Phase Of Order Parameter Research Articles

Topological superconductivity without proximity effect

Majorana fermions, strange particles that are their own antiparticles, were predicted in 1937 and have been sought after ever since. In condensed matter they are predicted to exist as vortex core or edge excitations in certain exotic superconductors. These are topological superconductors whose order parameter phase winds nontrivially in momentum space. In recent years, a new and promising route for realizing topological superconductors has opened due to advances in the field of topological insulators. Current proposals are based on semiconductor heterostructures, where spin-orbit-coupled bands are split by a band gap or Zeeman field and superconductivity is induced by proximity to a conventional superconductor. Topological superconductivity is obtained in the interface layer. The proposed heterostructures typically include two or three layers of different materials. In the current work we propose a device based on materials with inherent spin-orbit coupling and an intrinsic tendency for superconductivity, eliminating the need for a separate superconducting layer. We study a lattice model that includes spin-orbit coupling as well as on-site and nearest-neighbor interaction. Within this model we show that topological superconductivity is possible in certain regions of parameter space. These regions of nontrivial topology can be understood as a nodeless superconductor with $d$-wave symmetry which, due to the spin-orbit coupling, acquires an extra phase twist of $2\ensuremath{\pi}$.

Guest–host interaction of some chloroanthraquinone dyes doped in liquid crystalline matrix and effect of addition of carbon nanotube

Liquid crystals (LCs) are commonly used in displays. For practical guest–host applications, it is important to choose dyes with a high ability of orientation in the liquid crystal matrix. In this work, two different nematic liquid crystals (E7 and ZLI-1132) were separately doped (1% m/m) with four different dyes (1-chloro, 2-chloro, 1,5-dichloro and 1,8-dichloro anthraquinone). Their solubilities, textures, phase transition temperatures and order parameters were determined. At the second stage, carbon nanotubes (CNTs) were added (0.05% m/m) to these solutions and the same parameters except solubilities were studied again. Although the solubilities of dyes in the liquid crystal ZLI-1132 were lower than those of E7, the order parameters were much higher. Addition of carbon nanotubes as dopant resulted in an increase in order parameter. Nematic/isotropic microphase separation in doped liquid crystal samples was detected by polarised microscopy. Determination of both phase transition temperatures and phase type was done by temperature dependent texture investigations between crossed polarisers. The dyes and CNTs did not significantly destabilise the mesomorphic phase of nematic hosts. When passing a phase transition, characteristic textures and structures changed with the temperature increasing and decreasing. The nematic–isotropic transition occurred in several pictures (textures). An appreciable change in textures was not observed with the addition of dopant(s) when compared with pure liquid crystal textures.

Coherent quantum transport of charge density waves

Recent experiments show oscillations of dominant period $h/2e$ in conductance vs magnetic flux of charge density wave (CDW) rings above 77 K, revealing macroscopically observable quantum behavior. The time-correlated soliton tunneling model discussed here is based on coherent, Josephson-like tunneling of microscopic quantum solitons of charge $2e$. The model interprets the CDW threshold electric field as a Coulomb blockade threshold for soliton pair creation, often much smaller than the classical depinning field but with the same impurity dependence (e.g., $\ensuremath{\sim}{n}_{i}^{2}$ for weak pinning). This picture draws upon the theory of time-correlated single-electron tunneling to interpret CDW dynamics above threshold. Similar to Feynman's derivation of the Josephson current-phase relation for a superconducting tunnel junction, the picture treats the Schr\"odinger equation as an emergent classical equation to describe the time-evolution of Josephson-coupled order parameters related to soliton dislocation droplets. Vector or time-varying scalar potentials can affect the order parameter phases to enable magnetic quantum interference in CDW rings or lead to interesting behavior in response to oscillatory electric fields. The ability to vary both magnitudes and phases is an aspect important to future applications in quantum computing.

Hysteresis phenomena in shape memory alloys by non-isothermal Ginzburg–Landau models

In this paper, we propose the new one- and three- dimensional models for the description of hysteretic phenomena in shape memory alloys (SMAs). These thermodynamic models are non-isothermal and allow to account for the thermo-mechanical material properties of both austenite and martensite phases based on the local phase value of the order parameter. They are based on the Ginzburg–Landau free energy and the phase field theory. The core of the models is a phase evolution governed by the time dependent Ginzburg–Landau (TDGL) equation and the conservation balance laws with nonlinear coupling between stress, strain and the phase order parameter. The models account for the gradient energy and have been tested in the study of material properties evolution under harmonic stress loading for all important practical cases. The representative numerical simulations have been carried out here without the gradient energy term. The developed models account for the phase dependent properties based on the compliance tensor as a function of the order parameter and stress. We also compared the results obtained with these models and observed differences in homogeneous and inhomogeneous situations due to the change in compliance. In this way, the description of quasiplastic and pseudoelastic behaviors in SMA specimens is improved and becomes in an agreement with existing experiments.

Collective Dipole Behavior and Unusual Morphotropic Phase Boundary in Ferroelectric Pb(Zr0.5Ti0.5)O3 Nanowires

Dipole collective behavior and phase transition in ferroelectric (FE) Pb(Zr(0.5)Ti(0.5))O(3) nanowires, caused by modulated electric fields, are reported. Our result also leads to the finding of a rather outstanding electromechanical d(31) response in a 8.4 nm diameter PZT wire, which may potentially outperform bulk PMN-PT and PZN-PT. Moreover, we further demonstrate the existence of a new type of morphotropic phase boundary (MPB) that bridges two dissimilar structure phases of different order parameters. Microscopic insights for understanding the collective behavior and the structural phase within the new MPB are provided.

Global Order Parameter Critical Exponent: A Different Calculation Approach

In this paper we present an approach that permits to study the behavior of the nematic phase's order parameter exponent (β) for all temperatures of the phase; our method makes an independent calculation of β for each temperature value T. Here use hypothetical data to analyze the consistence of the results, the limitation of the experimental data usability and the influences of the experimental errors on the β(T) curves. After that, we use experimental data to show that the order parameter critical-like exponent presents a constant behavior along the entire domain of the nematic phase.

Orientational order parameter studies in two symmetric dimeric liquid crystals – an optical study

The optical technique developed by [W. Kuczynski, B. Zywucki, and J. Malecki, Determination of orientational order parameter in various liquid-crystalline phases, Mol. Cryst. Liq. Cryst. 381 (2002), pp. 1–19; B.J. Zywucki and W. Kuczynski, IEEE transactions on optical phenomena – The orientational order in nematic liquid crystals from birefringence measurements, Dielectr. Electr. Insul. 8 (2001), pp. 512–515] is fabricated and used to determine the orientational order parameter in two dimeric liquid crystalline compounds nematic and SmA phases of α,ω-bis(4-alkylanilinebenzylidene-4′-oxy)alkane (m.OnO.m) homologous series. The compounds studied are 5.O8O.5 and 5.O10O.5 which exhibit nematic and SmA, and nematic phases, respectively. The orientational order parameter in both the phases of nematic and SmA phases of the compound one and the nematic phase of the compound two are obtained using the principle of Newton's rings which gives directly the birefringence, δn of the liquid crystal dimer. The merits of the technique used are presented over the conventional techniques for the determination of orientational order parameter. The results for the two compounds are compared with those values estimated from n e, n o and density using the two internal field models due to Vuks and Neugebauer applicable to nematic phase.

Liquid crystal parameters through image analysis

A technique which combines image analysis and polarising optical microscope (POM) is a useful tool for the physical investigation of discotic liquid crystals, such as hexabutoxytriphenylene and hexahexyloxytriphenylene. This investigation includes the phase transitions, optical properties and order parameter as a function of temperature. Textures of discotic liquid crystals are captured as a function of temperature using POM. These microscopic textures are analysed using MATLAB software to compute statistical parameters, Legendre moments, optical parameters and order parameters of discotic liquid crystal samples. Compared with other techniques in the literature, the proposed methodology is a reliable and very simple technique for the physical investigation of liquid crystals.

Thermal Stability and Ordering Study of Long- and Short-Alkyl Chain Phosphonic Acid Multilayers

Long-range order evolution of self-assembled phosphonic acid multilayers as a function of temperature is studied here for two molecules with different alkyl chain length. By using synchrotron conventional diffraction, distinct order configurations are retrieved on phosphonic acid multilayers and their thermodynamic behavior monitored by energy-dispersive diffraction. This later technique allows us to observe the system behavior near order-disorder temperatures, as well as to determine the most stable configurations in the range from room temperature up to 120 °C. Planar order is also addressed by wide-angle X-ray scattering (WAXS) transmission experiments. Order parameter phase diagrams are built based on the experimental results, showing the dominant configuration at each temperature. The multilayer molecular long-range order retrieved from the experiments is corroborated by first principles calculations based on the Density Functional Theory. The bulk configurations depicted in this work are produced by molecule-molecule interactions and allow for future comparisons with the behavior of ordered molecules in few-monolayers configurations, commonly used in organic devices, where the presence of surfaces and interfaces strongly affects the molecule packing.

Description of hard-sphere crystals and crystal-fluid interfaces: A comparison between density functional approaches and a phase-field crystal model

In materials science the phase-field crystal approach has become popular to model crystallization processes. Phase-field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase-field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three-dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions, and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase-field crystal model. Thereby it turns out that the order parameter of the phase-field crystal model is more consistent with a smeared density field (shifted and rescaled) than with the shifted and rescaled density itself. In brief, we conclude that fundamental measure theory is very accurate and can serve as a benchmark for the other theories. Taylor expansion strongly affects free energies, surface tensions, and vacancy concentrations. Furthermore it is phenomenologically misleading to interpret the phase-field crystal model as stemming directly from Taylor-expanded density functional theory.

Phase solitons and subgap excitations in two-band superconductors

A phase soliton is a topological defect peculiar to two-band superconductors, which is associated with a $2\ensuremath{\pi}$ winding of the relative phase of the two superconducting condensates. I study the quasiparticle spectrum in the presence of a single planar phase soliton. I show that the order-parameter phase variation in each of the bands leads to the existence of subgap states bound to the soliton. Calculation of the soliton energy valid at all temperatures is presented with exact analytical results obtained for a simple soliton model.

Analysis of XY Model with Mexican-Hat Interaction on a Circle –Derivation of Saddle Point Equations and Study of Bifurcation Structure–

In our previous study, we investigated a classical XY model on a circle by adopting the Mexican-hat type interaction, which is composed of uniform and location-dependent interactions. We solved the saddle point equations numerically and found three non-trivial solutions. In this study, we determined the phases of complex order parameters and derived the saddle point equations for stable and unstable nontrivial solutions and the formula of boundaries of bistable regions analytically. We performed Markov Chain Monte Carlo simulations and confirmed that the numerical and theoretical results agree well.

The Josephson Current in the SFS Sandwich Taking into Account the Proximity Effect and Umklapp Processes

We consider the Josephson effect in a three-layer symmetric superconductor-ferromagnet-superconductor (SFS) system. In the framework of the proximity effect theory we calculate the Josephson current as a function of the ferromagnet thickness, taking into account the Umklapp processes at the internal boundary and the critical temperature dependence of the order parameter phase difference. The results of the calculations are in good agreement with experimental data.

IN-PHASE BURST SYNCHRONIZATION AND RHYTHM DYNAMICS OF COMPLEX NEURONAL NETWORKS

In-phase burst synchronization, spatiotemporal order and rhythm dynamics of a complex neuronal network with electrical or chemically excitatory synapses are studied in this paper. A quantitative characteristic, the width factor, is introduced to describe the rhythm dynamics of an individual neuron, and the average width factor is used to characterize the rhythm dynamics of a neural network. The in-phase burst synchronization is studied in terms of the burst phase order parameter. We also study the effects of the coupling schemes, the intrinsic neuronal property and the network topology on the rhythm dynamics of the network. It is found that the neuronal network with electrical coupling is easier to realize the in-phase burst synchronization than that with the chemically excitatory coupling. The bursting type of short bursting neuronal networks is unchanged for different coupling schemes with the coupling strength increasing. Moreover, the short bursting type is robust both to the coupling strength and the coupling scheme. As for the network topology, more links can only change the bursting type of long bursting neurons, but short bursting neurons are robust to the link numbers.

SYNCHRONIZABILITY OF COMPLEX NETWORKS WITH COMMUNITY STRUCTURE

Many real-world networks show community structure characterized by dense intra-community connections and sparse inter-community links. In this paper we investigated the synchronization properties of such networks. In this work we constructed such networks in a way that they consist of a number of communities with scale-free or small-world structure. Furthermore, with a probability, the intra-community connections are rewired to inter-community links. Two synchronizability measures were considered as the eigenratio of the Laplacian matrix and the phase order parameter obtained for coupled nonidentical Kuramoto oscillators. We found a power-law relation between the eigenratio and the inter-community rewiring probability in which as the rewiring probability increased, the eigenratio decreased, and hence, the synchronizability enhanced. The phase order parameter also increased by increasing the rewiring probability. Also, small-world networks with community structure showed better synchronization properties as compared to scale-free networks with community structure.

Modeling of nonlinear and non-stationary multi-vortex behavior of CDWs at nanoscales in restricted geometries of internal junctions

We report on studies of stationary states and their transient dynamic for an incommensurate charge density wave (ICDW) in a restricted geometry of two spatial dimensions. The model takes into account multiple fields in mutual nonlinear interactions: the amplitude and the phase of the complex order parameter, and distributions of the electric and chemical potentials, of the density and the current of normal carriers. We observed spontaneous formation of vortices (the ICDW dislocations), and followed events of their creation and the subsequent evolution. The vortices appear when the voltage across, or the current through, the sample exceed a threshold. The number of vortices remnant in the reconstructed stationary state increases stepwise – in agreement with experiments, while a much greater number of vortices appears during the intermediate transient states. The vortex core concentrates the electric dipole leading to sharp drops of the electric and chemical potentials across the core. That can lead to enhanced inter-layer tunneling making the core to be a self-tuned microscopic tunneling junction. The results are applied to experiments on nano-fabricated mesa-junctions. They also appeal to modern efforts of the field-effect transformations in correlated electronic systems.

Phase fluctuations and the absence of topological defects in a photo-excited charge-ordered nickelate

The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La(1.75)Sr(0.25)NiO(4) to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.

Order Parameter Distribution and Phase Transition Temperature for a Thin Film With Asymmetric Boundaries

The phenomenological theory was developed for the ferroic phase transition in a thin film with asymmetric boundary conditions which simulate the real situation of a film on the substrate or a layer between two different materials. The solutions of the boundary value problem for the order parameter were obtained numerically for some particular sets of phenomenological parameters in the Landau expansion and extrapolation lengths. The main attention was focused on the case of opposite signs of the extrapolation lengths at film surfaces. It was shown that the mean order parameter is close to that in bulk and phase transition temperature remains weakly dependent on film thickness when the extrapolation lengths have similar absolute values and opposite signs.

Scaling with System Size of the Lyapunov Exponents for the Hamiltonian Mean Field Model

The Hamiltonian Mean Field model is a prototype for systems with long-range interactions. It describes the motion of N particles moving on a ring, coupled with an infinite-range potential. The model has a second-order phase transition at the energy density Uc =3/4 and its dynamics is exactly described by the Vlasov equation in the N→∞ limit. Its chaotic properties have been investigated in the past, but the determination of the scaling with N of the Lyapunov Spectrum (LS) of the model remains a challenging open problem. Here we show that the N −1/3 scaling of the Maximal Lyapunov Exponent (MLE), found in previous numerical and analytical studies, extends to the full LS; scaling is “precocious” for the LS, meaning that it becomes manifest for a much smaller number of particles than the one needed to check the scaling for the MLE. Besides that, the N −1/3 scaling appears to be valid not only for U>Uc , as suggested by theoretical approaches based on a random matrix approximation, but also below a threshold energy Ut ≈0.2. Using a recently proposed method (GALI) devised to rapidly check the chaotic or regular nature of an orbit, we find that Ut is also the energy at which a sharp transition from weak to strong chaos is present in the phase-space of the model. Around this energy the phase of the vector order parameter of the model becomes strongly time dependent, inducing a significant untrapping of particles from a nonlinear resonance.

Coexistence of Ferromagnetism and Superconductivity in Noncentrosymmetric Materials with Cubic Symmetry

This is a model study for the emergence of superconductivity in ferromagnetically ordered phases of cubic materials whose crystal structure lacks inversion symmetry. A Ginzburg–Landau-type theory is used to find the ferromagnetic state and to determine the coupling of magnetic order to superconductivity. It is found that noncentrosymmetricity evokes a helical magnetic phase. If the wavelength of the magnetic order is long enough, it gives rise to modulations of the order parameter of superconductivity, both in modulus and complex phase. At magnetic domain walls the nucleation of superconductivity is found to be suppressed as compared to the interior of ferromagnetic domains.