Amplitude Of Order Parameter Research Articles

Charge ordering induced by intrinsic defects in Sn/Ge(111) submonolayers with a coverage close to 1/3

A thermodynamic model is suggested for a (3×3)-type structure formation with a charge density wave (CDW) arising against the background of a \((\sqrt 3 \times \sqrt 3 )R30^\circ\)-type structure in a Group IV metal (Sn, Pb) submonolayer adsorbed with a coverage of ≈1/3 at the (Ge, Si) semiconductor (111) surface. Calculations are carried out by using a self-consistent theory for static fluctuations of the order parameter amplitude. It is shown that the low-symmetry (3×3) phase can nucleate at point defects of the submonolayer as charge-ordered areas of finite radius. The spatial configuration of the CDW and its temperature dependence are calculated. The results obtained are compared with the experimental data for the Sn/Ge(111) system.

Collective modes in the superconducting ground states in the gauge theory description of the cuprates

In the slave boson mean field treatment of the t-J model, the ground state for small doping is a d-wave superconductor. A conventional superconductor has collective modes associated with the amplitude and phase of the pairing order parameter. Here, the hopping matrix element $\chi_{ij}$ is also a mean field order parameter. We therefore expect that new collective modes will be introduced with these additional complex degrees of freedom. We compute the new collective modes and their spectral functions by numerically diagonalizing the matrix which describes the fluctuations about the mean field solution. We also show that the SU(2) gauge theory formulation allows us to predict and classify these collective modes. Indeed, the SU(2) formulation is essential in order to avoid spurious collective modes as the doping $x$ goes to zero. The most important new collective modes are the $\theta$ mode and the longitudinal and transverse $\phi$ gauge modes. The $\theta$ mode corresponds to fluctuations of the staggered flux phase and creates orbital current fluctuations. The $\phi$ gauge modes correspond to out-of-phase fluctuations of the {\em amplitudes} of the pairing and the hopping matrix elements. We compute the neutron scattering cross-section which couples to the $\theta$ mode and inelastic X-ray scattering cross-section which couples to the fluctuation in the real part of $\chi_{ij}$. In addition, we show that the latter fluctuation at $(\pi,\pi)$ may be coupled to the buckling phonon mode in the LTO phase of LSCO and may be detected optically. Experimental searches of these collective modes will serve as important tests of this line of attack on the high T$_c$ problem.

On Fulde–Ferrel–Larkin–Ovchinnikov phases

We have investigated analytically the nature of the transition to the Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) superfluid phases in the vicinity of the tricritical point (TCP), where these phases begin to appear. Near the TCP, one can make an expansion of the free energy up to sixth order, both in the order parameter amplitude and wave vector. Restricting ourselves to the order parameter subspace (LO subspace) made of superposition of plane waves of the same wavelength, we obtain first order transitions and a cos( q · r ) form as the stablest FFLO phase. Moreover, going out of the LO subspace, combining analytical and numerical studies, we show that the actual order parameter at the transition is very close to the simple cos( q · r ) form.

Study of the Order Parameter Symmetry in Overdoped Y1−xCaxBa2Cu3O7−δ by Measurement of Andreev Reflection, Evidence for Enhancement of the Sub Dominant Order Parameter Amplitude in High Transparency Contacts

We have measured the differential conductance of Au/Y1−xCaxBa2Cu3O7−δ point contacts in the regime where it is dominated by Andreev reflection, which enhances its value at low bias. We find that the characteristics can not be fitted by a pure d-wave Order Parameter (OP). Using the formalism developed by Kashiwaya and Tanaka, the best fits are obtained by adding a sub-dominant imaginary OP, whose amplitude appears to depend on the transparency of the contact. At high transparencies it can reach up to 60% of the total amplitude of the OP, for lower transparencies it is substantially smaller. We attribute this enhancement, at high transparencies to a proximity effect between the Au tip and the superconducting electrode.

Spinor Bose-Einstein condensates with many vortices

Vortex-lattice structures of antiferromagnetic spinor Bose-Einstein condensates with hyperfine spin $F=1$ are investigated theoretically based on the Ginzburg-Pitaevskii equations near ${T}_{c}.$ The Abrikosov lattice with clear core regions is never found to be stable at any rotation drive $\ensuremath{\Omega}.$ Instead, each component ${\ensuremath{\Psi}}_{i}(i=0,\ifmmode\pm\else\textpm\fi{}1)$ prefers to shift the core locations away from the others to realize almost uniform order-parameter amplitude with complicated magnetic-moment configurations. This system is characterized by many competing metastable structures so that quite a variety of vortices may be realized with a small change in external parameters.

Quantum-kinetic Langevin fluctuations for exciton Bose-Einstein condensation

The time-dependent correlation function of the order parameter of Bose-Einstein condensation is calculated for a dilute interacting exciton gas cooled by a cold phonon bath. This calculation is achieved by combining two theoretical concepts: (i) a non-Markovian quantum kinetics, which is necessary in order to include the changing single-particle spectrum during the condensation self-consistently, and (ii) the stochastic non-Markovian Langevin fluctuations which are connected with the dissipative scattering integrals. A linearization around the mean quantum kinetics is used in order to determine the order parameter's fluctuations around its mean value. Similarly as in the laser theory the linewidth or the coherence time of the coherent order parameter amplitude is determined. The results show a clear reduction of the linewidth of the coherent exciton amplitude as the system cools down in time through the threshold of the Bose-Einstein condensation. The observation of this line narrowing by nonlinear optical spectroscopy would give a direct indication of the temporal build-up of an exciton condensate in a semiconductor.

Transition to Fulde-Ferrel-Larkin-Ovchinnikov phases near the tricritical point: an analytical study

We explore analytically the nature of the transition to the Fulde-Ferrel-Larkin-Ovchinnikov superfluid phases in the vicinity of the tricritical point, where these phases begin to appear. We make use of an expansion of the free energy up to an overall sixth order, both in order parameter amplitude and in wavevector. We first explore the minimization of this free energy within a subspace, made of arbitrary superpositions of plane waves with wavevectors of different orientations but same modulus. We show that the standard second order FFLO phase transition is unstable and that a first order transition occurs at higher temperature. Within this subspace we prove that it is favorable to have a real order parameter and that, among these states, those with the smallest number of plane waves are preferred. This leads to an order parameter with a cos( . ) dependence, in agreement with preceding work. Finally we show that the order parameter at the transition is only very slightly modified by higher harmonics contributions when the constraint of working within the above subspace is released.

Self-Consistent Theory of Transport in Quasi–One-Dimensional Superconducting Wires

We study superconducting transport in quasi–one-dimensional homogeneous wires in the cases of both equilibrium and nonequilibrium quasiparticle populations, using the quasiclassical Green's function technique. We consider superconductors with arbitrary current densities and impurity concentrations ranging from the clean to the dirty limit. Local current conservation is guaranteed by ensuring that the order parameter satisfies the self-consistency equation at each point. For equilibrium transport, we compute the current, the order parameter amplitude, and the quasiparticle density of states as a function of the superfluid velocity, temperature, and disorder strength. Nonequilibrium is characterized by incoming quasiparticles with different chemical potentials at each -end of the superconductor. We calculate the profiles of the electrostratic potential, order parameter, and effective quasiparticle gap. We find that a transport regime of current-induced gapless superconductivity can be achieved in clean superconductors, the stability of this state being enhanced by nonequilibrium.

On the Ginzburg–Landau analysis of a mixed s–d x2− y2-wave superconducting mesoscopic square

The self-consistent solution of the coupled Ginzburg–Landau equations for the s- and d-wave order parameters is obtained in a mesoscopic square of a mixed s–d x 2− y 2 -wave superconductor which serves as a model of high- T c cuprates. The spatial distributions of the order parameters in the square are shown to be fourfold symmetric. The shape of the calculated distributions reflects the internal symmetry of the d-wave electron pairing as well as the geometry of the mesoscopic square. The analysis of the phase and the amplitude of the d-wave order parameter for low applied magnetic fields reveals a specific behaviour of the current which appears in an external lead connected to the midpoints of the adjacent sides of the square. For a YBa 2Cu 3O 7 square with a side length of 1 μm, the current reaches its maximal value ∼2.2 μA at zero applied magnetic field.

Phase transition into the superconducting mixed state and the de Haas-van Alphen effect

Abstract The Landau expansion for the free energy of the superconducting mixed state near the upper critical field in powers of the sauare modulus of the order parameter averaged over an Abrikosov lattice is derived. The analytical calculations have been carried out in the framework of the Gor'kov formalism for a 3-dimensional isotropic BCS model beyond the limits of the quasiclassical approximation, that is, with Landau auantization of the auasiparticle energy levels taken into consideration. The derivation is performed at Iow temperature for finite but high enough crystal purity. The effect of Pauli paramagnetic terms is taken into account. The quantum oscillations of the critical temperature, the order parameter's amplitude and the magnetization (de Haas-van Alphen effect) in the mixed state are found. The limitation for the validity of a mean field approach due to critical fluctuations (Ginzburg criterion) for the phase transition under consideration is established.

Phase transition into the superconducting mixed state and the de Haas-van Alphen effect

Abstract The Landau expansion for the free energy of the superconducting mixed state near the upper critical field in powers of the sauare modulus of the order parameter averaged over an Abrikosov lattice is derived. The analytical calculations have been carried out in the framework of the Gor'kov formalism for a 3-dimensional isotropic BCS model beyond the limits of the quasiclassical approximation, that is, with Landau auantization of the auasiparticle energy levels taken into consideration. The derivation is performed at Iow temperature for finite but high enough crystal purity. The effect of Pauli paramagnetic terms is taken into account. The quantum oscillations of the critical temperature, the order parameter's amplitude and the magnetization (de Haas-van Alphen effect) in the mixed state are found. The limitation for the validity of a mean field approach due to critical fluctuations (Ginzburg criterion) for the phase transition under consideration is established.

Molecular segregation in lyotropic complex fluids: A phenomenological approach

A phenomenological approach describing the formation of segregated lyotropic mesophases from the isotropic solution is proposed. It provides the order-parameter symmetries of the transitions to the main periodically ordered mesophases. The order-parameter amplitudes are shown to be periodic functions of the probabilities for the surfactant molecules to be in the segregated regions. It allows us to work out the phase diagrams associated with the isotropic to segregated states. These phase diagrams exhibit regions of stability for partially and fully segregated states, and for direct and inverted mesophases.

Duality between Single-Electron Phenomena and Flux Quantization in Mesoscopic Superconductors

In this paper we present experimental results of the order parameter amplitudes in mesoscopic superconductors. We adopted single-electron transistors to detect the amplitude sensitively and with negligible interference to the mesoscopic superconductivity. The emphasis is on the high duality between the single-electron phenomena and the flux quantization in mesoscopic superconductors.

ANISOTROPIC STRONG COUPLING CALCULATION OF THE LOCAL ELECTROMAGNETIC RESPONSE OF HIGH- Tc SUPERCONDUCTORS

The electromagnetic response of the CuO 2-planes is calculated within a strong coupling theory using model tight binding bands and momentum dependent pairing interactions representing spin fluctuation and phonon exchange. The superconducting state resulting from these interactions has d-wave symmetry. With phonon exchange included the order parameter amplitude grows rapidly below T c at elevated frequencies which leads to improved agreement with the observed temperature dependence of the penetration depth. Good agreement between theory and experiment can only be achieved if it is assumed that the strength of the quasiparticle interaction decreases with temperature in the superconducting state. The amount of this reduction depends sensitively on the momentum dependence of the interactions, the energy dispersion and the position of the Fermi line.

Collective oscillations in two-band superconducting systems with low carrier density

We study the collective oscillations in two-band superconducting systems with all possible intra-and interband interactions for arbitrary values of carrier density N0, including low carrier densities, when μ∼Δ. Allowance for processes of scattering of an interband Cooper pair into an intraband pair leads to the emergence of a new excitonic mode in addition to the Bogolyubov-Anderson acoustic mode and an excitonic mode of the Leggett type. The presence of a new order parameter Δ2, in addition to Δ11 and Δ22, and the asymmetric cutoff of integrals lead to the mixing of fluctuations of the phases and amplitudes of the order parameters of different bands. This mixing and the dependence of the order parameters on N0 result in a strong dependence of these two excitonic modes on the carrier density N0.

Collective oscillation in a three-band superconductor with reduced charge carrier density

Collective oscillations in a superconductor with three energy bands overlapping on the Fermi surface were studied. The equation determining the frequency of collective oscillations was obtained both for large and reduced charge carrier densities μ< ω D ( μ is chemical potential, ω D is Debye frequency). Two additional exciton-like collective modes as well as the acoustical Bogolubov–Anderson mode appeared under certain relationships between the theory parameters. For a large charge carrier density, these two collective modes were caused by the fluctuations of phases of order parameters from different bands. For a reduced charge carrier density, these two collective modes become essentially dependent on the chemical potential. This effect results from mixing the fluctuations of phases and amplitudes of order parameters from different bands.

Tunneling in the topological mechanism of superconductivity

We compute the order parameter and Josephson tunneling amplitude in a two-dimensional model of topological superconductivity which captures the physics of the doped Mott insulator. The hydrodynamics of topological electronic liquid consists of the compressible charge sector and the incompressible chiral topological spin liquid. We show that ground states differing by an odd number of particles are orthogonal and insertion of two extra electrons is followed by the emission of soft modes of the transversal spin current. The orthogonality catastrophe makes the physics of superconductivity drastically different from the BCS theory but similar to the physics of one-dimensional electronic liquids. The wave function of a pair is dressed by soft modes. As a result the two-particle matrix element forms a complex d-wave representation (i.e., changes sign under $90\ifmmode^\circ\else\textdegree\fi{}$ rotation), although the gap in the electronic spectrum has no nodes. In contrast to the BCS theory the tunneling amplitude has an asymmetric broad peak (much bigger than the gap) around the Fermi surface. We develop an operator algebra, that allows one to compute other correlation functions.

Critical unmixing of polymer solutions

We present Monte Carlo simulations of semidilute solutions of long self-attracting chain polymers near their Ising type critical point. The polymers are modeled as monodisperse self-avoiding walks on the simple cubic lattice with attraction between nonbonded nearest neighbors. Chain lengths are up to N=2048, system sizes are up to 221 lattice sites and 2.8×105 monomers. These simulations used the recently introduced pruned-enriched Rosenbluth method, which proved extremely efficient, together with a histogram method for estimating finite size corrections. Our clearest result is that chains at the critical point are Gaussian for large N, having end-to-end distances R∼N. Also, the distance TΘ−Tc(N) [where TΘ=limN→∞Tc(N)] scales with the mean field exponent, TΘ−Tc(N)∼1/N. The critical density seems to scale with a nontrivial exponent similar to that observed in experiments. But we argue that this is due to large logarithmic corrections. These corrections are similar to the very large corrections to scaling seen in recent analyses of Θ polymers, and qualitatively predicted by the field theoretic renormalization group. The only serious deviation from this simple global picture concerns the N-dependence of the order parameter amplitudes, which disagrees with a minimalistic ansatz of de Gennes. But this might be due to problems with finite size scaling. We find that the finite size dependence of the density of states P(E,n) (where E is the total energy and n is the number of chains) is slightly but significantly different from that proposed recently by several authors.

In-plane surface impedance of epitaxialYBa2Cu3O7−δfilms: Comparison of experimental data taken at 87 GHz withd- ands-wave models of superconductivity

We have measured the temperature dependence of both the surface resistance and the change of the penetration depth in two optimized epitaxial $c$-axis oriented YBa${}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (YBCO) films at 87 GHz by incorporating each film as an end plate in a cylindrical copper cavity. A high frequency is used in order to increase losses in the superconducting samples relative to the losses in the copper cavity. It is found that our measuring frequency is of a magnitude comparable to the relevant low-temperature scattering rates, so that the real part of the conductivity would be expected to display significant frequency dependence. The two films investigated were both 350 nm thick, but prepared by different techniques. The experimental results are compared to weak-coupling $d$- and $s$-wave models of superconductivity which incorporate both inelastic and elastic scattering, with the latter forming a small part of the total scattering. The sizable surface resistance at low temperatures and the approximately linear temperature variation can be accounted for without subtracting an extrinsic residual surface resistance, if $d$- or anisotropic $s$-wave order parameters with nearly vanishing Fermi surface averages and scattering phase shifts close to 0.4$\ensuremath{\pi}$ are assumed. Large low-temperature losses are obtained theoretically in spite of the fact that order parameter amplitudes must be in the range of $2{\ensuremath{\Delta}}_{0}{(0)/k}_{B}{T}_{c}=6.0--7.5$, considerably larger than the corresponding weak-coupling values, in order to describe the data at higher temperatures. When inelastic scattering is represented by a phenomenological temperature-dependent scattering rate, a quantitative fit to the experimental data for both the surface resistance and the penetration depth of YBCO over the whole measured temperature range from 4.2 to 145 K can be obtained within a single model. Some discrepancy between theory and experiment remains near the transition temperature where fluctuation effects, not treated in this paper, are clearly visible. While very different parameter sets can be found that would fit the real part of the conductivity, having to explain both penetration depth and surface resistance puts severe constraints on the available parameter space. A description of the inelastic scattering on the basis of spin fluctuation exchange within the nested Fermi-liquid model with full frequency dependence taken into account still gives reasonable fits to the data, even though only a single parameter, fixed by the normal-state resistivity, is involved. For $s$-wave states, whose Fermi surface average is a sizable fraction of the order-parameter amplitude, scattering rates drop well below the experimental frequency at sufficiently low temperatures for the whole range of scattering phase shifts. Thermally excited quasiparticles still present then act as a nearly ideally conducting system which results in losses too low to be compatible with the experimental observations.

Tunneling and Orthogonality Catastrophe in the Topological Mechanism of Superconductivity

We compute the angular dependence of the order parameter and tunneling amplitude in a model exhibiting topological superconductivity and sketch its derivation as a model of a doped Mott insulator. We show that ground states differing by an odd number of particles are orthogonal and the order parameter is in the d-representation, although the gap in the electronic spectrum has no nodes. We also develop an operator algebra, that allowes one to compute off-diagonal correlation functions.