontrivial amplitude death state emerges as a consequence of balanced linear loss and gain of the coupled PT-symmetric systems, where gain in the amplitude of oscillation in one oscillator is exactly balanced by the loss in the other. Further, quasiperiodic attractors exist in the parameter space of a neutrally stable trivial steady state. We deduce analytical critical curves enclosing the stable regions of a nontrivial fixed point, leading to the manifestation of nontrivial amplitude death state, and neutrally stable trivial steady state. The latter loses its stability leading to the emergence of the former. The analytical critical curves exactly match with the simulation boundaries. There is also a reemergence of dynamical states as a function of the coupling strength and multistability among the observed dynamical states. The basin of attraction provides an explanation for the observed probability of dynamical states.