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Equations and Integrals of Motion in Discrete Integrable $A_{k-1}$
Algebra Models | We study integrals of motion for Hirota bilinear difference equation that is
satisfied by the eigenvalues of the transfer-matrix. The combinations of the
eigenvalues of the transfer-matrix are found, which are integrals of motion for
integrable discrete models for the $A_{k-1}$ algebra with zero and
quasiperiodic boundary conditions. Discrete analogues of the equations of
motion for the Bullough-Dodd model and non-Abelian generalization of Liouville
model are obtained.
|
Construction of variable mass sine-Gordon and other novel inhomogeneous
quantum integrable models | The inhomogeneity of the media or the external forces usually destroy the
integrability of a system. We propose a systematic construction of a class of
quantum models, which retains their exact integrability inspite of their
explicit inhomogeneity. Such models include variable mass sine-Gordon model,
cylindrical NLS, spin chains with impurity, inhomogeneous Toda chain, the
Ablowitz-Ladik model etc.
|
Quantum Lax scheme for Ruijsenaars models | We develop a quantum Lax scheme for IRF models and difference versions of
Calogero-Moser-Sutherland models introduced by Ruijsenaars. The construction is
in the spirit of the Adler-Kostant-Symes method generalized to the case of face
Hopf algebras and elliptic quantum groups with dynamical R-matrices.
|
N=4 Sugawara construction on affine sl(2|1), sl(3) and mKdV-type
superhierarchies | The local Sugawara constructions of the "small" N=4 SCA in terms of
supercurrents of N=2 extensions of the affinization of the sl(2|1) and sl(3)
algebras are investigated. The associated super mKdV type hierarchies induced
by N=4 SKdV ones are defined. In the sl(3) case the existence of two
inequivalent Sugawara constructions is found. The long one involves all the
affine sl(3)-valued currents, while the "short" one deals only with those from
the subalgebra sl(2)\oplus u(1). As a consequence, the sl(3)-valued affine
superfields carry two inequivalent mKdV type super hierarchies induced by the
correspondence between "small" N=4 SCA and N=4 SKdV hierarchy. However, only
the first hierarchy posseses genuine global N=4 supersymmetry. We discuss
peculiarities of the realization of this N=4 supersymmetry on the affine
supercurrents.
|
Integrable Couplings of Soliton Equations by Perturbations I. A General
Theory and Application to the KdV Hierarchy | A theory for constructing integrable couplings of soliton equations is
developed by using various perturbations around solutions of perturbed soliton
equations being analytic with respect to a small perturbation parameter.
Multi-scale perturbations can be taken and thus higher dimensional integrable
couplings can be presented. The theory is applied to the KdV soliton hierarchy.
Infinitely many integrable couplings are constructed for each soliton equation
in the KdV hierarchy, which contain integrable couplings possessing quadruple
Hamiltonian formulations and two classes of hereditary recursion operators, and
integrable couplings possessing local 2+1 dimensional bi-Hamiltonian
formulations and consequent 2+1 dimensional hereditary recursion operators.
|
Generalized KP hierarchy: M\"obius Symmetry, Symmetry Constraints and
Calogero-Moser System | Analytic-bilinear approach is used to study continuous and discrete
non-isospectral symmetries of the generalized KP hierarchy. It is shown that
M\"obius symmetry transformation for the singular manifold equation leads to
continuous or discrete non-isospectral symmetry of the basic (scalar or
multicomponent KP) hierarchy connected with binary B\"acklund transformation. A
more general class of multicomponent M\"obius-type symmetries is studied. It is
demonstrated that symmetry constraints of KP hierarchy defined using
multicomponent M\"obius-type symmetries give rise to Calogero-Moser system.
|
Group Theoretical Properties and Band Structure of the Lame Hamiltonian | We study the group theoretical properties of the Lame equation and its
relation to su(1,1) and su(2). We compute the band structure, dispersion
relation and transfer matrix and discuss the dynamical symmetry limits.
|
Dynamical Symmetry Approach to Periodic Hamiltonians | We show that dynamical symmetry methods can be applied to Hamiltonians with
periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf
potential and its extensions using representations of su(1,1) and so(2,2).
Energy bands and gaps are readily understood in terms of representation theory.
We compute the transfer matrices and dispersion relations for these systems,
and find that the complementary series plays a central role as well as
non-unitary representations.
|
The Pfaff lattice, Matrix integrals and a map from Toda to Pfaff | We study the Pfaff lattice, introduced by us in the context of a Lie algebra
splitting of gl(infinity) into sp(infinity) and lower-triangular matrices. We
establish a set of bilinear identities, which we show to be equivalent to the
Pfaff Lattice. In the semi-infinite case, the tau-functions are Pfaffians;
interesting examples are the matrix integrals over symmetric matrices
(symmetric matrix integrals) and matrix integrals over self-dual quaternionic
Hermitean matrices (symplectic matrix integrals).
There is a striking parallel of the Pfaff lattice with the Toda lattice, and
more so, there is a map from one to the other. In particular, we exhibit two
maps, dual to each other,
(i) from the the Hermitean matrix integrals to the symmetric matrix
integrals, and
(ii) from the Hermitean matrix integrals to the symplectic matrix integrals.
The map is given by the skew-Borel decomposition of a skew-symmetric
operator. We give explicit examples for the classical weights.
|
Quantum Lax Pair From Yang-Baxter Equations | We show explicitly how to construct the quantum Lax pair for systems with
open boundary conditions. We demonstrate the method by applying it to the
Heisenberg XXZ model with general integrable boundary terms.
|
Real forms of the complex twisted N=2 supersymmetric Toda chain
hierarchy in real N=1 and twisted N=2 superspaces | Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda
chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is
demonstrated that they possess a global twisted N=2 supersymmetry. We discuss a
new superfield basis in which the supersymmetry transformations are local.
Furthermore, a representation of this hierarchy is given in terms of two
twisted chiral N=2 superfields. The relations to the s-Toda hierarchy by H.
Aratyn, E. Nissimov and S. Pacheva (solv-int/9801021) as well as to the
modified and derivative NLS hierarchies are established.
|
Liouville equation under perturbation | Small perturbation of the Liouville equation under smooth initial data is
considered. Asymptotic solution which is available for a long time interval is
constructed by the two scale method.
|
Whitham-Toda Hierarchy in the Laplacian Growth Problem | The Laplacian growth problem in the limit of zero surface tension is proved
to be equivalent to finding a particular solution to the dispersionless Toda
lattice hierarchy. The hierarchical times are harmonic moments of the growing
domain. The Laplacian growth equation itself is the quasiclassical version of
the string equation that selects the solution to the hierarchy.
|
Singular solution of the Liouville equation under perturbation | Small perturbation of the Liouville equation under singular initial data is
considered. An asymptotics of the singular solution is constructed by the
method which is similar to Bogolubov -- Krylov one. The main object is an
asymptotics of the singular lines.
|
Vertex operator solutions to the discrete KP-hierarchy | Vertex operators, which are disguised Darboux maps, transform solutions of
the KP equation into new ones. In this paper, we show that the bi-infinite
sequence obtained by Darboux transforming an arbitrary KP solution recursively
forward and backwards, yields a solution to the discrete KP-hierarchy. The
latter is a KP hierarchy where the continuous space x-variable gets replaced by
a discrete n-variable. The fact that these sequences satisfy the discrete KP
hierarchy is tantamount to certain bilinear relations connecting the
consecutive KP solutions in the sequence. At the Grassmannian level, these
relations are equivalent to a very simple fact, which is the nesting of the
associated infinite-dimensional planes (flag).
It turns out that many new and old systems lead to such discrete
(semi-infinite) solutions, like sequences of soliton solutions, with more and
more solitons, sequences of Calogero-Moser systems, having more and more
particles, band matrices, etc... ; this will be developped in another paper. In
this paper, as an other example, we show that the q-KP hierarchy maps, via a
kind of Fourier transform, into the discrete KP hierarchy, enabling us to write
down a very large class of solutions to the q-KP hierarchy.
|
Vector NLS hierarchy solitons revisited: dressing transformation and tau
function approach | We discuss some algebraic aspects of the integrable vector non-linear
Schr\"{o}dinger hierarchies (GNLS$_{r}$). These are hierarchies of
zero-curvature equations constructed from affine Kac-Moody algebras
$\hat{sl}_{r+1}$. Using the dressing transformation method and the tau-function
formalism, we construct the N-soliton solutions of the GNLS$_{r}$ systems. The
explicit matrix elements in the case of GNLS$_{1}$ are computed using level one
vertex operator representations.
|
On the Miura map between the dispersionless KP and dispersionless
modified KP hierarchies | We investigate the Miura map between the dispersionless KP and dispersionless
modified KP hierarchies. We show that the Miura map is canonical with respect
to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki
and Takebe, the twistor construction of solution structure for the
dispersionless modified KP hierarchy is given.
|
Spin pseudo-gap and interplane coupling in Y_2Ba_4Cu_7O_{15}: a ^{63}Cu
nuclear spin-spin relaxation study | We report measurements of the Gaussian contribution, T_{2G}, to the plane
^{63}Cu nuclear spin--spin relaxation time in the YBa_2Cu_3O_7 and YBa_2Cu_4O_8
blocks of normal and superconducting Y_2Ba_4Cu_7O_{15}. The data confirm our
previous results that adjacent CuO_2 planes have different doping levels and
that these planes are strongly coupled. -- The static spin susceptibility at
the anti-ferromagnetic wave vector exhibits a Curie--Weiss like temperature
dependence in the normal state. -- The Y_2Ba_4Cu_7O_{15} data are incompatible
with a phase diagram based on a single CuO_2 plane theory and suggest that the
appearance of a spin gap implies interplane coupling. Additional data for
YBa_2Cu_4O_8 and YBa_2Cu_3O_{6.982} are in accord with the single plane theory.
-- The temperature dependence of T_{2G,ind} below T_c excludes isotropic s-wave
superconductivity in all three compounds.
|
Spin Dynamics of La_2CuO_4 and the Two-Dimensional Heisenberg Model | The spin-lattice relaxation rate $1/T_1$ and the spin echo decay rate
$1/T_{2G}$ for the 2D Heisenberg model are calculated using quantum Monte Carlo
and maximum entropy analytic continuation. The results are compared to recent
experiments on La$_2$CuO$_4$, as well as predictions based on the non-linear
$\sigma$-model.
|
Density of states of a layered S/N d-wave superconductor | We calculate the density of states of a layered superconductor in which there
are two layers per unit cell. One of the layers contains a d-wave pairing
interaction while the other is a normal metal. The goal of this article is to
understand how the d-wave behaviour of the system is modified by the coupling
between the layer-types. This coupling takes the form of coherent, single
particle tunneling along the c-axis. We find that there are two physically
different limits of behaviour, which depend on the relative locations of the
Fermi surfaces of the two layer-types. We also discuss the interference between
the interlayer coupling and pairing interaction and we find that this
interference leads to features in the density of states.
|
Onset of Vortices in Thin Superconducting Strips and Wires | Spontaneous nucleation and the consequent penetration of vortices into thin
superconducting films and wires, subjected to a magnetic field, can be
considered as a nonlinear stage of primary instability of the current-carrying
superconducting state. The development of the instability leads to the
formation of a chain of vortices in strips and helicoidal vortex lines in
wires. The boundary of instability was obtained analytically. The nonlinear
stage was investigated by simulations of the time-dependent generalized
Ginzburg-Landau equation.
|
Multiple Scattering Analysis of Cu-K EXAFS in Bi_2Sr_1.5Ca_1.5Cu_2O_8+d | We have analyzed the Cu K-EXAFS of Bi_2Sr_1.5Ca_1.5Cu_2O_8+d using a full
multiple scattering analysis in a cluster with diameter d = 7.6 AA. The
numerous quasi one-dimensional structural elements give rise to significant
multiple scattering contributions in the EXAFS. We confirm the Sr/Ca ratio of
the sample is 1:1, and one Ca atom is located close to a nominal Sr-site. At 40
K the dimpling angle in the $\rm CuO_2-plane is found to be < 3.5 degrees.
|
Phonon Assisted Multimagnon Optical Absorption and Long Lived Two-Magnon
States in Undoped Lamellar Copper Oxides | We calculate the effective charge for multimagnon infrared (IR) absorption
assisted by phonons in the parent insulating compounds of cuprate
superconductors and the spectra for two-magnon absorption using interacting
spin-wave theory. Recent measured bands in the mid IR [Perkins et al. Phys.
Rev. Lett. {\bf 71} 1621 (1993)] are interpreted as involving one phonon plus a
two-magnon virtual bound state, and one phonon plus higher multimagnon
absorption processes. The virtual bound state consists of a narrow resonance
occurring when the magnon pair has total momentum close to $(\pi,0)$.
|
Anomalous Normal-State Properties of High-T$_c$ Superconductors --
Intrinsic Properties of Strongly Correlated Electron Systems? | A systematic study of optical and transport properties of the Hubbard model,
based on Metzner and Vollhardt's dynamical mean-field approximation, is
reviewed. This model shows interesting anomalous properties that are, in our
opinion, ubiquitous to single-band strongly correlated systems (for all spatial
dimensions greater than one), and also compare qualitatively with many
anomalous transport features of the high-T$_c$ cuprates. This anomalous
behavior of the normal-state properties is traced to a ``collective single-band
Kondo effect,'' in which a quasiparticle resonance forms at the Fermi level as
the temperature is lowered, ultimately yielding a strongly renormalized Fermi
liquid at zero temperature.
|
Verification of a New Non-Linear IV-exponent: Simulation of the 2D
Coulomb Gas with Langevin Dynamics. | It has recently been suggested from scaling arguments that the non-linear
IV-exponent a, for a two-dimensional superconductor is different from the
exponent originally suggested by Ambegaokar et al. The relation between the new
and the old exponent is a=a_AHNS-3. The new scaling behaviour is linked to the
logarithmic vortex interaction and the long range time tail which this gives
rise to. Consequently one may expect that the scaling behavior is generic for
models which have these basic features. The simplest model of this type is the
two-dimensional Coulomb gas model with Langevin dynamics. We here explicitly
verify, through computer simulations, that the IV-characteristics of this model
indeed scales according to the new scaling exponent a. Keywords: vortex,
Coulomb gas, IV-exponent, Simulations, Langevin, 2D superconductor, thin films.
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Two-hole bound states in modified t-J model | We consider modified $t-J$ model with minimum of single-hole dispersion at
the points $(0,\pm \pi)$, $(\pm \pi,0)$. It is shown that two holes on
antiferromagnetic background produce a bound state which properties strongly
differs from the states known in the unmodified $t-J$ model. The bound state is
d-wave, it has four nodes on the face of the magnetic Brillouin zone. However,
in the coordinate representation it looks like as usual s-wave.
|
Self-Organized Criticality Effect on Stability: Magneto-Thermal
Oscillations in a Granular YBCO Superconductor | We show that the self-organized criticality of the Bean's state in each of
the grains of a granular superconductor results in magneto-thermal oscillations
preceding a series of subsequent flux jumps. We find that the frequency of
these oscillations is proportional to the external magnetic field sweep rate
and is inversely proportional to the square root of the heat capacity. We
demonstrate experimentally and theoretically the universality of this
dependence that is mainly influenced by the granularity of the superconductor.
|
Microwave Properties of Borocarbide Superconductors LnNi2B2C (Ln = Y,
Er, Tm, Ho) | We report measurements of the microwave surface impedance of the borocarbide
family of superconductors LnNi2B2C (Ln=Y, Er, Tm, Ho). The experiments enable
direct measurements of the superfluid density, and are particularly sensitive
to the influence of magnetic pairbreaking.
In HoNi2B2C the antiferromagnetic transition is clearly observed at zero
field, and leads to a drastic reduction of the superfluid density, which
recovers at lower temperatures.
In ErNi2B2C the antiferromagnetic transition is not seen in zero field data.
Magnetic effects are responsible for anomalies in the low temperature surface
impedance below approximately 4K in HoNi2B2C and TmNi2B2C. The temperature
dependence of the microwave impedance disagrees with simple BCS calculations.
|
Microwave Surface Impedance of YBCO:123 crystals: Experiment and
comparison to a d-wave model | We present measurements of the microwave surface resistance Rs and the
penetration depth lambda of YBCO:123 crystals. At low T obeys lambda(T) a
polynomial behavior, while Rs displays a characteristic non-monotonic
T-dependence.
A detailed comparison of the experimental data is made to a model of d-wave
superconductivity which includes both elastic and inelastic scattering. While
the model reproduces the general features of the experimental data, three
aspects of the parameters needed are worth noting. The elastic scattering rate
required to fit the data is much smaller than measured from the normal state,
the scattering phase shifts have to be close to pi/2 and a strong coupling
value of the gap parameter 2\Delta(0)/kTc = 6 is needed. On the experimental
side the uncertainties regarding the material parameters lambda(0) and
Rs,res(0) further complicate a quantitative comparison.
For one sample does Rs,res(0) agree with the intrinsic value which results
from the d-wave model.
|
Superconductivity from correlated hopping | We consider a chain described by a next-nearest-neighbor hopping combined
with a nearest-neighbor spin flip. In two dimensions this three-body term
arises from a mapping of the three-band Hubbard model for CuO$_2$ planes to a
generalized $t-J$ model and for large O-O hopping favors resonance-valence-bond
superconductivity of predominantly $d$-wave symmetry. Solving the ground state
and low-energy excitations by analytical and numerical methods we find that the
chain is a Luther-Emery liquid with correlation exponent $K_{\rho} =
(2-n)^2/2$, where $n$ is the particle density.
|
Neutron Scattering Study of Crystal Field Energy Levels and Field
Dependence of the Magnetic Order in Superconducting HoNi2B2C | Elastic and inelastic neutron scattering measurements have been carried out
to investigate the magnetic properties of superconducting (Tc~8K) HoNi2B2C. The
inelastic measurements reveal that the lowest two crystal field transitions out
of the ground state occurat 11.28(3) and 16.00(2) meV, while the transition of
4.70(9) meV between these two levels is observed at elevated temperatures. The
temperature dependence of the intensities of these transitions is consistent
with both the ground state and these higher levels being magnetic doublets. The
system becomes magnetically long range ordered below 8K, and since this
ordering energy kTN ~ 0.69meV << 11.28meV the magnetic properties in the
ordered phase are dominated by the ground-state spin dynamics only. The low
temperature structure, which coexists with superconductivity, consists of
ferromagnetic sheets of Ho{3+ moments in the a-b plane, with the sheets coupled
antiferromagnetically along the c-axis. The magnetic state that initially forms
on cooling, however, is dominated by an incommensurate spiral antiferromagnetic
state along the c-axis, with wave vector qc ~0.054 A-1, in which these
ferromagnetic sheets are canted from their low temperature antiparallel
configuration by ~17 deg. The intensity for this spiral state reaches a maximum
near the reentrant superconducting transition at ~5K; the spiral state then
collapses at lower temperature in favor of the commensurate antiferromagnetic
state. We have investigated the field dependence of the magnetic order at and
above this reentrant superconducting transition. Initially the field rotates
the powder particles to align the a-b plane along the field direction,
demonstrating that the moments strongly prefer to lie within this plane due to
the crystal field anisotropy. Upon subsequently increasing the field at
|
Quantum Resistive Transition in Type II Superconductors under Magnetic
Field | It is shown that, within a Ginzburg-Landau (GL) formalism, the
superconducting fluctuation is insulating at zero temperature even if the
fluctuation dynamics is metallic (dissipative). Based on this fact, the low
temperature behavior of the $H_{c2}$-line and the resistivity curves near a
zero temperature transition are discussed. In particular, it is pointed out
that the neglect of quantum fluctuations in data analysis of the dc resistivity
may lead to an under-estimation of the $H_{c2}$ values near zero temperature.
|
First-Order Vortex Lattice Melting and Magnetization of
YBa$_2$Cu$_3$O$_{7-\delta} | We present the first non-mean-field calculation of the magnetization $M(T)$
of YBa$_2$Cu$_3$O$_{7-\delta}$ both above and below the flux-lattice melting
temperature $T_m(H)$. The results are in good agreement with experiment as a
function of transverse applied field $H$. The effects of fluctuations in both
order parameter $\psi({\bf r})$ and magnetic induction $B$ are included in the
Ginzburg-Landau free energy functional: $\psi({\bf r})$ fluctuates within the
lowest Landau level in each layer, while $B$ fluctuates uniformly according to
the appropriate Boltzmann factor. The second derivative $(\partial^2 M/\partial
T^2)_H$ is predicted to be negative throughout the vortex liquid state and
positive in the solid state. The discontinuities in entropy and magnetization
at melting are calculated to be $\sim 0.034\, k_B$ per flux line per layer and
$\sim 0.0014$~emu~cm$^{-3}$ at a field of 50 kOe.
|
The Flux-Line Lattice in Superconductors | Magnetic flux can penetrate a type-II superconductor in form of Abrikosov
vortices. These tend to arrange in a triangular flux-line lattice (FLL) which
is more or less perturbed by material inhomogeneities that pin the flux lines,
and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many
properties of the FLL are well described by the phenomenological
Ginzburg-Landau theory or by the electromagnetic London theory, which treats
the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft
mainly because of the large magnetic penetration depth: The shear modulus of
the FLL is thus small and the tilt modulus is dispersive and becomes very small
for short distortion wavelength. This softness of the FLL is enhanced further
by the pronounced anisotropy and layered structure of HTSC's, which strongly
increases the penetration depth for currents along the c-axis of these uniaxial
crystals and may even cause a decoupling of two-dimensional vortex lattices in
the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause
thermally activated depinning of the flux lines or of the 2D pancake vortices
in the layers. Various phase transitions are predicted for the FLL in layered
HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to
interesting effects which strongly depend on the geometry of the experiment.
|
Flux Creep and Flux Jumping | We consider the flux jump instability of the Bean's critical state arising in
the flux creep regime in type-II superconductors. We find the flux jump field,
$B_j$, that determines the superconducting state stability criterion. We
calculate the dependence of $B_j$ on the external magnetic field ramp rate,
$\dot B_e$. We demonstrate that under the conditions typical for most of the
magnetization experiments the slope of the current-voltage curve in the flux
creep regime determines the stability of the Bean's critical state, {\it i.e.},
the value of $B_j$. We show that a flux jump can be preceded by the
magneto-thermal oscillations and find the frequency of these oscillations as a
function of $\dot B_e$.
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Percolation transition of the vortex lattice and c-axis resistivity in
high-temperature superconductors | We use the three-dimensional Josephson junction array system as a model for
studying the temperature dependence of the c-axis resistivity of high
temperature superconductors, in the presence of an external magnetic field H
applied in the c-direction. We show that the temperature at which the
dissipation becomes different from zero corresponds to a percolation transition
of the vortex lattice. In addition, the qualitative features of the resistivity
vs. temperature curves close to the transition are obtained starting from the
geometrical configurations of the vortices. The results apply to the cases H
greater than 0 and H=0.
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Renormalization group approach to layered superconductors | A renormalization group theory for a system consisting of coupled
superconducting layers as a model for typical high-temperature superconducters
is developed. In a first step the electromagnetic interaction over infinitely
many layers is taken into account, but the Josephson coupling is neglected. In
this case the corrections to two-dimensional behavior due to the presence of
the other layers are very small. Next, renormalization group equations for a
layered system with very strong Josephson coupling are derived, taking into
account only the smallest possible Josephson vortex loops. The applicability of
these two limiting cases to typical high-temperature superconductors is
discussed. Finally, it is argued that the original renormalization group
approach by Kosterlitz is not applicable to a layered system with intermediate
Josephson coupling.
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Low-Field Phase Diagram of Layered Superconductors: The Role of
Electromagnetic Coupling | We determine the position and shape of the melting line in a layered
superconductor taking the electromagnetic coupling between layers into account.
In the limit of vanishing Josephson coupling we obtain a new generic reentrant
low-field melting line. Finite Josephson coupling pushes the melting line to
higher temperatures and fields and a new line shape $B_{{\rm m}} \propto
(1-T/T_c)^{3/2}$ is found. We construct the low-field phase diagram including
melting and decoupling lines and discuss various experiments in the light of
our new results.
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Vortex Dynamics and the Hall-Anomaly: a Microscopic Analysis | We present a microscopic derivation of the equation of motion for a vortex in
a superconductor. A coherent view on vortex dynamics is obtained, in which {\it
both} hydrodynamics {\it and} the vortex core contribute to the forces acting
on a vortex. The competition between these two provides an interpretation of
the observed sign change in the Hall angle in superconductors with mean free
path $l$ of the order of the coherence length $\xi$ in terms of broken
particle-hole symmetry, which is related to details of the microscopic
mechanism of superconductivity.
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Constants of motion in the dynamics of a 2N-junction SQUID | We show that a 2N junction SQUID (Superconducting QUantum Interference
Device) made of 2N overdamped, shunted, identical junctions may be described as
a system having only 6 degrees of freedom for any N > 2. This is achieved by
means of the reduction introduced by Watanabe and Strogatz (Physica D, Vol. 74,
(1994) p. 197) for series biased arrays. In our case 6 rather than 3 degrees of
freedom are necessary to describe the system, due to the requirement of phase
quantization along the superconducting loop constituting the device.
Generalization to multijunction parallel arrays is straightforward.
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Screening current effects in Josephson junction arrays | The purpose of this work is to compare the dynamics of arrays of Josephson
junctions in presence of magnetic field in two different frameworks: the so
called XY frustrated model with no self inductance and an approach that takes
into account the screening currents (considering self inductances only). We
show that while for a range of parameters the simpler model is sufficiently
accurate, in a region of the parameter space solutions arise that are not
contained in the XY model equations.
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Nonlinear optical response in doped conjugated polymers | Exciton effects on conjugated polymers are investigated in soliton lattice
states. We use the Su-Schrieffer-Heeger model with long-range Coulomb
interactions. The Hartree-Fock (HF) approximation and the single-excitation
configuration- interaction (single-CI) method are used to obtain optical
absorption spectra. The third-harmonic generation (THG) at off-resonant
frequencies is calculated as functions of the soliton concentration and the
chain length of the polymer. The magnitude of the THG at the 10 percent doping
increases by the factor about 10^2 from that of the neutral system. This is
owing to the accumulation of the oscillator strengths at the lowest exciton
with increasing the soliton concentration. The increase by the order two is
common for several choices of Coulomb interaction strengths.
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Nucleation and Growth of Normal Phase in Thin Superconducting Strips | We investigate the kinetics of normal phase nucleation and flux line
condensation in the type-II superconductors by numerical study of the
time-dependent Ginzburg-Landau equation. We have shown that under the
sufficient transport current the normal phase nucleates in the superconducting
strips in a form of the macroscopic droplets having the multiple topological
charge. We discuss the stability and the dynamics of the droplets. We found
that pinning suppresses the droplet formation.
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$s$- and $d_{xy}$-wave components induced around a vortex in
$d_{x^2-y^2}$-wave superconductors | Vortex structure of $d_{x^2-y^2}$-wave superconductors is microscopically
analyzed in the framework of the quasi-classical Eilenberger equations. If the
pairing interaction contains an $s$-wave ($d_{xy}$-wave) component in addition
to a $d_{x^2-y^2}$-wave component, the $s$-wave ($d_{xy}$-wave) component of
the order parameter is necessarily induced around a vortex in
$d_{x^2-y^2}$-wave superconductors. The spatial distribution of the induced
$s$-wave and $d_{xy}$-wave components is calculated. The $s$-wave component has
opposite winding number around vortex near the $d_{x^2-y^2}$-vortex core and
its amplitude has the shape of a four-lobe clover. The amplitude of
$d_{xy}$-component has the shape of an octofoil. These are consistent with
results based on the GL theory.
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Superconducting, magnetic, and charge correlations in the doped
two-chain Hubbard model | Superconducting, magnetic, and charge correlation functions and dynamic spin
correlation functions of the doped two-chain Hubbard model is studied with the
projector Quantum Monte carlo method and Lanczos recursion method. Of the three
correlation functions, the interchain singlet superconducting correlation
function is the most long range. Our data is not consistent with the
Luther-Emery picture.
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The Bean Critical State: Infinitely Unstable | The threshold for creep in the Bean critical state is investigated. We
perturb the Bean state by an energy $\Delta\epsilon$. We find that no matter
how small $\Delta\epsilon$ is it will always be able to induce creep somewhere
on the Bean profile. This finding has important consequences for the
interpretation of low temperature creep phenomena in terms of quantum creep.
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Nonlinear Flux Diffusion and ac Susceptibility of Superconductors -
Exact Numerical Results | The ac response of a slab of material with electrodynamic characteristics
$E\sim j^{\kappa+1}$, $\kappa\geq0$, is studied numerically. From the solutions
of the nonlinear diffusion equation, the fundamental and higher-order
components of the harmonic susceptibility are obtained. A large portion of the
data for every $\kappa$ can be scaled by a single parameter, $\xi$
=$t^{1/(\kappa+2)}\cdot H_0^{\kappa/(\kappa+2)}/D$, where $t$ is the period of
the ac field at the surface, $H_0$ is its amplitude and $D$ is the slab
thickness. This is, however, only an approximate scaling property: The field
penetration into a nonlinear medium is a more complex phenomenon than in the
linear case. In particular, the susceptibility values are not uniquely defined
by a set of only two parameters, such as $\kappa$ and $\xi$, while one
parameter, i.e. $t^{1/2}$/D, is sufficient to describe the electrodynamic
response of a linear medium.
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Magnetostriction of a Superconductor: -Results from the Critical-State
Model | In many cases, the critical-state theory can be treated as a suffi ciently
accurate approximation for the modelling of the magnetic properties of
superconductors. In the present work, the magnetostrictive hysteresis is
computed for a quite general case of the modified Kim-Anderson model. The
results obtained reproduce many features of the giant magnetostriction
(butterfly-shaped curves) reported in the literature for measurements made on
single-crystal samples of the high-temperature superconductor
$Bi_2Sr_2CaCu_2O_8$. It is shown that addition of a contribution to the
magnetostriction in the superconducting state which is of similar origin as in
the normal state, offers a broader phenomenological interpretation of the
complex magnetostriction hysteresis found in such heavy-fermion compounds as
$UPt_3$, $URu_2Si_2$ or $UBe_{13}$.
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Langevin Simulations of Two Dimensional Vortex Fluctuations: Anomalous
Dynamics and a New $IV$-exponent | The dynamics of two dimensional (2D) vortex fluctuations are investigated
through simulations of the 2D Coulomb gas model in which vortices are
represented by soft disks with logarithmic interactions. The simulations
trongly support a recent suggestion that 2D vortex fluctuations obey an
intrinsic anomalous dynamics manifested in a long range 1/t-tail in the vortex
correlations. A new non-linear IV-exponent a, which is different from the
commonly used AHNS exponent, a_AHNS and is given by a = 2a_AHNS - 3, is
confirmed by the simulations. The results are discussed in the context of
earlier simulations, experiments and a phenomenological description.
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The string model of the Cooper pair in the anisotropic superconductor | The analogy between the Cooper pair in high temperature superconductor and
the quark-antiquark pair in quantum chromodynamics (QCD) is proposed. In QCD
the nonlinear chromodynamical field between a quark and an antiquark is
confined to a tube. So we assume that there is the strong interaction between
phonons which can confine them to some tube too. This tube is described using
the nonlinear Schr\"odinger equation. We show that it has an infinite spectrum
of axially symmetric (string) solutions with negative finite linear energy
density. The one-dimensional nonlinear Schr\"odinger equation has a finite
spectrum (hence, it has a steady-state) which describes the Cooper pair
squezeed between anisotropy planes in the superconductor. It is shown that in
this model the transition temperature is approximately 45 K.
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Polaronic optical absorption in electron-doped and hole-doped cuprates | Polaronic features similar to those previously observed in the photoinduced
spectra of cuprates have been detected in the reflectivity spectra of
chemically doped parent compounds of high-critical-temperature superconductors,
both $n$-type and $p$-type. In Nd$_2$CuO$_{4-y}$ these features, whose
intensities depend both on doping and temperature, include local vibrational
modes in the far infrared and a broad band centered at $\sim$ 1000 cm$^{-1}$.
The latter band is produced by the overtones of two (or three) local modes and
is well described in terms of a small-polaron model, with a binding energy of
about 500 cm$^{-1}$. Most of the above infrared features are shown to survive
in the metallic phase of Nd$_{2-x}$Ce$_x$Cu0$_{4-y}$, Bi$_2$Sr$_2$CuO$_6$, and
YBa$_2$Cu$_3$O$_{7-y}$, where they appear as extra-Drude peaks. The occurrence
of polarons is attributed to local modes strongly coupled to carriers, as shown
by a comparison with tunneling results.
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Synchronization in one-dimensional array of Josephson coupled thin
layers | We obtain self-consistent macroscopic equations describing interlayer
Josephson effect and intralayer disequilibrium in one-dimensional array of
Josephson coupled layers. We show that ``nonequilibrium coupling'' can lead to
effective spatial and time synchronization and formation of coherent dynamic
resistive state (collective Josephson effect) in Nb-AlO-Nb stacked junctions
and HTSC (intrinsic Josephson effect). We propose it to be the origin of
collective switching phenomena observed in PbBiSrCaCuO.
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S-35 Beta Irradiation of a Tin Strip in a State of Superconducting
Geometrical Metastability | We report the first energy loss spectrum obtained with a geometrically
metastable type I superconducting tin strip irradiated by the beta-emission of
S-35. (Nucl. Instr. Meth. A, in press)
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Vortex structure in $d$-wave superconductors | Vortex structure of pure $d_{x^2-y^2}$-wave superconductors is
microscopically analyzed in the framework of the quasi-classical Eilenberger
equations. Selfconsistent solution for the $d$-wave pair potential is obtained
for the first time in the case of an isolated vortex. The vortex core
structure, i.e., the pair potential, the supercurrent and the magnetic field,
is found to be fourfold symmetric even in the case that the mixing of $s$-wave
component is absent. The detailed temperature dependences of these quantities
are calculated. The fourfold symmetry becomes clear when temperature is
decreased. The local density of states is calculated for the selfconsistently
obtained pair potential. From the results, we discuss the flow trajectory of
the quasiparticles around a vortex, which is characteristic in the
$d_{x^2-y^2}$-wave superconductors. The experimental relevance of our results
to high temperature superconductors is also given.
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Beta Irradiation of a Geometrically Metastable Superconducting Strip
Detector with a Magnetic Flux Penetration Read-Out | Geometrical metastability, observed in superconducting type I tin flat
strips, has been previously proposed as a principle for particle detection. The
energy deposition of an incoming beta-particle induces the rupture of the
metastability and consequently the penetration of multiquantum flux tubes into
a superconducting tin strip. We present here the first absorption spectra from
two beta sources, which demonstrate the linearity and energy-resolution of
these detectors (presented at the 6th International Workshop on Low Temperature
Detectors for Dark Matter and Neutrinos (LTD-6), Interlaken, Switzerland, Sept.
1995)
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Vortex structure and resistive transitions in high-Tc superconductors | The nature of the resistive transition for a current applied parallel to the
magnetic field in high-Tc materials is investigated by numerical simulation on
the three dimensional Josephson junction array model. It is shown by using
finite size scaling that for samples with disorder the critical temperature Tp
for the c axis resistivity corresponds to a percolation phase transition of
vortex lines perpendicularly to the applied field. The value of Tp is higher
than the critical temperature for j perpendicular to H, but decreases with the
thickness of the sample and with anisotropy. We predict that critical behavior
around Tp should reflect in experimentally accessible quantities, as the I-V
curves.
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Updating the theoretical analysis of the weak gravitational shielding
experiment | The most recent data about the weak gravitational shielding produced recently
through a levitating and rotating HTC superconducting disk show a very weak
dependence of the shielding value ($\sim 1 \%$) on the height above the disk.
We show that whilst this behaviour is incompatible with an intuitive vectorial
picture of the shielding, it is consistently explained by our theoretical
model. The expulsive force observed at the border of the shielded zone is due
to energy conservation.
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Vortex Plastic Flow, $B(x,y,H(t)), M(H(t)), J_c(B(t))$, Deep in the Bose
Glass and Mott-Insulator Regimes | We present simulations of flux-gradient-driven superconducting vortices
interacting with strong columnar pinning defects as an external field $H(t)$ is
quasi-statically swept from zero through a matching field $B_{\phi}$. We
analyze several measurable quantities, including the local flux density $
B(x,y,H(t))$, magnetization $M(H(t))$, critical current $J_{c}(B(t))$, and the
individual vortex flow paths. We find a significant change in the behavior of
these quantities as the local flux density crosses $B_{\phi}$, and quantify it
for many microscopic pinning parameters. Further, we find that for a given pin
density $J_c(B)$ can be enhanced by maximizing the distance between the pins
for $ B < B_{\phi} $.
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s and d-wave symmetries of the solutions of the Eliashberg equations | We examine the different possible symmetries of the superconducting gap
obtained by solving the Eliashberg equations. We consider an electron-phonon
interaction in a strong coupling scenario. The Coulomb pseudopotential plays
the crucial role of providing the repulsion needed to favour the d-wave
symmetry. But the key parameter that allows very anisotropic solutions even
with very strong coupling is the small angular range of the interaction due to
predominantly electron-phonon forward scattering that is found in the high-Tc
superconductors. We find both s and d-wave solutions whose stability depends
mainly on the angular range of the interaction.
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Vortex Response and Critical Fields observed via rf penetration depth
measurements on the superconductor YNi_2B_2C | Measurements of the rf penetration depth \lambda(T,H,\theta ) are used to
study the superconducting order parameter, vortex dynamics in the mixed state
and delineate critical fields in the borocarbide superconductor YNi_2B_2C. The
lower critical field has an anomalous T dependence, H_{c1}(T)=1.12[1-(T/T_c)]
kOe, which is however consistent with independent superfluid density
measurements at microwave frequencies. The vortex response is dominated by
viscous flux flow, indicative of extremely weak pinning, and is parametrized by
a field scale H_{c2,eff}. The angular dependence of the vortex contribution
\lambda(\theta) is in good agreement with the Coffey-Clem model. Structure is
seen in the depairing transition in the vicinity of the upper critical field,
with the existence of well-defined critical fields H_{c2a}, H_{c2b} and
H_{c2c}, with the vortex field scale H_{c2,eff} closest to H_{c2b}. Overall the
measurements indicate that YNi_2B_2C has a rich and unusual field dependence of
its transport parameters.
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Vortex loops entry into type--II superconductors | The magnetic field distribution, the magnetic flux, and the free energy of an
Abrikosov vortex loop near a flat surface of type--II superconductors are
calculated in the London approximation. The shape of such a vortex line is a
semicircle of arbitrary radius. The interaction of the vortex half--ring and an
external homogeneous magnetic field applied along the surface is studied. The
magnitude of the energy barrier against the vortex expansion into
superconductor is found. The possibilities of formation of an equilibrium
vortex line determined by the structure of the applied magnetic field by
creating the expanding vortex loops near the surface of type--II superconductor
are discussed.
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Low temperature thermal conductivity of Zn-doped YBCO: evidence for
impurity-induced electronic bound states | The thermal conductivity of Zn-doped YBCO crystals was studied at low
temperature (0.15 < T < 0.8 K) for different concentrations of Zn impurities. A
small amount of Zn induces a dramatic decrease in the non-linear component of
the low-temperature thermal conductivity. Moreover, the magnitude of the linear
component (obtained by extrapolating the data to T=0) is found to depend on Zn
concentration. After an initial decrease, this linear term, associated with the
electronic contribution to the conductivity, increases with increasing Zn
dopage. Such an increase is consistent with the introduction of low-energy
excitations by Zn impurities as expected for a $d_{x^2-y^2}$ superconducting
state in contrast to an anisotropic s-wave gap. The results are compared to
quantitative predictions of available theoretical models.
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Irreversible magnetization in thin YBCO films rotated in external
magnetic field | The magnetization M of a thin YBaCuO film is measured as a function of the
angle $\theta $ between the applied field H and the c-axis. For fields above
the first critical field, but below the Bean's field for first penetration H*,
M is symmetric with respect to $\theta =\pi $ and the magnetization curves for
forward and backward rotation coincide. For H>H* the curves are asymmetric and
they do not coincide. These phenomena have a simple explanation in the
framework of the Bean critical state model.
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Coupling of Josephson flux-flow oscillators to an external RC load | We investigate by numerical simulations the behavior of the power dissipated
in a resistive load capacitively coupled to a Josephson flux flow oscillator
and compare the results to those obtained for a d.c. coupled purely resistive
load. Assuming realistic values for the parameters R and C, both in the high-
and in the low-Tc case the power is large enough to allow the operation of such
a device in applications.
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New Universality Class in the Superconductive Phase Transition | The superconductive phase transition in the Ginzburg-Landau theory (or
Coulomb-Higgs phase transition of scalar QED in 3D) is discussed in a dual
formulation which focuses on the magnetic rather than the electric excitations
of the system. Renormalization group analysis of the dual formulation reveals
the transition to be of second order and of a new universality class. Whereas
coherence length and specific heat have XY-model exponents, the magnetic
penetration depth shows mean-field behavior. Experimental evidence for these
predictions is discussed.
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Star-shaped Local Density of States around Vortices in a Type II
Superconductor | The electronic structure of vortices in a type II superconductor is analyzed
within the quasi-classical Eilenberger framework. The possible origin of a
sixfold ``star'' shape of the local density of states, observed by scanning
tunneling microscope experiments on NbSe$_2$, is examined in the light of the
three effects; the anisotropic pairing, the vortex lattice, and the anisotropic
density of states at the Fermi surface. Outstanding features of split parallel
rays of this star are well explained in terms of an anisotropic $s$-wave
pairing. This reveals a rich internal electronic structure associated with a
vortex core.
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Plastic vortex-creep in YBa$_2$Cu$_3$O$_{7-x}$ crystals | Local magnetic relaxation measurements in YBa$_2$Cu$_3$O$_{7-x}$ crystals
show evidence for plastic vortex-creep associated with the motion of
dislocations in the vortex lattice. This creep mechanism governs the vortex
dynamics in a wide range of temperatures and fields below the melting line and
above the field corresponding to the peak in the ''fishtail'' magnetization. In
this range the activation energy $U_{pl}$, which decreases with field, drops
below the elastic (collective) creep activation energy, $U_{el}$, which
increases with field. A crossover in flux dynamics from elastic to plastic
creep is shown to be the origin of the fishtail in YBa$_2$Cu$_3$O$_{7-x}$.
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On Mean-Field Theory of Quantum Phase Transition in Granular
Superconductors | In previous work on quantum phase transition in granular superconductors,
where mean-field theory was used, an assumption was made that the order
parameter as a function of the mean field is a convex up function. Though this
is not always the case in phase transitions, this assumption must be verified,
what is done in this article.
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Ginzburg-Landau Theory of Josephson Field Effect Transistors | A theoretical model of high-T_c Josephson Field Effect Transistors (JoFETs)
based on a Ginzburg-Landau free energy expression whose parameters are field-
and spatially- dependent is developed. This model is used to explain
experimental data on JoFETs made by the hole-overdoped Ca-SBCO bicrystal
junctions (three terminal devices). The measurements showed a large modulation
of the critical current as a function of the applied voltage due to charge
modulation in the bicrystal junction. The experimental data agree with the
solutions of the theoretical model. This provides an explanation of the large
field effect, based on the strong suppresion of the carrier density near the
grain boundary junction in the absence of applied field and the subsequent
modulation of the density by the field.
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Flux flow resistivity and vortex viscosity of high-Tc films | The flux flow regime of high-T$_{\rm c}$ samples of different normal state
resistivities is studied in the temperature range where the sign of the Hall
effect is reversed. The scaling of the vortex viscosity with normal state
resistivity is consistent with the Bardeen-Stephen theory. Estimates of the
influence of possible mechanisms suggested for the sign reversal of the Hall
effect are also given.
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Comments on "Vortex Glass and Lattice Melting Transitions in a YNi_2B_2C
Single Crystal" | Recently, Mun et.al. (Phys. Rev. Lett., 76, 2790 (1996)) have published their
results on single crystal YNi_2B_2C, claiming that their experimental
observations can be explained in terms of formation of Vortex Glass and Lattice
melting. Our experiments, carried out on samples obtained from the SAME source,
reveal a much richer phase diagram and span wider regions of experimental
parameter space than Mun et. al. that encompasses most of their observations.
We speculate that this material has anomalous intrinsic properties and the
results cannot be explained by simple models about the flux lattice.
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Spatio-temporal dynamics and plastic flow of vortices in superconductors
with periodic arrays of pinning sites | We present simulations of flux-gradient-driven superconducting rigid vortices
interacting with square and triangular arrays of columnar pinning sites in an
increasing external magnetic field. These simulations allow us to
quantitatively relate spatio-temporal microscopic information of the vortex
lattice with typically measured macroscopic quantities, such as the
magnetization $M(H)$. The flux lattice does not become completely commensurate
with the pinning sites throughout the sample at the magnetization matching
peaks, but forms a commensurate lattice in a region close to the edge of the
sample. Matching fields related to unstable vortex configurations do not
produce peaks in $M(H)$. We observe a variety of evolving complex flux
profiles, including flat terraces or plateaus separated by winding
current-carrying strings and, near the peaks in $M(H)$, plateaus only in
certain regions, which move through the sample as the field increases.
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Strong Pinning and Plastic Deformations of the Vortex Lattice | We investigate numerically the dynamically generated plastic deformations of
a 3D vortex lattice (VL) driven through a disorder potential with isolated,
strong pinning centers (point-like or extended along the field direction). We
find that the VL exhibits a very peculiar dynamical behavior in the plastic
flow regime, in particular, topological excitations consisting of three or four
entangled vortices are formed. We determine the critical current density $j_c$
and the activation energy for depinning $U_c$ in the presence of a finite
density of strong pinning centers.
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Towards a Microscopic Theory for Metallic Heavy-Fermion Point Contacts | The bias-dependent resistance R(V) of NS-junctions is calculated using the
Keldysh formalism in all orders of the transfer matrix element. We present a
compact and simple formula for the Andreev current, that results from the
coupling of electrons and holes on the normal side via the anomalous Green's
function on the superconducting side. Using simple BCS Nambu-Green's functions
the well known Blonder-Tinkam-Klapwijk theory can be recovered. Incorporating
the energy-dependent quasi-particle lifetime of the heavy fermions strongly
reduces the Andreev-reflection signal.
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Topology and Phase Transitions in the Little-Parks Experiment | This is an analytic study of the problem of transitions between normal and
superconducting phases for a sample which encloses a magnetic flux. A
preliminary study of this problem, based on numerical minimization of the free
energy for a particular form of the thickness of the sample, was published in
Phys. Rev. Lett. {\bf 75}, 320 (1995). For a sample of uniform thickness the
order parameter is uniform, but even infinitesimal deviations from uniform
thickness give rise to a singly connected state in which the order parameter
vanishes at a suitable layer, so that the superconducting part does not enclose
the magnetic field. The stability domain of this singly connected state is a
line segment in the magnetic field-temperature plane, delimited by two critical
points. The phase diagram contains several bifurcation lines, which are
systematically analyzed.
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c-Axis Infrared Conductivity of a d_{x^2-y^2}-Wave Superconductor with
Impurity and Spin-Fluctuation Scattering | Results of a calculation of the c-axis infrared conductivity sigma_c for a
d_{x^2-y^2}-wave superconductor which include both elastic impurity and
inelastic spin-fluctuation scattering are presented and compared with the
ab-plane conductivity sigma_{ab} in the same model. In this model,the
interlayer c-axis coupling is taken to be weak and diffusive. While in clean
systems, inelastic scattering leads to a peak at omega = 4*Delta_0 in
sigma_{ab} for T < T_c, it has little effect on the corresponding sigma_c,
which exhibits structure only at omega = 2*Delta_0 and is directly related to
the single-particle density of states N(omega). The c-axis penetration depth
lambda_c in the same model is predicted to vary as T^3 at low temperatures in
clean samples. We discuss recent optical experiments on the cuprates and
compare with these predictions.
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Extended bound states and resonances of two fermions on a periodic
lattice | The high-$T_c$ cuprates are possible candidates for d-wave superconductivity,
with the Cooper pair wave function belonging to a non-trivial irreducible
representation of the lattice point group. We argue that this d-wave symmetry
is related to a special form of the fermionic kinetic energy and does not
require any novel pairing mechanism. In this context, we present a detailed
study of the bound states and resonances formed by two lattice fermions
interacting via a non-retarded potential that is attractive for nearest
neighbors but repulsive for other relative positions. In the case of strong
binding, a pair formed by fermions on adjacent lattice sites can have a small
effective mass, thereby implying a high condensation temperature. For a weakly
bound state, a pair with non-trivial symmetry tends to be smaller in size than
an s-wave pair. These and other findings are discussed in connection with the
properties of high-$T_c$ cuprate superconductors.
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Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II
2-dimensional Superconductor | We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a
type-II two-dimensional superconductor within a self-consistent Gor'kov
perturbation scheme. Assuming that the order parameter forms a vortex lattice
we can calculate the expansion coefficients exactly to any order. We have
tested the results of the perturbation theory to fourth and eight order against
an exact numerical solution of the corresponding Bogoliubov-de Gennes
equations. The perturbation theory is found to describe the onset of
superconductivity well close to the transition point $H_{c2}$. Contrary to
earlier calculations by other authors we do not find that the perturbative
scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we
obtain a substantial damping of the magnetic oscillations in the mixed state as
compared to the normal state. We have examined the effect of an oscillatory
chemical potential due to particle conservation and the effect of a finite
Zeeman splitting. Furthermore we have investigated the recently debated issue
of a possibility of a sign change of the fundamental harmonic of the magnetic
oscillations. Our theory is compared with experiment and we have found good
agreement.
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Evidence for Quasiparticle Decay in Photoemission from Underdoped
Cuprates | I argue that the ``gap'' recently observed at the Brillouin zone face of
cuprate superconductors in photoemission by Marshall et al [Phys. Rev. Lett.
76, 4841 (1996)] and Ding et al [Nature 382, 54 (1996)] is evidence for the
decay of the injected hole into a spinon-holon pair.
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Strong coupling theory of the interlayer tunneling model for high
temperature superconductors | The interlayer pair tunneling model of Anderson et al. is generalized to
include the strong coupling effects associated with in-plane interactions. The
equations for the superconducting transition temperature T_{c} are solved
numerically for several models of electron-optical phonon coupling. The
nonmagnetic in-plane impurity scattering suppresses T_{c} in all cases
considered, and it is possible to obtain a fair agreement with experiments for
a reasonable choice of parameters. For the anisotropic electron-phonon coupling
proposed by Song and Annett we find that the interlayer pair tunneling can
stabilize the d_{x^2-y^2}-wave superconducting state with a high T_{c}.
Moreover, in this case there is a possibility of an impurity induced crossover
from the d$_{x^2-y^2}$-wave state stabilized by the interlayer tunneling to the
s-wave state at a low impurity concentration. We also calculate the isotope
effect associated with the in-plane oxygen optic mode and its dependence on the
strength of the interlayer pair tunneling. Small positive values of the isotope
exponent are obtained for strengths of pair tunneling that give high transition
temperatures.
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The Fluctuation Induced Pseudogap in the Infrared Optical Conductivity
of High Temperature Superconductors | We study the effect of fluctuations on the {\bf ac} conductivity of a layered
superconductor both for $c$-axis and $ab$-plane electromagnetic wave
polarizations. The fluctuation contributions of different physical nature and
signs (paraconductivity, Maki-Thompson anomalous contribution, one-electron
density of states renormalization) are found to be suppressed by the external
field at different characterisitic frequencies ($ \omega_{\rm AL}\sim T-T_{\rm
c}$, $\omega_{\rm MT} \sim \max\{ T-T_{\rm c}, \tau_{\varphi}^{-1}\}$, $
\omega_{\rm DOS} \sim \min\{T,\tau ^{-1}\}$ for the $2D$ case). As a result the
appearance of the nonmonotonic frequency dependence (pseudogap) in the infrared
optical conductivity of HTS film is predicted. The effect has to be especially
pronounced in the case of the electromagnetic field polarization along
$c$-axis.
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On the origin of the irreversibility line in thin YBaCuO7 films with and
without columnar defects | We report on measurements of the angular dependence of the irreversibility
temperature $T_{irr}(\theta) $ in $YBa_2Cu_3O_{7-\delta }$ thin films, defined
by the onset of a third harmonic signal and measured by a miniature Hall probe.
From the functional form of $T_{irr}(\theta)$ we conclude that the origin of
the irreversibility line in unirradiated films is a dynamic crossover from an
unpinned to a pinned vortex liquid. In irradiated films the irreversibility
temperature is determined by the trapping angle.
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Nonlinear Response of HTSC Thin Film Microwave Resonators in an Applied
DC Magnetic Field | The non-linear microwave surface impedance of patterned YBCO thin films, was
measured using a suspended line resonator in the presence of a perpendicular DC
magnetic field of magnitude comparable to that of the microwave field.
Signature of the virgin state was found to be absent even for relatively low
microwave power levels. The microwave loss was initially found to decrease for
small applied DC field before increasing again. Also, non-linearities inherent
in the sample were found to be substantially suppressed at low powers at these
applied fields. These two features together can lead to significant improvement
in device performance.
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Critical State Flux Penetration and Linear Microwave Vortex Response in
YBa_2Cu_3O_{7-x} Films | The vortex contribution to the dc field (H) dependent microwave surface
impedance Z_s = R_s+iX_s of YBa_2Cu_3O_{7-x} thin films was measured using
suspended patterned resonators. Z_s(H) is shown to be a direct measure of the
flux density B(H) enabling a very precise test of models of flux penetration.
Three regimes of field-dependent behavior were observed: (1) Initial flux
penetration occurs on very low field scales H_i(4.2K) 100Oe, (2) At moderate
fields the flux penetration into the virgin state is in excellent agreement
with calculations based upon the field-induced Bean critical state for thin
film geometry, parametrized by a field scale H_s(4.2K) J_c*d 0.5T, (3) for very
high fields H >>H_s, the flux density is uniform and the measurements enable
direct determination of vortex parameters such as pinning force constants
\alpha_p and vortex viscosity \eta. However hysteresis loops are in
disagreement with the thin film Bean model, and instead are governed by the low
field scale H_i, rather than by H_s. Geometric barriers are insufficient to
account for the observed results.
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Density of States and NMR Relaxation Rate in Anisotropic
Superconductivity with Intersecting Line Nodes | We show that the density of states in an anisotropic superconductor with
intersecting line nodes in the gap function is proportional to $E log (\alpha
\Delta_0 /E)$ for $|E| << \Delta_0$, where $\Delta_0$ is the maximum value of
the gap function and $\alpha$ is constant, while it is proportional to $E$ if
the line nodes do not intersect. As a result, a logarithmic correction appears
in the temperature dependence of the NMR relaxation rate and the specific heat,
which can be observed experimentally. By comparing with those for the heavy
fermion superconductors, we can obtain information about the symmetry of the
gap function.
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Ginzburg Landau theory for d-wave pairing and fourfold symmetric vortex
core structure | The Ginzburg Landau theory for d_{x^2-y^2}-wave superconductors is
constructed, by starting from the Gor'kov equation with including correction
terms up to the next order of ln(T_c/T). Some of the non-local correction terms
are found to break the cylindrical symmetry and lead to the fourfold symmetric
core structure, reflecting the internal degree of freedom in the pair
potential. Using this extended Ginzburg Landau theory, we investigate the
fourfold symmetric structure of the pair potential, current and magnetic field
around an isolated single vortex, and clarify concretely how the vortex core
structure deviates from the cylindrical symmetry in the d_{x^2-y^2}-wave
superconductors.
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