Order Parameter Field Research Articles

Model description of the supersolid state in YBa2Cu3O6+x

I employ a semiphenomenological model introduced by Tsvelik and Chubukov [Phys. Rev. Lett. 98, 237001 (2007)] to describe the state with coexisting superconductivity (SC) and charge density wave (CDW) recently discovered in YBa${}_{2}$Cu${}_{3}$O${}_{6+x}$ (YBCO). The SC and the CDW order parameter fields are united in a single pseudospin and can be rotated into each other. It is suggested that disorder creates isolated pseudospins which become centers of inelastic scattering of electrons. It is suggested that this scattering is responsible for the logarithmic upturn in the resistivity $\ensuremath{\rho}(T)\ensuremath{\sim}\ensuremath{-}\mathrm{ln}T$ observed at low doping.

Gauge theory approach to glass transition

This approach combines the gauge field theory of spin-glasses [1, 2, 3, 4] with the critical dynamics methods in order to describe the glass transition. The glass transition is regarded as a phase transition, which is interrupted because of premature critical slowing down, caused by the frustrations. The frustrations induce sources of the gauge field which are additional to the thermal activated spin vortexes. Interaction of this field with the order parameter field leads to the system's critical slowing at the glass transition temperature, and to the freezing of disordered structure.

Optimal distribution of temperature points in μSR measurement of local field

Three possible distributions of temperature points in the μSR measurement of local field (order parameter) are discussed. The least square method is applied to estimate the scale of the deviations of the fitted parameters from the true values. It indicates that the distribution corresponding to a uniform section of the order parameter values (uniform-in-signal) incurs the smallest errors. The distribution constructed on the basis of the zeros of the Chebyshev polynomials yields comparable uncertainties, while the uniform-in-temperature distribution turns out to be least effective incurring considerably larger errors. These findings can be useful while planning an order parameter measurement in the μSR experiment.

Emergent states in dense systems of active rods: from swarming to turbulence

Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore the generic diagram of emerging states over a large range of rod densities and aspect ratios. The dynamics is studied using a simple numerical scheme for the overdamped noiseless frictional dynamics of a many-body system in which steric forces are dominant over hydrodynamic ones. The different emergent states are identified by various characteristic correlation functions and suitable order parameter fields. At low density and aspect ratio, a disordered phase with no coherent motion precedes a highly cooperative swarming state with giant number fluctuations at large aspect ratio. Conversely, at high densities weakly anisometric particles show a distinct jamming transition whereas slender particles form dynamic laning patterns. In between there is a large window corresponding to strongly vortical, turbulent flow. The different dynamical states should be verifiable in systems of swimming bacteria and artificial rod-like micro-swimmers.

1H and 195Pt NMR Study of the Parallel Two-Chain Compound Per2[Pt(mnt)2

1H and 195Pt NMR are used to probe the spin ½ anion chain in the quasi-one-dimensional conductor Per2[Pt(mnt)2], which exhibits nearly simultaneous charge density wave (CDW) and spin-Peierls (SP) transitions at low temperatures (Tc ~ 8 K). Below Tc the [Pt(mnt)2] chain forms a spin-singlet state that is evident in 1H NMR spectra and spin relaxation (1/T1) rates; however minority unpaired Pt spins may remain in the SP ground state. With increasing magnetic field, the SP and CDW order parameters decrease in unison, indicating they are coupled up to a critical field Bc ~ 20 T. Above Bc, the spin singlet evolves into a spin-polarized configuration. The 195Pt NMR signals vanish as either Tc or Bc are approached from within the SP ground state, suggesting the hyperfine field of the Pt nucleus is significantly stronger than at the proton sites. Simulations yield a consistent picture of the angular, temperature, and magnetic field-dependent spectral features.

Modeling the structure of liquids and crystals using one- and two-component modified phase-field crystal models

A modified phase-field crystal model in which the free energy may be minimized by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where modulated and uniform phases are formed and also regions where localized states are formed. We investigate the effectiveness of the phase-field crystal model for describing fluids and crystals with defects. We further consider a two-component model and elucidate how the structure transforms from hexagonal crystalline ordering to square ordering as the concentration changes. Our conclusion contains a discussion of possible interpretations of the order parameter field.

Vortex lines in a ferromagnetic spin-triplet superconductor

Based on Duan's topological current theory, we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines. Such defects are different from the Abrikosov vortices in one-component condensate systems. We investigate the inner topological structure of the vortex lines. The topological charge density, velocity, and topological current of the vortex lines can all be expressed in terms of δ function, which indicates that the vortices can only arise from the zero points of an order parameter field. The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping. The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function. Finally, based on the implicit function theorem and the Taylor expansion, we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.

Phase field simulation for the evolution of textured ceramics microstructure

A modified model using phase field method in order to describe grain-oriented growth is developed. The evolution of the long-range order (lro) parameter fields is governed by the time-dependent Ginzburg–Landau equation. Periodic boundary conditions are implemented in simulation. The gradient energy coefficient ki is allowed to depend on both the parameters along x-axis (kx) and z-axis (kz). Anisotropic coefficient C is proposed to describe the ratio of kx to kz. Interface energy anisotropy causes significant deviation of grain growth kinetics from the one observed in isotropic system and does change the size and shape of grains. When the interface energy is anisotropic, the ratio of the average mean linear intercept (MLI) in the different direction is time-dependent and self-similarity does not hold anymore. The value of anisotropic coefficient C strongly influences grain growth behavior. The simulation result is consistent with the experimental result of textured ceramics prepared by reaction templated grain growth.

Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory – A brief overview

A conventional superconductor is described by a single complex order parameter field which has two fundamental length scales, the magnetic field penetration depth λ and the coherence length ξ. Their ratio κ determines the response of a superconductor to an external field, sorting them into two categories as follows; type-I when κ<1/2 and type-II when κ>1/2. We overview here multicomponent systems which can possess three or more fundamental length scales and allow a separate “type-1.5” superconducting state when, e.g. in two-component case ξ1<2λ<ξ2. In that state, as a consequence of the extra fundamental length scale, vortices attract one another at long range but repel at shorter ranges. As a consequence the system should form an additional Semi-Meissner state which properties we discuss below. In that state vortices form clusters in low magnetic fields. Inside the cluster one of the component is depleted and the superconductor-to-normal interface has negative energy. In contrast the current in second component is mostly concentrated on the cluster’s boundary, making the energy of this interface positive. Here we briefly overview recent developments in Ginzburg–Landau and microscopic descriptions of this state.

Hybrid models for perfect complex fluids with multipolar interactions

Multipolar order in complex fluids is described by statistical correlations. This paper presents a novel dynamical approach, which accounts for microscopic effects on the order parameter space. Indeed, the order parameter field is replaced by a statistical distribution function that is carried by the fluid flow. Inspired by Doi's model of colloidal suspensions, the present theory is derived from a hybrid moment closure for Yang-Mills Vlasov plasmas. This hybrid formulation is constructed under the assumption that inertial effects dominate over dissipative phenomena, so that the total energy is conserved. After presenting the basic geometric properties of the theory, the effect of Yang-Mills fields is considered and a direct application is presented to magnetized fluids with quadrupolar order (spin nematic phases). Hybrid models are also formulated for complex fluids with symmetry breaking. For the special case of liquid crystals, the moment method can be applied to the hybrid formulation to study to the dynamics of cubatic phases.

Atomic-scale evolution of modulated phases at the ferroelectric–antiferroelectric morphotropic phase boundary controlled by flexoelectric interaction

Physical and structural origins of morphotropic phase boundaries (MPBs) in ferroics remain elusive despite decades of study. The leading competing theories employ either low-symmetry bridging phases or adaptive phases with nanoscale textures to describe different subsets of the macroscopic data, while the decisive atomic-scale information has so far been missing. Here we report direct atomically resolved mapping of polarization and structure order parameter fields in a Sm-doped BiFeO(3) system and their evolution as the system approaches a MPB. We further show that both the experimental phase diagram and the observed phase evolution can be explained by taking into account the flexoelectric interaction, which renders the effective domain wall energy negative, thus stabilizing modulated phases in the vicinity of the MPB. Our study highlights the importance of local order-parameter mapping at the atomic scale and establishes a hitherto unobserved physical origin of spatially modulated phases existing in the vicinity of the MPB.

Multiphase Field Modeling Chemical Vapor Infiltration of SiC/SiC Composite

AbstractA novel multiphase field model is formulated to describe the complex microstructure evolution during Chemical Vapor Infiltration(CVI), which is one of the important method to produce the SiC matrix composites reinforced by SiC fibers in ceramic engineer. The model is composed of a set of nonlinear partial differential equations by coupling Ginzburg‐Landau type phase field equations with mass balance equation. Mathematically, the codeposition of SiC, Si and C during CVI process is a typical free boundary problem. When this problem is handled by multiphase field method, it's greatly facilitated because of the implicitly boundary‐tracking technique by phase field order parameters. This typical multiphysic field problem is solved by finite element software COMSOL. The numerical results show good agreement with experimental research. (© 2011 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Fermionic Hopf solitons and Berry phase in topological surface superconductors

An interesting phenomenon in many-body physics is that quantum statistics may be an emergent property. This was first noted in the Skyrme model of nuclear matter, where a theory of a bosonic order parameter field contains fermionic excitations. These excitations are smooth field textures and are believed to describe neutrons and protons. We argue that a similar phenomenon occurs in topological insulators when superconductivity gaps out their surface states. Here, a smooth texture is naturally described by a three-component vector. Two components describe superconductivity, while the third captures the band topology. Such a vector field can assume a ``knotted'' configuration in three-dimensional space---the Hopf texture---that cannot smoothly be unwound. Here we show that the Hopf texture is a fermion. To describe the resulting state, the regular Landau-Ginzburg theory of superconductivity must be augmented by a topological Berry phase term. When the Hopf texture is the cheapest fermionic excitation, unusual consequences for tunneling experiments on mesoscopic samples are predicted. This framework directly generalizes the phenomenon of period doubling of Josephson effect to three-dimensional topological insulators with surface superconductivity.

Microscopic and macroscopic theories for the dynamics of polar liquid crystals

We derive and analyze the dynamic equations for polar liquid crystals in two spatial dimensions in the framework of classical dynamical density functional theory (DDFT). Translational density variations, polarization, and quadrupolar order are used as order-parameter fields. The results are critically compared with those obtained using the macroscopic approach of time-dependent Ginzburg-Landau (GL) equations for the analogous order-parameter fields. We demonstrate that, for both the microscopic DDFT and the macroscopic GL approach, the resulting dissipative dynamics can be derived from a dissipation function. We obtain microscopic expressions for all diagonal contributions and for many of the cross-coupling terms emerging from a GL approach. Thus, we establish a bridge between molecular correlations and macroscopic modeling for the dissipative dynamics of polar liquid crystals.

Well-posedness and long term behavior of a simplified Ericksen-Leslie non-autonomous system for nematic liquid crystal flows

We analyze a simplified Ericksen-Leslie model for nematic liquid crystal flows firstly introduced in [18] with non-autonomous forcing bulk term and boundary conditions on the order parameter field. We obtain existence of weak solutions in the two- and three-dimensional cases. We prove uniqueness, continuous dependence on initial conditions, forcing and boundary terms and also existence of strong solutions in the 2D case. Focusing on the 2D case, we then study the long term behavior of solutions by obtaining existence of global attractors for normal forcing terms (according to [21]). Finally, we prove the existence of exponential attractors for quasi-periodic forcing terms in the 2D model.

Generic first-order versus continuous quantum nucleation of supersolidity

We analyze the nucleation of supersolid order out of the superfluid ground state of bosons on the triangular lattice. While the stability of supersolidity against phase separation in this system is by now well established for nearest-neighbor and long-range dipolar interactions, relevant for two-dimensional arrays of ultra-cold polar molecules, here we address directly the nature of the superfluid-to-supersolid transition. Based on symmetry arguments and quantum Monte Carlo simulations, we conclude that this quantum phase transition is driven first-order beyond the line of particle-hole symmetry. Along this line, the transition is continuous and its scaling behavior consistent with the three-dimensional (3D) XY universality class. We relate this finding to a 3D Z6 clock model description of the enlarged symmetry of the solid order parameter field. In the generic case however, the symmetry reduces to that of a 3D Z3 clock model, which reflects the first-order nature of the generic superfluid-to-supersolid quantum phase transition on the triangular lattice.

Excitation spectra of bosons in optical lattices from the Schwinger-Keldysh calculation

Within the Schwinger-Keldysh formalism we derive a Ginzburg-Landau theory for the Bose-Hubbard model which describes the real-time dynamics of the complex order parameter field. Analyzing the excitations in the vicinity of the quantum phase transition it turns out that particle/hole dispersions in the Mott phase map continuously onto corresponding amplitude/phase excitations in the superfluid phase, which have been detected recently by Bragg spectroscopy measurements.

Self-organized superconducting textures in thin films

The interplay between the superconducting order parameter and elastic fields, which are intimately connected to the very existence of the superconductivity itself, can result in a novel superconducting state: a regular self-organized texture of superconducting islands. We study the formation of these islands in a system of a thin superconducting film coupled elastically to a more rigid substrate and derive the phase diagram below the superconducting critical temperature depending on the elastic coupling constant of both subsystems. The fact that this pattern is a result of the Ginzburg-Landau description of superconductivity indicates that the formation of regular structures may be a common feature of the superconductor transition in the presence of long-range coupling.

Real-time Ginzburg-Landau theory for bosons in optical lattices

Within the Schwinger-Keldysh formalism we derive a Ginzburg-Landau theory for the Bose-Hubbard model which describes the real-time dynamics of the complex order parameter field. Analyzing the excitations in the vicinity of the quantum phase transitions it turns out that particle/hole dispersions in the Mott phase map continuously onto corresponding amplitude/phase excitations in the superfluid phase. Furthermore, in the superfluid phase we find a sound mode, which is in accordance with recent Bragg spectroscopy measurements in the Bogoliubov regime, as well as an additional gapped mode, which seems to have been detected via lattice modulation.

Mean field theory of dynamic phase transitions in ferromagnets

We have studied the second order dynamic phase transition (DPT) of the two-dimensional kinetic Ising model by means of numerical calculations. While it is well established that the order parameter Q of the DPT is the average magnetization per external field oscillation cycle, the possible identity of the conjugate field has been addressed only recently. In this work, we demonstrate that our entire set of numerical data is fully consistent with the applied bias field Hb being the conjugate field of order parameter Q. For this purpose, we have analyzed the Q(Hb)-dependence and we have found that it follows the expected power law behavior with the same critical exponent as the mean field equilibrium case.