Local moment formation in the superconducting state of a doped Mott insulator

A microscopic theory is presented for the local moment formation near a nonmagnetic impurity or a copper defect in high-Tc superconductors. We use a renormalized mean-field theory of the t-J model for a doped Mott insulator and study the fully self-consistent, spatially unrestricted solutions of the d-wave superconducting (SC) state in both the spin S=0 and S=1/2 sectors. We find a transition from the singlet d-wave SC state to a spin doublet SC state when the renormalized exchange coupling exceeds a doping dependent critical value. The induced S=1/2 moment is staggered and localized around the impurity. It arises from the binding of an S=1/2 nodal quasiparticle to the impurity. The local density of states is calculated and connections to NMR and STM experiments are discussed.     

Extinction of quasiparticle scattering interference in cuprate superconductors

The quasiparticle scattering interference phenomenon characterized by the peaks in the local density of states is studied within the kinetic energy driven superconducting mechanism in the presence of a single impurity. By calculation of the Fourier transformed ratio of the local density of states at opposite energy, it is shown that the quasiparticle scattering interference phenomenon can be described qualitatively by a single impurity in the kinetic energy driven homogeneous d-wave superconducting state. The amplitude of the peak increases with increasing energy at the low energy, and reaches a maximum at the intermediate energy, then diminishes to zero at the high energy. The theory also predicts that with increasing doping, the position of the peak along the nodal direction moves towards to the center of the Brillouin zone, while the position of the peak along the antinodal direction is shifted to large momentum region.     

Anatomy of Gossamer superconductivity

There are many systems in which two order parameters compete with each other. Of particular interest are systems in which these order parameters are both unconventional. In this contribution, we examine the representative example of a d-wave superconductor in the presence of a d-wave density wave, which has been suggested as a model for the pseudogap phase in the high-T_c superconductors. The physical properties of unconventional superconductivity in the presence of an anisotropic charge density wave are investigated within mean field theory. This model describes many features that were anticipated by an earlier phenomenological treatment of Tallon and Loram. In addition, the quasiparticle density of states in the presence of these two order parameters is calculated, which should be accessible by scanning tunneling microscopy.     

Spin-dependent quasiparticle reflection and bound States at interfaces with itinerant antiferromagnets

We find a novel channel of quasiparticle reflection from the simplest two-sublattice antiferromagnet (AF) on a bipartite lattice. Low-energy quasiparticles in a normal metal (N) experience spin-dependent retroreflection at AF/N interfaces. As a combined effect of antiferromagnetic and Andreev reflections, subgap Andreev states arise at an AF/superconductor (SC) interface. When the antiferromagnetic reflection dominates the specular one, Andreev bound states have almost zero energy on AF/s-wave superconductor (sSC) interfaces, whereas there are no low-energy subgap states on AF/d-wave superconductor (dSC) boundaries. For an sSC/AF/sSC junction, the bound states are found to split, due to the finite width of the AF interlayer, and carry the supercurrent. The theory developed in the present Letter is based on a novel quasiclassical approach, which applies to interfaces involving itinerant antiferromagnets.     

Quasiparticle conductivities in disordered d-wave superconductors

We study the quasiparticle transport coefficients in disordered d-wave superconductors. We find that spin and charge excitations are generally localized unless magnetic impurities are present. If the system is close to a nesting point in the impurity-scattering unitary limit, the tendency towards localization is reduced while the quasiparticle density of states gets enhanced by disorder. We also show that the residual repulsive interaction among quasiparticles has a delocalizing effect and increases the density of states.     

Quasiparticle decoherence in d-wave superconducting qubits

It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the d-wave superconducting gap should strongly decohere the quantum states of a d-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response nonequilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a d-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be detectable in a qubit containing a d-wave junction with appropriate parameters.     

Details of disorder matter in 2D d-wave superconductors

Within numerically exact solutions of the Bogoliubov-de Gennes equations, we demonstrate that discrepancies between predicted low-energy quasiparticle properties in disordered 2D d-wave superconductors occur because of the unanticipated importance of disorder model details and normal state particle-hole symmetry. For the realistic case, which is best described by a binary alloy model without particle-hole symmetry, we predict density-of-state suppression below an energy scale which appears to be correlated with the corresponding single impurity resonance.     

Low-energy quasiparticles in high- T c cuprates

The aim of this review is to summarize existing experimental investigations on the nature of the low-energy quasiparticle excitations in high- T c cuprates, and to examine critically recent claims of consistency between the experimentally determined low-temperature thermodynamic and transport properties in certain cuprates and theoretical predictions based on standard perturbation theory for a BCS d-wave superconductor. Measurements of the low-temperature specific heat, thermal conductivity, microwave conductivity, penetration depth and scanning tunnelling microscopy are described, both in the Meissner state and in the mixed state. These results are then compared with the predictions of quasi-classical theory of a d-wave BCS superconductor and the self-consistent T-matrix approximation for both a single impurity and a finite impurity concentration. Detailed inspection reveals that significant discrepancies still exist between experiment and theory, with important implications for the development of a coherent model, perhaps beyond standard perturbation theory. Finally, I discuss how considerations of the possible effects of band structure, anisotropic scattering and low carrier concentration in the underdoped region of the cuprate phase diagram might reconcile some of the discrepancies that have emerged.     

Quasiparticle scattering interference in electron-doped cuprate superconductors

By considering the nonmonotonic d-wave gap effect, the energy and momentum dependence of quasiparticle scattering interference is studied in the presence of a single impurity. It is shown that the pattern of the quasiparticle scattering peaks in the full Brillouin zone of electron-doped cuprate superconductors is very different from that in the hole-doped case described by the Octet model. This difference is the result of the nonmonotonic d-wave superconducting gap in the electron-doped case. As the energy increases, the position of the local peaks in the Brillouin zone moves rapidly. In particular, the characteristic peaks of the electron-doped cuprate superconductors appear between the antinodal and nodal directions, unlike in the hole-doped case.     

The vortex physics which comes from the vortex core

A theoretical view of vortex core states and of their effects on physics of vortices in clean s- and d-wave-type II superconductors is presented based on a semi-classical picture of a vortex core as an Andreev potential well containing many quasiparticle states. We discuss the density of states, the vortex dissipation, Hall effect, and the vortex mass. The dynamic characteristics are determined by relaxation of core excitations driven by a moving vortex. In a d-wave superconductor, gap nodes make the core states more extended and introduce novel features into thermodynamics and kinetics of vortices.     

Semiclassical theory of integrable and rough Andreev billiards

We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding light onto the origin of the differences between the semiclassical theory and the corresponding result derived from random matrix models. Applications to a square billiard geometry and billiards with boundary roughness are discussed. The saturation of the quasiparticle excitation spectrum is related to the classical dynamics of the billiard. The influence of weak magnetic fields on the proximity effect in rough Andreev billiards is discussed and an analytical formula is derived. The semiclassical theory provides an interpretation for the suppression of the proximity effect in the presence of magnetic fields as a coherence effect of time reversed trajectories. It is shown to be in good agreement with quantum mechanical calculations. Received 21 August 1999 and Received in final form 21 March 2001     

Shadow on the wall cast by an Abrikosov vortex

At the surface of a d-wave superconductor, a zero-energy peak in the quasiparticle spectrum can be observed. This peak appears due to Andreev bound states and is maximal if the nodal direction of the d-wave pairing potential is perpendicular to the boundary. We examine the effect of a single Abrikosov vortex in front of a reflecting boundary on the zero-energy density of states. We can clearly see a splitting of the low-energy peak and therefore a suppression of the zero-energy density of states in a shadowlike region extending from the vortex to the boundary. This effect is stable for different models of the single Abrikosov vortex, for different mean free paths and also for different distances between the vortex center and the boundary. This observation promises to have also a substantial influence on the differential conductance and the tunneling characteristics for low excitation energies.     

Large Eddy Simulation of Turbulent Channel Flow with 3D Roughness Using a Roughness Element Model

Large eddy simulation of turbulent channel flow with dense and small 3D roughness elements is carried out using a roughness element model Profiles of mean Reynolds stress, mean velocity and rms velocity as well as turbulent structures near the wall are obtained. The shear stress in the rough wall is larger than that in the smooth wall side and the rough wall has a larger influence on the channel flow. Profiles of mean streamwise velocity near the wall have logarithmic velocity distributions for both smooth and roughness walls, while there is a velocity decrease for the rough wall due to larger fractional drag. All the three components of rms velocities in the rough wall region are larger than that in the smooth wall region, and the roughness elements on the wall increase turbulent intensity in all directions. The s~reak spacing and average diameter of near wall quasi-s~reamwise vortices increase with the presence of roughness elements on the wall and it is shown that the rough wall induces complex and strong streamwise vortices. Results of dense and small 3D roughness elements in both turbulent statistics and structure, obtained with a relatively simple method, are found to be comparable to related experiments.     

Two-dimensional density of states for electrons bound to impurities inside inversion layers at the semiconductor-insulator interface

The density of states for electrons bound to Na⁺ impurities inside the inversion layer at the semiconductor-insulator interface of an MOS structure is calculated as a function of impurity concentration. The impurity potential is considered unscreened and the electrical quantum limit is assumed. A simple one-electron Hamiltonian is used and the disorder is treated through a cluster calculation. It is shown that the impurity band has a considerable bandwidth for impurity concentrations in a range of the experimental regime (this result agrees with the experimental findings of Hartstein and Fowler), and that the upper Hubbard band stands well above the lower band at very low concentration (in rough agreement with recent calculation done by Phelps and Bajaj on D^? state).     

Turbulent plane wall jets over smooth and rough surfaces

Large-eddy simulations were carried out to study the effects of surface roughness on a plane wall-jet using the Lagrangian dynamic eddy-viscosity subgrid-scale model, at Re = 7500 (based on the jet bulk velocity and height). Results over both smooth and rough surfaces were validated by experimental data at the same Reynolds number. As the jet is injected into the still environment, large-scale rollers are generated in the shear layer between the high-momentum fluid of the jet and the surrounding and are convected downstream with the flow. To understand the extent to which the outer-layer structures modify the flow in the inner layer and the extent to which the effect of roughness spreads away from the wall, both instantaneous and mean flow fields were investigated. The results revealed that, for the Reynolds number and roughness height considered in this study, the effect of roughness is mostly confined to the near-wall region of the wall jet. There is no structural difference between the outer layer of the wall jet over the smooth and rough surfaces. Roughness does not affect the size of the outer-layer structures or the scaling of the profiles of Reynolds stresses in the outer layer. However, in the inner layer, roughness redistributes stresses from streamwise to wall-normal and spanwise directions toward isotropy. Contours of joint probability-density function of the streamwise and wall-normal velocity fluctuations at the bottom of the logarithmic region match those of the turbulent boundary layer at the same height; while the traces of the outer-layer structure were detected at the top of the logarithmic region, indicating that they do not affect the flow very close to the wall, but still modify a major portion of the inner layer. This modification must be taken into consideration when the inner layer of a wall jet is compared with the conventional turbulent boundary layer.     

Staggered flux fluctuations and the quasiparticle scattering rate in the SU(2) gauge theory of the t-J model

We study staggered flux fluctuations around the superconducting state of the SU(2) mean-field theory for the two-dimensional t-J model and their effect on the electron spectral function. The quasiparticle peaks near (pi,0),(0,pi) get strongly broadened and partially wiped out by these fluctuations while the quasiparticle peaks near the nodes of the d-wave gap are preserved over a wide parameter range. The strength of these effects is governed by an energy scale that decreases towards zero for doping x-->0 and that is related to the energy splitting between the SU(2)-related superconducting and staggered flux mean-field states.     

Weak-Localization Effect on the Density of States in Disordered d-wave Superconductors

The weak-localization effect on the quasiparticle density of states (DOS) is studied with the diagrammatic technique in the binary-alloy model of disordered two-dimensional d-wave superconductors both in the Born and the unitary limits. We derive in details the expressions of the Goldstone modes (cooperon and diffuson) for quasiparticle diffuson. For generic Fermi surfaces, the DOS is shown to be subject to a quantum interference correction of logarithmic suppression. In the combined limit of unitarity and nested Fermi surface (the UN limit), it is found that the self-energy diagrams with two π-mode diffusons make additional contributions to the weak-localization effect, which has not been considered in the previous diagrammatic analysis. Due to the contributions of these new diagrams, the DOS in the UN limit is shown to have also a negative logarithmic correction, which is qualitatively different from the previous prediction.     

Weak-Localization Effect on the Density of States in Disordered d-wave Superconductors

The weak-localization effect on the quasiparticle density of states (DOS) is studied with the diagrammatic technique in the binary-alloy model of disordered two-dimensional d-wave superconductors both in the Born and the unitary limits. We derive in details the expressions of the Goldstone modes (cooperon and diffuson) for quasiparticle diffuson. For generic Fermi surfaces, the DOS is shown to be subject to a quantum interference correction of logarithmic suppression. In the combined limit of unitarity and nested Fermi surface (the UN limit), it is found that the self-energy diagrams with two π-mode diffusons make additional contributions to the weak-localization effect, which has not been considered in the previous diagrammatic analysis. Due to the contributions of these new diagrams, the DOS in the UN limit is shown to have also a negative logarithmic correction, which is qualitatively different from the previous prediction.     

Quantum interference phenomena between impurity states in d-wave superconductors

We investigate the mutual influence of impurities in two-dimensional d-wave superconductors involving self-consistent solutions of the Bogoliubov-de Gennes equations. The local order parameter suppression, the local density of states as well as the interference of impurity-induced structures are analyzed. We employ an impurity position averaging scheme for the density of states that does not neglect these interference effects, as the commonly used T-matrix approaches do.     

Donor Impurity States on Rough Semiconductor Interface

Ground state energies of shallow states of donor impurities on cosine-shaped, periodically rough interfaces formed by two isotropic semiconductors, such as GaAs/Ga_1-xAl_xAs or GaAs/vacuum, are calculated variationally with the approximation that the interfaces represent infinitely high potential barriers. The results show that changes in the ground state energies of in teriaces impurity states caused by rough in teriace are not negligible especially for GaAs/Ga_1-xAl_xAs interfaces with sharp or dense interface defects.