arXiv subjects
Publications and source records attributed to Oriol T. Valls.
In a recent Letter (Phys. Rev. Lett. 81, p.5640 (1998), cond-mat/9808249 v3), it was suggested that nonlocal effects may prevent observation of the nonlinear Meissner effect in YBCO. We argue that this claim is incorrect with regards to measurements of the nonlinear transverse magnetic moment, and that the most likely reason for a null result lies elsewhere.
The angular dependence of the nonlinear transverse magnetic moment of untwinned high-quality single crystals of optimally doped YBCO have been studied at a temperature of 2.5K using a low frequency AC technique. The absence of any signature at angular period 2π/4is analyzed in light of the numerical predictions of such a signal for a pure d-wave order parameter with line nodes. Implications of this null result for the existence of a non-zero gap at all angles on the Fermi surface are discussed.
The topography of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form is investigated numerically using a ``microcanonical'' Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space ``distance'' between different minima. We find evidence for the existence of pairs of closely related glassy minima (``two-level systems''). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.
We consider an unconventional superconductor in a low frequency harmonic magnetic field. In the Meissner regime at low T a nonlinear magnetic response arises from quasiparticle excitations near minima in the energy gap. Various physical quantities then acquire higher harmonics of the frequency of the applied field. We discuss how examination of the field and angular dependence of these harmonics allows determination of the structure of the energy gap. We show how to distinguish nodes from small finite minima ("quasinodes"). Gaps with nodal lines give rise to universal power law field dependences for the nonlinear magnetic moment and the nonlinear torque. They both have separable temporal and angular dependences. In contrast, when there are quasinodes these quantities have more complicated and nonseparable field, temporal, and angular dependences. We illustrate this on the example of an s+id gap. We discuss how to perform measurements so as to maximize the nonlinear signal and how to investigate in detail the properties of the superconducting minima, thus determining the gap function symmetry.
Many problems in computational magnetics involve computation of fields which decay within a skin depth $δ$, much smaller than the sample size $d$. We discuss here a novel perturbation method which exploits the smallness of $ε\equiv δ/ d$ and the asymptotic behavior of the solution in the exterior and interior of a sample. To illustrate this procedure we consider the computation of the magnetic dipole and quadrupole moments of an anisotropic, unconventional, three dimensional superconductor. The method significantly reduces the required numerical work and can be implemented in different numerical algorithms.
We discuss the influence of lowest Landau level (LLL) fluctuations near H_{c2}(T) on flux lattice melting in YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO). We show that the specific heat step of the flux lattice melting transition in YBCO single crystals can be attributed largely to the degrees of freedom associated with LLL fluctuations. These degrees of freedom have already been shown to account for most of the latent heat. We also show that these results are a consequence of the correspondence between flux lattice melting and the onset of LLL fluctuations.
Transitions between ``glassy'' local minima of a model free-energy functional for a dense hard-sphere system are studied numerically using a ``microcanonical'' Monte Carlo method that enables us to obtain the transition probability as a function of the free energy and the Monte Carlo ``time''. The growth of the height of the effective free energy barrier with density is found to be consistent with a Vogel-Fulcher law. The dependence of the transition probability on time indicates that this growth is primarily due to entropic effects arising from the difficulty of finding low-free-energy saddle points connecting glassy minima.
We present a method to determine the nodal structure of the energy gap of unconventional superconductors such as high $T_c$ materials. We show how nonlinear electrodynamics phenomena in the Meissner regime, arising from the presence of lines on the Fermi surface where the superconducting energy gap is very small or zero, can be used to perform ``node spectroscopy'', that is, as a sensitive bulk probe to locate the angular position of those lines. In calculating the nonlinear supercurrent response, we include the effects of orthorhombic distortion and $a-b$ plane anisotropy. Analytic results presented demonstrate a systematic way to experimentally distinguish order parameters of different symmetries, including cases with mixed symmetry (for example, $d+s$ and $s+id$). We consider, as suggested by various experiments, order parameters with predominantly $d$-wave character, and describe how to determine the possible presence of other symmetries. The nonlinear magnetic moment displays a distinct behavior if nodes in the gap are absent but regions with small, finite, values of the energy gap exist.
We present a method to compute the magnetic moment of a bulk, finite-size, three-dimensional, anisotropic superconductor. Our numerically implemented perturbative procedure is based on a solution of the nonlinear Maxwell- London equations, where we include the nonlinear relation between current and gauge invariant velocity. The method exploits the small ratio of penetration depth to sample size. We show how to treat the open boundary conditions over an infinite domain and the continuity requirement at the interface. We demonstrate how our method substantially reduces the computational work required and discuss its implementation to an oblate spheroid. The numerical solution is obtained from a finite difference method. We briefly discuss the relevance of this work to similar problems in other fields.
We study the applicability of magnetization and specific heat equations derived from a lowest-Landau-level (LLL) calculation, to the high-temperature superconducting (HTSC) materials of the YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO) family. We find that significant information about these materials can be obtained from this analysis, even though the three-dimensional LLL functions are not quite as successful in describing them as the corresponding two-dimensional functions are in describing data for the more anisotropic HTSC Bi- and Tl-based materials. The results discussed include scaling fits, an alternative explanation for data claimed as evidence for a second order flux lattice melting transition, and reasons why 3DXY scaling may have less significance than previously believed. We also demonstrate how 3DXY scaling does not describe the specific heat data of YBCO samples in the critical region. Throughout the paper, the importance of checking the actual scaling functions, not merely scaling behavior, is stressed.
We consider the nonlinear transverse magnetic moment that arises in the Meissner state of superconductors with strongly anisotropic order parameter. We compute this magnetic moment as a function of applied field and geometry, assuming d-wave pairing, for realistic samples, finite in all three dimensions, of high temperature superconducting materials. Return currents, shape effects and the anisotropy of the penetration depth are all included. We numerically solve the nonlinear Maxwell-London equations for a finite system. The effect, which is a probe of the order parameter symmetry in the bulk of the sample, should be readily measurable if pairing is in a d-wave state. Failure to observe it would set a lower bound to the s-wave component.
Time scales associated with activated transitions between glassy metastable states of a free energy functional appropriate for a dense hard sphere system are calculated by using a new Monte Carlo method for the local density variables. We calculate the time the system,initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum before making a transition to the basin of attarction of another free energy minimum. This time scale is found to increase with the average density. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This scale shows no evidence of dependence on sample size.
We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through stretched exponential decay and two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wavenumber dependence of the kinetics is extensively explored. The connection of our results with experiment, mode coupling theory, and molecular dynamics results is discussed.