arXiv subjects

M. Franz

Publications and source records attributed to M. Franz.

104 records · Page 6Linked to original sources

arXiv1999

Mixed-state quasiparticle transport in high-T_c cuprates: localization by magnetic field

Theory of quasiparticle transport in the mixed state of a d-wave superconductor is developed under the assumption of disordered vortex array. A novel universal regime is identified at fields above H*= c*H_{c2}(T/T_c)^2, characterized by a field-independent longitudinal thermal conductivity. It is argued that this behavior is responsible for the high-field plateau in the thermal conductivity experimentally observed in cuprates by Krishana, Ong and co-workers.

cond-mat.supr-con↗

arXiv1998

Quasiparticle spectra in the vicinity of a d-wave vortex

We discuss the evolution of the local quasiparticle spectral density and the related tunneling conductance measurable by the scanning tunneling microscope, as a function of distance r and angle θfrom the vortex core in a d_{x^2-y^2} superconductor. We consider the effects of electronic disorder and of a strongly anisotropic tunneling matrix element, and show that in real materials they will likely obscure the ~1/r asymptotic tail in the zero-bias tunneling conductance expected from the straightforward semiclassical analysis. We also give a prediction for the tunneling conductance anisotropy around the vortex core and establish a connection to the structure of the tunneling matrix element.

cond-mat.supr-con↗

arXiv1998

Phase Fluctuations and Spectral Properties of Underdoped Cuprates

We consider the effect of classical phase fluctuations on the quasiparticle spectra of underdoped high-$T_c$ cuprate superconductors in the pseudogap regime above $T_c$. We show that photoemission and tunneling spectroscopy data are well accounted for by a simple model in which mean field d-wave quasiparticles are semiclasically coupled to supercurrents induced by fluctuating unbound vortex-antivortex pairs. We argue that the data imply that transverse phase fluctuations are important at temperatures above $T_c$, while longitudinal fluctuations are unimportant at all temperatures.

cond-mat.supr-con↗

arXiv1998

On the heavy quark mass expansion for the operator Qbar gamma_5 Q and the charm content of eta, eta'

Recently in the context of studies of the intrinsic charm content of the nucleon and of the eta' meson two groups have arrived at different results for the 1/m^3 term of the heavy quark expansion for operator $\bar Qγ_5Q$ differing by the factor of six. We show that the form of both results violates certain general conditions. Using the expression for the axial anomaly with the finite Pauli-Villars regularization we obtain a new expression for 1/m^3 term of the heavy quark expansion for $\bar Qγ_5 Q$. With this new result we obtain an estimate for the constant f_{η'}^{(c)}=-2 MeV.

hep-ph↗

arXiv1998

Low Temperature Behavior of the Vortex Lattice in Unconventional Superconductors

We study the effect of the superconducting gap nodes on the vortex lattice properties of high temperature superconductors at very low temperatures. The nonlinear, nonlocal and nonanalytic nature of this effect is shown to have measurable consequences for the vortex lattice geometry and the effective penetration depth in the mixed state as measured by muon-spin-rotation experiments.

cond-mat.supr-con↗

arXiv1998

Self-consistent electronic structure of a $d_{x^2-y^2}$ and a $d_{x^2-y^2}+id_{xy}$ vortex

We investigate quasiparticle states associated with an isolated vortex in a d-wave superconductor using a self-consistent Bogoliubov-de Gennes formalism. For a pure $d_{x^2-y^2}$ superconductor we find that there exist no bound states in the core; all the states are extended with continuous energy spectrum. This result is inconsistent with the existing experimental data on cuprates. We propose an explanation for this data in terms of a magnetic-field-induced $d_{x^2-y^2}+id_{xy}$ state recently invoked in connection with the thermal conductivity measurements on Bi$_2$Sr$_2$CaCu$_2$O$_8$.

cond-mat.supr-con↗

arXiv1997

Comment on ``Quasiparticle Spectra around a Single Vortex in a d-wave Superconductor''

In a recent Letter Morita, Kohmoto and Maki analyzed the structure of quasiparticle states near a single vortex in a d-wave superconductor using an approximate version of the Bogoliubov - de Gennes theory. Their principal result is the existence of a bound state within the core region at finite energy with full rotational symmetry, which they assert explains the recent scanning tunneling microscopy results on YBCO single crystals. Here we argue that the approximation used in this work is fundamentally inadequate for the description of a d-wave vortex and that the obtained circular symmetry of the local density of states is an unphysical artifact of this approximation.

cond-mat.supr-con↗

arXiv1997

Theory of equilibrium flux lattices in unconventional superconductors

We investigate equilibrium flux lattice structures in superconductors with unconventional order parameters, such as high-$T_c$ cuprates, using a generalized London model with non-local electrodynamics derived from a simple microscopic model. We find a rich phase diagram containing triangular, centered rectangular and square lattices with various orientations to the ionic lattice, as a function of magnetic field and temperature.

cond-mat.supr-con↗

arXiv1997

Critical temperature and superfluid density suppression in disordered high-$T_c$ cuprate superconductors

We argue that the standard Abrikosov-Gorkov (AG) type theory of $T_c$ in disordered $d$-wave superconductors breaks down in short coherence length high-$T_c$ cuprates. Numerical calculations within the Bogoliubov-de Gennes formalism demonstrate that the correct description of such systems must allow for the spatial variation of the order parameter, which is strongly suppressed in the vicinity of impurities but mostly unaffected elsewhere. Suppression of $T_c$ as measured with respect to the attendant decrease in the superfluid density is found to be significantly weaker than that predicted by the AG theory, in good agreement with experiment.

cond-mat.supr-con↗

arXiv1996

Impurity scattering and localization in $d$-wave superconductors

Strong evidence is presented for the localization of low energy quasiparticle states in disordered $d$-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of non-magnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to $50\times 50$ sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite size dependence of inverse participation ratios.

cond-mat↗

arXiv1995

Vortex State in a d-Wave Superconductor

We discuss the physics of the vortex state in a $d$-wave superconductor, using the phenomenological Ginzburg-Landau theory, where many novel phenomena arise from the small admixture of the $s$-wave component induced by spatial variations in the dominant $d$-wave. Properties of an isolated vortex and of the Abrikosov vortex lattice are studied by means of analytic and numerical methods. An isolated vortex has a considerable structure, with four ``extra'' nodes in the $s$-wave order parameter symmerically placed around the core and an amplitude forming a four-lobe profile decaying as $1/r^2$ at large distances. The supercurrent and magnetic field distributions are also calculated. The Abrikosov lattice is in general oblique with the precise shape determined by the magnetic field and $s$-$d$ mixing parameter $ε_v$. The magnetic field distribution in the Abrikosov state has two nonequivalent saddle points resulting in the prediction of a double peak line shape in $μ$SR and NMR experiments as a test of a $d$-wave symmetry. Detailed comparison is made with existing experimental data and new experiments are proposed to test for the predicted effects.

cond-mat↗

arXiv1995

GINZBURG-LANDAU THEORY OF VORTICES IN $d$-WAVE SUPERCONDUCTORS

Ginzburg-Landau theory is used to study the properties of single vortices and of the Abrikosov vortex lattice in a $d_{x^2-y^2}$ superconductor. For a single vortex, the $s$-wave order parameter has the expected four-lobe structure in a ring around the core and falls off like $1/r^2$ at large distances. The topological structure of the $s$-wave order parameter consists of one counter-rotating unit vortex, centered at the core, surrounded by four symmetrically placed positive unit vortices. The Abrikosov lattice is shown to have a triangular structure close to $T_c$ and an oblique structure at lower temperatures. Comparison is made to recent neutron scattering data.

cond-mat↗

arXiv1994

Vortex Lattice Melting in 2D Superconducting Networks and Films

We carry out MC studies of 2D superconducting networks, in an applied magnetic field, for square and honeycomb geometries. We consider both dilute systems (f=1/q) and systems near full frustration (f=1/2-1/q). For the dilute case (which models a film as q->infinity), we find two transitions: at T_c(f)~1/q there is a depinning transition from a pinned to a floating vortex lattice; at T_m(f)~constant the floating vortex lattice melts into an isotropic liquid. We analyze this melting according to the Kosterlitz- Thouless theory of dislocation mediated melting, and find that the melting is weakly first order. For the case near full frustration, the system can be described in terms of the density of defects in an otherwise fully frustrated vortex pattern. We find pinned solid, floating solid, and liquid defect phases, as well as a higher sharp transition corresponding to the disordering of the fully frustrated background.

cond-mat↗

arXiv1994

Vortex lattce melting in 2D superconductors and Josephson arrays

Monte Carlo simulations of 2D vortex lattice melting in a thin superconducting film (or alternatively an array of Josephson junctions) are performed in the London limit. Finite size scaling analyses are used to make a detailed test of the dislocation mediated melting theory of KTNHY. We find that the melting transition is weakly first order, with a jump in the shear modulus very close to that predicted by the KTNHY theory. No hexatic liquid phase is found.

cond-mat↗