arXiv subjects

W. A. Atkinson

Publications and source records attributed to W. A. Atkinson.

70 records · Page 4Linked to original sources

arXiv2001

Nesting symmetries and diffusion in disordered d-wave superconductors

The low-energy density of states (DOS) of disordered 2D d-wave superconductors is extremely sensitive to details of both the disorder model and the electronic band structure. Using diagrammatic methods and numerical solutions of the Bogoliubov-de Gennes equations, we show that the physical origin of this sensitivity is the existence of a novel diffusive mode with momentum close to $(π,π)$ which is gapless only in systems with a global nesting symmetry. We find that in generic situations, the DOS vanishes at the Fermi level. However, proximity to the highly symmetric case may nevertheless lead to observable non-monotonic behavior of the DOS in the cuprates.

cond-mat↗

arXiv2001

Density of states "width parity" effect in d-wave superconducting quantum wires

We calculate the density of states (DOS) in a clean mesoscopic d-wave superconducting quantum wire, i.e. a sample of infinite length but finite width $N$. For open boundary conditions, the DOS at zero energy is found to be zero if $N$ is even, and nonzero if $N$ is odd. At finite chemical potential, all chains are gapped but the qualtitative differences between even and odd $N$ remain.

cond-mat.supr-con↗

arXiv2000

Inhomogeneous order-parameter suppression in disordered d-wave superconductors

We report on a numerical study of disorder effects in 2D d-wave BCS superconductors. We compare exact numerical solutions of the Bogoliubov-deGennes (BdG) equations for the density of states $ρ(E)$ with the standard T-matrix approximation. Local suppression of the order parameter near impurity sites, which occurs in self-consistent solutions of the BdG equations, leads to apparent power law behavior $ρ(E) \sim |E|^α$ with non-universal $α$ over an energy scale comparable to the single impurity resonance energy $Ω_0$. We show that the novel effects arise from static spatial correlations between the order parameter and the impurity distribution.

cond-mat.supr-con↗

arXiv2000

Details of disorder matter in 2D d-wave superconductors

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. This conclusion follows from numerically exact evaluations of the quasiparticle density-of-states predicted by the Bogoliubov-deGennes (BdG) mean field equations for both binary alloy and random site energy disorder models. For the realistic case, which is best described by a binary alloy model without particle-hole symmetry, we predict density-of-states suppression below an energy scale which appears to be correlated with the corresponding single-impurity resonance.

cond-mat.supr-con↗

arXiv2000

Interlayer coupling in ferromagnetic semiconductor superlattices

We develop a mean-field theory of carrier-induced ferromagnetism in diluted magnetic semiconductors. Our approach represents an improvement over standard RKKY model allowing spatial inhomogeneity of the system, free-carrier spin polarization, finite temperature, and free-carrier exchange and correlation to be accounted for self-consistently. As an example, we calculate the electronic structure of a Mn$_x$Ga$_{1-x}$As/GaAs superlattice with alternating ferromagnetic and paramagnetic layers and demonstrate the possibility of semiconductor magnetoresistance systems with designed properties.

cond-mat.mes-hall↗

arXiv1999

Effect of Order-Parameter Suppression on Scattering by Isolated Impurities in Asymmetric Bands

The single-impurity problem in d-wave superconductors with asymmetric bands is discussed. The effect of local order parameter suppression near the impurity is to shift the quasiparticle resonance. Contrary to previous work [A. Shnirman et al., Phys. Rev. B 60, 7517 (1999)] we find that the direction of the shift is not universally towards the strong scattering limit.

cond-mat.supr-con↗

arXiv1999

Electrodynamics of a Clean Vortex Lattice

We report on a microscopic evaluation of electrodynamic response for the vortex lattice state of a model s-wave superconductor. Our calculation accounts self-consistently for both quasiparticle and order parameter response and establishes the collective nature of linear response in the clean limit. We discuss the effects of homogeneous and inhomogeneous pinning on the optical conductivity and the penetration depth, and comment on the relationship between macroscopic and local penetration depths. We find unexpected relationships between pinning arrangements and conductivity due to the strongly non-local response.

cond-mat.supr-con↗

arXiv1998

Disorder and chain superconductivity in YBa_2Cu_3O_{7-δ}

The effects of chain disorder on superconductivity in YBa_2Cu_3O_{7-δ} are discussed within the context of a proximity model. Chain disorder causes both pair-breaking and localization. The hybridization of chain and plane wavefunctions reduces the importance of localization, so that the transport anisotropy remains large in the presence of a finite fraction $δ$ of oxygen vacancies. Penetration depth and specific heat measurements probe the pair-breaking effects of chain disorder, and are discussed in detail at the level of the self-consistent T-matrix approximation. Quantitative agreement with these experiments is found when chain disorder is present.

cond-mat.supr-con↗

arXiv1997

The role of intermediate layers in the c-axis conductivity of layered superconductors

A simplified model of c axis transport in the high T_c superconductors is presented. Expressions are found for the c axis optical conductivity, the d.c. resistivity, and the c axis penetration depth. Within the framework of this model, the pseudogap in the optical conductivity arises naturally as a result of the layered band structure of the high T_c materials. We discuss the occurence of the pseudogap in terms of three parameters: a band gap Delta_{ps}, a temperature dependent scattering rate Gamma(T), and the strength of the interlayer coupling t_{perp}. We are also able to find analytic expressions for the d.c. conductivity and the low temperature penetration depth in terms of these three parameters. This work is an attempt to present a simple, unified picture of c axis properties in the high T_c cuprates.

cond-mat.supr-con↗

arXiv1997

C-axis Transport in Bilayer Cuprates and Relation to Pseudogap

We consider the effect of interband transitions on the c-axis conductivity, DC resistivity, and thermal conductivity in a plane-chain bilayer model of a cuprate. The relation between the c-axis resistivity and thermal conductivity is governed by the Wiedemann-Franz law. When the perpendicular hopping matrix element between chain and plane ($t_\perp$) is small, the c-axis DC resistivity shows a characteristic upturn as the temperature is lowered and the infrared conductivity develops a pseudogap. As $t_\perp$ is increased, intraband transitions start to dominate and a more conventional response is obtained. Analytical results for a simple plane-plane bilayer are also given, including the frequency sum rule of the optical conductivity.

cond-mat↗

arXiv1997

The c axis optical conductivity of layered systems in the superconducting state

In this paper, we discuss the c axis optical conductivity Re [sigma_c(omega)] in the high T_c superconductors, in the superconducting state. The basic premise of this work is that electrons travelling along the c axis between adjacent CuO_2 layers must pass through several intervening layers. In earlier work we found that, for weak inter-layer coupling, it is preferable for electrons to travel along the c axis by making a series of interband transitions rather than to stay within a single (and very narrow) band. Moreover, we found that many of the properties of the normal state optical conductivity, including the pseudogap could be explained by interband transitions. In this work we examine the effect of superconductivity on the interband conductivity. We find that, while the onset of superconductivity is clearly evident in the spectrum, there is no clear signature of the symmetry of the superconducting order parameter.

cond-mat.supr-con↗

arXiv1996

Effect of Interband Transitions on the c axis Penetration Depth of Layered Superconductors

The electromagnetic response of a system with two planes per unit cell involves, in addition to the usual intraband contribution, an added interband term. These transitions affect the temperature dependence and the magnitude of the zero temperature c-axis penetration depth. When the interplane hopping is sufficiently small, the interband transitions dominate the low temperature behaviour of the penetration depth which then does not reflect the linear temperature dependence of the intraband term and in comparison becomes quite flat even for a d-wave gap. It is in this regime that the pseudogap was found in our previous normal state calculations of the c-axis conductivity, and the effects are connected.

cond-mat.supr-con↗

arXiv1996

Interband effects in the c-axis optical conductivity in YBaCuO

The normal state optical conductivity is calculated for a layered metal with two layers per unit cell coupled through a transverse hopping matrix element $t_\perp$. The optical response involves an interband term in addition to the more familiar intraband term which leads to the usual Drude form. The interband term is only weakly temperature dependent, even for an inelastic scattering rate which is linear in T. It gives a $c$-axis response which extends in frequency over the entire band width although there can be structure on this energy scale which reflects details of the electronic structure. In particular, at low energy, the $c$-axis response can develop a gap or pseudogap as the temperature is lowered. At high temperature, a Drude response will be seen only if the intraband transitions, which are of order $t_\perp^4$, become important compared with the interband transitions which are of order $t_\perp^2$.

cond-mat↗

arXiv1995

Effect of Proximity Coupling of Chains and Planes on the Penetration Depth Anisotropy in Y_1Ba_2Cu_3O_7

We calculate the penetration depth $λ$ in the $a$, $b$ and $c$ directions for a simple model of YBa$_2$Cu$_3$O$_7$. In this model there are two layers---representing a CuO$_2$ plane and a CuO chain---per unit cell. There is a BCS--like pairing (both $s$ wave and $d$ wave are considered) interaction localised in the CuO$_2$ planes. The CuO chains become superconducting at temperatures lower than $T_c$ because of their proximity to the planes, and there is an induced gap in the chains. Since the temperature dependence of the penetration depth in the $b$ direction (along the chains) is sensitive to the size of the induced gap, the difference between the shapes of the penetration depth curves in the $a$ and $b$ directions reveals a great deal about the nature of the condensate in the chains. We find that in our proximity model there are always regions of the chain Fermi surface on which the induced gap is much smaller than $T_c$, so that the temperature dependence of $λ_b$ is always different than that of $λ_a$. Experimental observations of the of the $ab$ anisotropy show nearly identical temperature dependences. The main result of our paper, then, is that a simple proximity model in which the pairing interaction is localized to the planes, and the planes are coherently coupled to the chains cannot account for the superfluid on the chains.

cond-mat↗

arXiv1995

Critical Josephson Current in a Model Pb/YBa_2Cu_3O_7 Junction

In this article we consider a simple model for a c--axis Pb/YBa_2Cu_3O_{7-δ} Josephson junction. The observation of a nonzero current in such a junction by Sun et al. [A. G. Sun, D. A. Gajewski, M. B. Maple, R. C. Dynes, Phys. Rev. Lett. 72, 2267 (1994)] has been taken as evidence against d--wave superconductivity in YBa_2Cu_3O_{7-δ}. We suggest, however, that the pairing interaction in the CuO_2 planes may well be d--wave but that the CuO chains destroy the tetragonal symmetry of the system. We examine two ways in which this happens. In a simple model of an incoherent junction, the chains distort the superconducting condensate away from d_{x^2-y^2} symmetry. In a specular junction the chains destroy the tetragonal symmetry of the tunneling matrix element. In either case, the loss of tetragonal symmetry results in a finite Josephson current. Our calculated values of the critical current for specular junctions are in good agreement with the results of Sun and co-workers.

cond-mat↗

arXiv1994

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.

supr-con↗