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.

Effects of inhomogeneities and thermal fluctuations on the spectral function of a model d-wave superconductor

We compute the spectral function $A({\bf k}, \omega)$ of a model two-dimensional high-temperature superconductor, at both zero and finite temperatures $T$. We assume that an areal fraction $c_{\beta}$ of the superconductor has a large gap $\Delta$ ($\beta$ regions), while the rest has a smaller $\Delta$ ($\alpha$ regions), both of which are randomly distributed in space. We find that $A({\bf k}, \omega)$ is most strongly affected by inhomogeneity near the point $\mathbf k = (\pi, 0)$ (and the symmetry-related points). For $c_\beta\simeq 0.5$, $A({\bf k}, \omega)$ exhibits two double peaks (at positive and negative energy) near this k-point if the difference between $\Delta_\alpha$ and $\Delta_\beta$ is sufficiently large in comparison to the hopping integral. The strength of the inhomogeneity required to produce a split spectral function peak suggests that inhomogeneity is unlikely to be the cause of a second branch in the dispersion relation. Thermal fluctuations also affect $A({\bf k}, \omega)$ most strongly near $\mathbf k = (\pi,0)$. Typically, peaks that are sharp at $T = 0$ become reduced in height, broadened, and shifted toward lower energies with increasing $T$; the spectral weight near $\mathbf k = (\pi, 0)$ becomes substantial at zero energy for $T$ greater than the phase-ordering temperature.Comment: Accepted for publication in Phys. Rev. B. Scheduled Issue: 01 Jan 2008. 26 Pages and 10 figure

Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent

We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent $\nu\approx 1$, and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding $\nu<1$ are due to the improper neglect of these corrections.Comment: 5 pages, 4 figures -- slightly revised version as accepted for Phys. Rev. E Rapid Communication

Single-Particle Density of States of a Superconductor with a Spatially Varying Gap and Phase Fluctuations

Recent experiments have shown that the superconducting energy gap in some cuprates is spatially inhomogeneous. Motivated by these experiments, and using exact diagonalization of a model d-wave Hamiltonian, combined with Monte Carlo simulations of a Ginzburg-Landau free energy functional, we have calculated the single-particle density of states LDOS$(\omega,r)$ of a model high-T$_c$ superconductor as a function of temperature. Our calculations include both quenched disorder in the pairing potential and thermal fluctuations in both phase and amplitude of the superconducting gap. Most of our calculations assume two types of superconducting regions: $\alpha$, with a small gap and large superfluid density, and $\beta$, with the opposite. If the $\beta$ regions are randomly embedded in an $\alpha$ host, the LDOS on the $\alpha$ sites still has a sharp coherence peak at $T = 0$, but the $\beta$ component does not, in agreement with experiment. An ordered arrangement of $\beta$ regions leads to oscillations in the LDOS as a function of energy. The model leads to a superconducting transition temperature $T_c$ well below the pseudogap temperature $T_{c0}$, and has a spatially varying gap at very low $T$, both consistent with experiments in underdoped Bi2212. Our calculated LDOS$(\omega,r)$ shows coherence peaks for $T T_c$, in agreement with previous work considering phase but not amplitude fluctuations in a homogeneous superconductor. Well above $T_c$, the gap in the LDOS disappears.Comment: 37 pages, 12 figures. Accepted by Phys. Rev. B. Scheduled Issue: 01 Nov 200