1,800 research outputs found
The Intermodulation Coefficient of an Inhomogeneous Superconductor
The high-T_c cuprate superconductors are now believed to be intrinsically
inhomogeneous. We develop a theory to describe how this inhomogeneity affects
the intermodulation coefficient of such a material. We show that the continuum
equations describing intermodulation in a superconducting layer with spatially
varying properties are formally equivalent to those describing an inhomogeneous
dielectric with a nonzero cubic nonlinearity. Using this formal analogy, we
calculate the effect of inhomogeneity on the intermodulation coefficient in a
high-T_c material, using several assumptions about the topology of the layer,
and some simple analytical approximations to treat the nonlinearity. For some
topologies, we find that the intermodulation critical supercurrent density
J_{IMD} is actually enhanced compared to a homogeneous medium, thereby possibly
leading to more desirable material properties. We discuss this result in light
of recent spatial mappings of the superconducting energy gap in BSCCO-2212.Comment: 26 pages, 9 figures, accepted for publication in the Journal of
Applied Physic
High field magnetotransport in composite conductors: the effective medium approximation revisited
The self consistent effective medium approximation (SEMA) is used to study
three-dimensional random conducting composites under the influence of a strong
magnetic field {\bf B}, in the case where all constituents exhibit isotropic
response. Asymptotic analysis is used to obtain almost closed form results for
the strong field magnetoresistance and Hall resistance in various types of two-
and three-constituent isotropic mixtures for the entire range of compositions.
Numerical solutions of the SEMA equations are also obtained, in some cases, and
compared with those results. In two-constituent
free-electron-metal/perfect-insulator mixtures, the magnetoresistance is
asymptotically proportional to at {\em all concentrations above the
percolation threshold}. In three-constituent metal/insulator/superconductor
mixtures a line of critical points is found, where the strong field
magnetoresistance switches abruptly from saturating to non-saturating
dependence on , at a certain value of the
insulator-to-superconductor concentration ratio. This transition appears to be
related to the phenomenon of anisotropic percolation.Comment: 16 pages, 3 figure
Continuous phase transition of a fully frustrated XY model in three dimensions
We have used Monte Carlo simulations, combined with finite-size scaling and
two different real-space renormalization group approaches, to study a fully
frustrated three-dimensional XY model on a simple cubic lattice. This model
corresponds to a lattice of Josephson-coupled superconducting grains in an
applied magnetic field . We find that the
model has a continuous phase transition with critical temperature , where is the XY coupling constant, and critical exponents
, , and , where , , and describe the critical behavior of the
specific heat, helicity modulus, and correlation length. We briefly compare our
results with other studies of this model, and with a mean-field approximation.Comment: 34 pages, 13 figures, 1 table, Phys. Rev. B in pres
Faraday Rotation, Band Splitting, and One-Way Propagation of Plasmon Waves on a Nanoparticle Chain
We calculate the dispersion relations of plasmonic waves propagating along a
chain of semiconducting or metallic nanoparticles in the presence of both a
static magnetic field and a liquid crystalline host. The dispersion
relations are obtained using the quasistatic approximation and a dipole-dipole
approximation to treat the interaction between surface plasmons on different
nanoparticles. For a plasmons propagating along a particle chain in a nematic
liquid crystalline host with both and the director parallel to the
chain, we find a small, but finite, Faraday rotation angle. For
perpendicular to the chain, but director still parallel to the chain, the field
couples the longitudinal and one of the two transverse plasmonic branches. This
coupling is shown to split the two branches at the zero field crossing by an
amount proportional to . In a cholesteric liquid crystal host and an
applied magnetic field parallel to the chain, the dispersion relations for
left- and right-moving waves are found to be different. For some frequencies,
the plasmonic wave propagates only in one of the two directions.Comment: 6 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1502.0496
Model for Vortex Pinning in a Two-Dimensional Inhomogeneous d-wave Superconductor
We study a model for the pinning of vortices in a two-dimensional,
inhomogeneous, Type-II superconductor in its mixed state. The model is based on
a Ginzburg-Landau (GL) free energy functional whose coefficients are determined
by the mean-field transition temperature T_{c0} and the zero-temperature
penetration depth \lambda(0). We find that if (i) T_{c0} and \lambda(0) are
functions of position, and (ii) \lambda^2(0) is proportional to T_{c0}^y, with
y greater than 0, then the vortices tend to be pinned where T_{c0}, and hence
the magnitude of the superconducting order parameter \Delta, are large. This
behavior is in contrast to the usual picture of pinning in Type-II
superconductors, where pinning occurs in the small-gap regions. We also compute
the local density of states of a model BCS Hamiltonian with d-wave symmetry, in
which the pairing field is obtained from Monte Carlo simulations of a GL free
energy. Several features observed in scanning tunneling spectroscopy
measurements on YBa_2Cu_3O_{6+x} and Bi_2Sr_2CaCu_2O_{8+x} are well reproduced
by our model: far from the cores, the local density of states spectrum has a
small gap and sharp coherence peaks, while near the cores it has a larger gap
with low, broad peaks. Additionally, also in agreement with experiment, the
spectrum near the core does not exhibit a zero-energy peak which is, however,
observed in other theoretical studies.Comment: 25 pages, 11 figures. Accepted for publication in Phys. Rev.
Tight-Binding Model for Adatoms on Graphene: Analytical Density of States, Spectral Function, and Induced Magnetic Moment
In the limit of low adatom concentration, we obtain exact analytic
expressions for the local and total density of states (LDOS, TDOS) for a
tight-binding model of adatoms on graphene. The model is not limited to
nearest-neighbor hopping but can include hopping between carbon atoms at any
separation. We also find an analytical expression for the spectral function
of an electron of Bloch vector and energy E on the
graphene lattice, to first order in the adatom concentration. We treat the
electron-electron interaction by including a Hubbard term on the adatom, which
we solve within a mean-field approximation. For finite Hubbard , we find the
spin-polarized LDOS, TDOS, and spectral function self-consistently. For any
choice of parameters of the tight-binding model within mean field theory, we
find a critical value of above which a moment develops on the adatom. For
most choices of parameters, we find a substantial charge transfer from the
adatom to the graphene host.Comment: 11 Pages, 6 figures, 1 tabl
Thermophysical properties of simple liquid metals: A brief review of theory
In this paper, we review the current theory of the thermophysical properties of simple liquid metals. The emphasis is on thermodynamic properties, but we also briefly discuss the nonequilibrium properties of liquid metals. We begin by defining a 'simple liquid metal' as one in which the valence electrons interact only weakly with the ionic cores, so that the interaction can be treated by perturbation theory. We then write down the equilibrium Hamiltonian of a liquid metal as a sum of five terms: the bare ion-ion interaction, the electron-electron interaction, the bare electron-ion interaction, and the kinetic energies of electrons and ions. Since the electron-ion interaction can be treated by perturbation, the electronic part contributes in two ways to the Helmholtz free energy: it gives a density-dependent term which is independent of the arrangement of ions, and it acts to screen the ion-ion interaction, giving rise to effective ion-ion pair potentials which are density-dependent, in general. After sketching the form of a typical pair potential, we briefly enumerate some methods for calculating the ionic distribution function and hence the Helmholtz free energy of the liquid: monte Carlo simulations, molecular dynamics simulations, and thermodynamic perturbation theory. The final result is a general expression for the Helmholtz free energy of the liquid metal. It can be used to calculate a wide range of thermodynamic properties of simple metal liquids, which we enumerate. They include not only a range of thermodynamic coefficients of both metals and alloys, but also many aspects of the phase diagram, including freezing curves of pure elements and phase diagrams of liquid alloys (including liquidus and solidus curves). We briefly mention some key discoveries resulting from previous applications of this method, and point out that the same methods work for other materials not normally considered to be liquid metals (such as colloidal suspensions, in which the suspended microspheres behave like ions screened by the salt solution in which they are suspended). We conclude with a brief discussion of some non-equilibrium (i.e., transport) properties which can be treated by an extension of these methods. These include electrical resistivity, thermal conductivity, viscosity, atomic self-diffusion coefficients, concentration diffusion coefficients in alloys, surface tension and thermal emissivity. Finally, we briefly mention two methods by which the theory might be extended to non-simple liquid metals: these are empirical techniques (i.e., empirical two- and three-body potentials), and numerical many-body approaches. Both may be potentially applicable to extremely complex systems, such as nonstoichiometric liquid semiconductor alloys
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