Order Parameter Configurations Research Articles

Pair density waves in superconducting vortex halos

We analyze the interplay between a d-wave uniform superconducting and a pair-density-wave (PDW) order parameter in the neighborhood of a vortex. We develop a phenomenological nonlinear sigma-model, solve the saddle point equation for the order parameter configuration, and compute the resulting local density of states in the vortex halo. The intertwining of the two superconducting orders leads to a charge density modulation with the same periodicity as the PDW, which is twice the period of the charge-density-wave that arises as a second-harmonic of the PDW itself. We discuss key features of the charge density modulation that can be directly compared with recent results from scanning tunneling microscopy and speculate on the role PDW order may play in the global phase diagram of the hole-doped cuprates.

Deterministic phase slips in mesoscopic superconducting rings.

The properties of one-dimensional superconductors are strongly influenced by topological fluctuations of the order parameter, known as phase slips, which cause the decay of persistent current in superconducting rings and the appearance of resistance in superconducting wires. Despite extensive work, quantitative studies of phase slips have been limited by uncertainty regarding the order parameter's free-energy landscape. Here we show detailed agreement between measurements of the persistent current in isolated flux-biased rings and Ginzburg–Landau theory over a wide range of temperature, magnetic field and ring size; this agreement provides a quantitative picture of the free-energy landscape. We also demonstrate that phase slips occur deterministically as the barrier separating two competing order parameter configurations vanishes. These results will enable studies of quantum and thermal phase slips in a well-characterized system and will provide access to outstanding questions regarding the nature of one-dimensional superconductivity.

First order0–πphase transitions in superconductor/ferromagnet/superconductor trilayers

We study the thermodynamics of the diffusive SFS trilayer composed of thin superconductor (S) and ferromagnet (F) layers. On the basis the self-consistent solutions of nonlinear Usadel equations in the F and S layers we obtain the Ginzburg--Landau expansion and compute the condensation free energy and entropy of the $0$ (even) and $\pi$ (odd) order parameter configurations. The first order $0-\pi$ transition as a function of temperature $T$ occurs, which is responsible for a jump of the averaged magnetic field penetration depth $\lambda(T)$ recently observed on experiments [N.Pompeo, et. al., Phys. Rev. B 90, 064510 (2014)]. The generalized Ginzburg-Landau functional was proposed to describe SFS trilayer for arbitrary phase difference between the superconducting order parameters in the S layers. The temperature dependence of the SFS Josephson junction critical current demonstrates the strong anharmonicity of the corresponding current--phase relation in the vicinity of the $0-\pi$ transition. In rf SQUID, coexistence of stable and metastable $0$ and $\pi$ states provides integer and half--integer fluxoid configurations.

Investigation of half-quantum vortex in superfluid 3He-A phase

In superfluid 3He-A, it was theoretically predicted that the half-quantum vortex (HQV) is stable where the order parameters and are perpendicular to each other in the order parameter configuration. However, the existence of the HQV has not been reported experimentally. Now we are trying to detect the HQV in superfluid 3He-A confined in the parallel-plates sample cell with 12 μm gap, where and are perpendicular to each other, by using a NMR technique under a rotation at ISSP. In order to detect the HQV, we improved the magnet system for NMR so far, but we have not observed the HQV yet. We report here the experimental details and some results for investigating the HQV.

Multiple order parameter configurations in superconductor/ferromagnet multilayers

The coupling of two superconductors (S) through a ferromagnet (F) can lead to either a zero- or a $\ensuremath{\pi}$-phase difference between the superconducting banks. Most research in this area is performed on trilayer S/F/S film structures, in which two-order parameter configurations are possible. Increasing the number of layers and junctions leads to a larger number of possible configurations with, in principle, different properties such as the superconducting transition temperature ${T}_{c}$. Here we study the behavior of a series of multilayers made of superconducting Nb and ferromagnetic Pd${}_{81}$Ni${}_{19}$. We find that for the individual layer thicknesses used, the transition width $\ensuremath{\Delta}{T}_{c}$ increases with increasing number of bilayers in the multilayer, in a well-defined manner. That the broadening is not simply due to increased disorder in the larger stacks, it is shown from x-ray diffraction, which finds very sharp interfaces for all samples; and from the effect of the magnetic field on the transition, which shows a considerable sharpening. We can make a connection with the various order parameter configurations using a matrix formulation of quasiclassical theory based on the Usadel equations and show that these different configurations take part in the Josephson networks, which are building up in the transition to the superconducting state.

Magnetic resonance within vortex cores in the B phase of superfluidH3e

We investigate a magnetic susceptibility of vortices in the B phase of multicomponent triplet superfluid $^3$He focusing on a contribution of bound fermionic states localized within vortex cores. Several order parameter configurations relevant to different types of quantized vortices in $^3$He B are considered. It is shown quite generally that an ac magnetic susceptibility has a sharp peak at the frequency corresponding to the energy of interlevel spacing in the spectrum of bound fermions. We suggest that measuring of a magnetic resonance within vortex cores can provide a direct probe of a discrete spectrum of bound vortex core excitations.

First-order phase transitions in ferromagnet/superconductor layered structures

We study the thermodynamics of clean structures composed of superconductor (S) and ferromagnet (F) layers and consisting of one or more SFS junctions. We use fully self consistent numerical methods to compute the condensation free energies of the possible order parameter configurations as a function of temperature $T$. As $T$ varies, we find that there are phase transitions between states characterized by different junction configurations (denoted as ``0'' or ``$\pi$'' according to the phase difference of the order parameter in consecutive S layers). We show that these transitions are of first order. We calculate the associated latent heats and find them to be measurable.

Stability ofπ-junction configurations in ferromagnet-superconductor heterostructures

We investigate the stability of possible order parameter configurations in clean layered heterostructures of the $SFS...FS$ type, where $S$ is a superconductor and $F$ a ferromagnet. We find that for most reasonable values of the geometric parameters (layer thicknesses and number) and of the material parameters (such as magnetic polarization, wavevector mismatch, and oxide barrier strength) several solutions of the {\it self consistent} microscopic equations can coexist, which differ in the arrangement of the sequence of ``0'' and ``$\pi$'' junction types (that is, with either same or opposite sign of the pair potential in adjacent $S$ layers). The number of such coexisting self consistent solutions increases with the number of layers. Studying the relative stability of these configurations requires an accurate computation of the small difference in the condensation free energies of these inhomogeneous systems. We perform these calculations, starting with numerical self consistent solutions of the Bogoliubov-de Gennes equations. We present extensive results for the condensation free energies of the different possible configurations, obtained by using efficient and accurate numerical methods, and discuss their relative stabilities. Results for the experimentally measurable density of states are also given for different configurations and clear differences in the spectra are revealed. Comprehensive and systematic results as a function of the relevant parameters for systems consisting of three and seven layers (one or three junctions) are given, and the generalization to larger number of layers is discussed.

Velocity field vortices and Mermin-Ho vortices in two-component spinor BEC

In light of the φ-mapping topological current theory, two important vortex structures in two-component spinor BEC—the velocity field vortices and the Mermin-Ho vortices are discussed. It is revealed that these two different kinds of vortices are created respectively from the zero points of two different order parameter configurations in the condensates, and both their topological charges, locations and motions can be determined by the φ-mapping theory.

Magnetic field-induced changes in molecular order in nematic liquid crystals

there are two inherent characteristic lengths, the nematic correlation length \(\zeta\) and the magnetic coherence length \(\xi\). As the magnetic field increases the magnetic coherence length decreases and the relative ordering of the three length scales determines the director and scalar order parameter configuration through the cell. We use asymptotic expansions in regions defined by these length scales to analytically determine the molecular configuration in terms of these variables. Specifically, we investigate the boundary layer between the cell substrate and the bulk nematic material when strong anchoring forces the nematic director in a different direction to that of the applied field. We find that at low field strengths the classical picture of liquid crystal/magnetic field interaction occurs, that is, the director orientation is governed by the surface alignment until a transition occurs as the magnetic coherence length becomes comparable to the cell thickness and the director changes orientation so as to align with the magnetic field. At high field strengths, we find that a field-induced reduction of the molecular order occurs in a region close to the cell boundary. We are able to analytically determine the director and scalar order parameter configurations for the majority of field strengths and where analytical solutions are not found a numerical solution is presented. It is hoped that further work will extend this basis of analytical solutions to include a solution for all field strengths and for different cell configurations.

Director configuration and dynamics of a nematic liquid crystal around a two-dimensional spherical particle: Numerical analysis using adaptive grids

We study numerically the director and orientational order parameter configurations in a nematic liquid crystal around a two-dimensional spherical particle on the basis of the tensor order parameter formalism. To properly account for the large length scale difference between the particle and the accompanying orientational defect, we devise an adaptive grid scheme in which the lattice spacing is automatically and locally adjusted in response to the spatial gradient of the orientational order parameter. This adaptive grid scheme is useful in studying dynamical as well as static orientational structures. We present a simulation result which shows how a hedgehog defect of topological charge -1 becomes unstable in two dimensions, and splits into a defect pair of topological charge -1/2, located symmetrically around the particle.

Biaxial ordering and field-induced configurational transition in nematic liquid crystals

We show that the competition between the correlation of liquid crystalline order and the orienting effect of applied field is crucial in determining the characteristic behaviour of local ordering in the boundary layer, close to the substrates with strong anchoring. The equilibrium states for the low and the high field are found to be distinct. In particular, varying the field strength can induce a phase transition, across which the order parameter configuration changes continuously from one to the other of the two limiting equilibrium states.

Vortex state in unconventional junctions of superconductors withd+issymmetry

Based on the Ginzburg-Landau theory, we derive a general current expression for a Josephson junction made of two superconductors with order parameters of different mixing of d-wave and s-wave symmetry. It is found that the characteristic phase ${\ensuremath{\varphi}}_{c}$ occurring in the current-phase relation is crucially determined by the two-component order-parameter configuration. By solving the sine-Gordon equation constructed from this expression, we study the static properties of a frustrated Josephson junction consisting of two junctions with characteristic phases ${\ensuremath{\varphi}}_{c1}$ and ${\ensuremath{\varphi}}_{c2}$. In the short junction limit, the order-parameter symmetry can manifest in the diffraction pattern of the critical current passing through the junction. In the long junction limit, we show that a spontaneous vortex with the flux ${\ensuremath{\Phi}}_{0}[1\ensuremath{-}({\ensuremath{\varphi}}_{c2}\ensuremath{-}{\ensuremath{\varphi}}_{c1})/2\ensuremath{\pi}]$ is induced near the center of the junction. As a result, the interference pattern of the critical currents versus an applied magnetic field is insensitive to the order-parameter profile. These analyses could be used to describe both $d+is$-wave/s-wave superconducting corner junctions and $d+is$-wave tricrystal junctions.

Soliton Lattice in Trans-Polyacetylene with Random Site-Type impurities11The project supported by National Natural Science Foundation of China with Grant No. 1947007 and the Trans-Century Training Programme Foundation for the Talents by the State Education Commission of China

In order to understand the effect of disorder of impurities in doped trans-polyacetylene, we investigate the electronic states of trans-PA with random site-type impurities, especially, taken into account the Coulomb interaction between impurity ions. The randomness of impurity ions can obviously affect the electronic structures of trans-PA chain for the intermediate doping regime (%). With increasing doping level, this in turn leads to widen the soliton band and narrow the band gap. Moreover, the upper gap will appear a maximum at the critical doping level ( 6%). In addition, when the doping concentration is larger than 12%, the random distribution of impurities tends to be uniform because of being concerned with the Coulomb interaction between ions. Meanwhile, the order parameter configuration indicates that it will appear soliton lattice.

The Order Parameter Length Scale of a Vortex Line in a Type II Superconductor

In this paper, we show that the scale of spatial variation of the order parameter ~ in extreme type II superconductors has a temperature dependence other than that of the temperature dependent Ginzburg Landau coherence length ~o( T). Furthermore for temperatures in the vicinity of the critical temperature Tc our results indicate that ~/~o( T) decreases with decreasing temperature. When an external magnetic field is applied to a type II superconductor, vortex lines form provided that the magnetic field is below the upper critical field H e2• 1 ) For temperatures just below the superconducting transition temperature T e, or for a magnetic field just below H e2, such vortices can be analysed within the Ginzburg Landau (GL) framework. 2 ) For temperatures further below Te the Eilenberger and Bogoliubov equations have been investigated, through interative or variational methods. 3 )-5) Kramer et a1. 3 ) and Gygi et a1. 4 ) find that the scale of spatial variation of the order parameter divided by the GL temperature dependent coherence length decreases with decreasing temperature. On the other hand Dorsey et a1. 5 ) claim that there is no appreciable temperature dependence in this quantity. Instead of formulating the problem in terms of Green's functions and the order parameter we adopt a path integral approach. Here the fermion fields associated with the electrons are integrated out, resulting in a formal expression for the free energy in terms of a functional determinant. The order parameter configuration is then given by minimisation of the free energy. In this paper we will be concerned with the quantity ?.=~/J[~o(T), where ~ is the scale of spatial variation of the order parameter and ~o( T) is the GL temperature dependent coherence length. Any temperature dependence of?. indicates that ~ has a temperature dependence that is different from the GL variation. This work aims to determine whether? has any temperature dependence. The vortex free energy, relative to that of the uniform configuration, at finite temperature, T=l//3, can be written as a ratio of two path integrals over Grassmann fields 6

Topological charges of gauge field configurations and order parameter configurations in heterophase systems

Analysis is performed of general features of schemes for calculating the topological charges of heterophase gauge field configurations and order parameter configurations. The feasibility is substantiated of using the results and methods of the theory of topologically non-trivial order parameter configurations for studying complicated heterophase gauge field configurations and vice versa. Structures are revealed of topological charges for string-like configurations of the order parameter which contain ball defects in their cores, as well as for string-like configurations of gauge fields, containing ball monopoles in their cores. Within the framework of the topological approach, string-like defects are studied in superfluid 3He and nematic liquid crystals, as well as string-like configurations of gauge fields in the gauge theory with SU(3) symmetry.