arXiv subjects

F. Marsiglio

Publications and source records attributed to F. Marsiglio.

At least 109 records · Page 6Linked to original sources

arXiv2002

Spin Wave Response in the Dilute Quasi-one Dimensional Ising-like Antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3

Inelastic neutron scattering profiles of spin waves in the dilute quasi-one-dimensional Ising-like antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3 have been investigated. Calculations of S^{xx}(Q,omega), based on an effective spin Hamiltonian, accurately describe the experimental spin wave spectrum of the 2J mode. The Q dependence of the energy of this spin wave mode follows the analytical prediction omega_{xx}(Q)=(2J)(1-5epsilon^{2}cos^{2}Qa+2epsilon^{2})^{1/2}, calculated by Ishimura and Shiba using perturbation theory.

cond-mat↗

arXiv2001

Sum rule for the optical scattering rates

An important quantity in electronic systems is the quasiparticle scattering rate (QPSR). A related optical scattering rate (OSR) is routinely extracted from optical data, and, while it is not the same as the QPSR, it nevertheless displays many of the same features. We consider a sum rule which applies to the area under a closely related quantity, almost equal to the OSR in the low energy region. We focus on the readjustment caused by, for example, a quasiparticle density of states change due to the superconducting transition. Unfortunately, no general statement about mechanism can be made solely on the energy scale in which the spectral weight readjustment on the OSR occurs.

cond-mat.supr-con↗

arXiv2001

Implications of reflectance measurements on the mechanism for superconductivity in MgB$_2$

Recent optical studies in c-axis oriented superconducting MgB$_2$ films indicate that the electron-phonon coupling is weak [tu01]. We reinforce this conclusion by examining the raw reflectance data; its frequency dependence is incompatible with strong electron-phonon scattering. This is further strengthened by analysis of the real part of the conductivity, and by the temperature dependence of the effective Drude scattering rate. Using a realistic electron-phonon spectral shape [kong01], we find $λ_{\rm tr} \approx 0.15$, in agreement with Tu et al. [tu01]. To the extent that $λ_{\rm tr} \approx λ$, this disagrees sharply with model calculations [kong01,kortus01,an01], and is far too low to provide the means for $T_c = 39 $ K. A simple model is constructed with coupling to a high frequency excitation, which is consistent with both the low frequency optical data and the high $T_c$.

cond-mat.supr-con↗

arXiv2001

Electron - Phonon Superconductivity

In this chapter we review the essentials of conventional electron-phonon superconductivity, as provided through the Migdal-Eliashberg formalism. Signatures of the electron-phonon interaction, as they appear in conventional superconductors, are described in detail. An appendix briefly describes more recent attempts to understand the electron-phonon interaction for all coupling strengths.

cond-mat.supr-con↗

arXiv2001

Constraints from $T_c$ and the isotope effect for MgB$_2$

With the constraint that $T_c = 39$ K, as observed for MgB$_2$, we use the Eliashberg equations to compute possible allowed values of the isotope coefficient, $β$. We find that while the observed value $β= 0.32$ can be obtained in principle, it is difficult to reconcile a recently calculated spectral function with such a low observed value.

cond-mat.supr-con↗

arXiv2001

Electron-Phonon or Hole Superconductivity in $MgB_2$?

The BCS electron-phonon mechanism and the unconventional 'hole mechanism' have been proposed as explanations for the high temperature superconductivity observed in $MgB_2$. It is proposed that a critical test of which theory is correct is the dependence of $T_c$ on hole doping: the hole mechanism predicts that $T_c$ will drop rapidly to zero as holes are added, while the electron-phonon mechanism appears to predict increasing $T_c$ for a substantial range of hole doping. Furthermore, the hole mechanism and electron-phonon mechanism differ qualitatively in their predictions of the effect on $T_c$ of change in the $B-B$ distances. We discuss predictions of the hole mechanism for a variety of observables as a function of doping, emphasizing the expected differences and similarities with the electron-phonon explanation. The hole mechanism predicts coherence length and penetration depth to increase and decrease monotonically with hole doping respectively.

cond-mat.supr-con↗

arXiv2000

Feedback effects and the self-consistent Thouless criterion of the attractive Hubbard model

We propose a fully microscopic theory of the anomalous normal state of the attractive Hubbard model in the low-density limit that accounts for propagator renormalization. Our analytical conclusions, which focus on the thermodynamic instabilities contained in the self-consistent equations associated with our formulation, have been verified by our comprehensive numerical study of the same equations. The resulting theory is found to contain no transitions at non-zero temperatures for all finite lattices, and we have confirmed, using our numerical studies, that this behaviour persists in the thermodynamic limit for low-dimensional systems.

cond-mat.str-el↗

arXiv2000

Anisotropic penetration depth and optical sum rule violation in La_(2-x)Sr_xCuO_4

We calculate the doping dependence of the penetration depths and optical sum rule violation in La_(2-x)Sr_xCuO_4 within the model of hole superconductivity. In the clean limit the predicted in-plane sum rule violation is larger than the c-axis one, however in the presence of disorder the latter one becomes very substantially enhanced.

cond-mat.supr-con↗

arXiv2000

Optical sum rule violation, superfluid weight and condensation energy in the cuprates

The model of hole superconductivity predicts that the superfluid weight in the zero-frequency $δ$-function in the optical conductivity has an anomalous contribution from high frequencies, due to lowering of the system's kinetic energy upon entering the superconducting state. The lowering of kinetic energy, mainly in-plane in origin, accounts for both the condensation energy of the superconductor as well as an increased potential energy due to larger Coulomb repulsion in the paired state. It leads to an apparent violation of the conductivity sum rule, which in the clean limit we predict to be substantially larger for in-plane than for c-axis conductivity. However, because cuprates are in the dirty limit for c-axis transport, the sum rule violation is found to be greatly enhanced in the c-direction. The model predicts the sum rule violation to be largest in the underdoped regime and to decrease with doping, more rapidly in the c-direction that in the plane. So far, experiments have detected sum rule violation in c-axis transport in several cuprates, as well as a decrease and disappearance of this violation for increasing doping, but no violation in-plane. We explore the predictions of the model for a wide range of parameters, both in the absence and in the presence of disorder, and the relation with current experimental knowledge.

cond-mat.supr-con↗

arXiv2000

The Anderson prescription for surfaces and impurities

We test the Anderson prescription [1], a BCS formalism for describing superconductivity in inhomogeneous systems, and compare results with those obtained from the Bogoliubov-de Gennes formalism, using the attractive Hubbard model with surfaces and nonmagnetic impurities. The Anderson approach captures the essential features of the spatial variation of the gap parameter and electron density around a surface or an impurity over a wide range of parameters. It breaks down, however, in the strong-coupling regime for a weak impurity potential. [1] P. W. Anderson, J. Phys. Chem. Solids 11, 26 (1959).

cond-mat.supr-con↗

arXiv2000

Anderson's "Theorem" and Bogoliubov-de Gennes Equations for Surfaces and Impurities

In order to incorporate spatial inhomogeneity due to nonmagnetic impurities, Anderson [1] proposed a BCS-type theory in which single-particle states in such an inhomogeneous system are used. We examine Anderson's proposal, in comparison with the Bogoliubov-de Gennes equations, for the attractive Hubbard model on a system with surfaces and impurities. [1] P. W. Anderson, J. Phys. Chem. Solids {\bf 11}, 26 (1959).

cond-mat.supr-con↗

arXiv1999

Fixed Number and Quantum Size Effects in Nanoscale Superconductors

In recent experiments on nanoscale Al particles, whose electron number was fixed by charging effects, a ``negative gap'' was observed in particles with an odd number of electrons. This observation has called into question the use of a grand canonical ensemble in describing superconductivity in such ultrasmall particles. We have studied the effects of fixed electron number and finite size in nanoscale superconductors, by applying the canonical BCS theory for the attractive Hubbard model. The ground state energy and the energy gap are compared with the conventional and parity-projected grand canonical BCS results, and in one dimension also with the exact solutions by the Bethe ansatz. The crossover from the bulk to quantum limit is studied for various regimes of electron density and coupling strength. The effects of boundary conditions and different lattice structures are also examined. A ``negative gap'' for odd electron number emerges most naturally in the canonical scheme. For even electron number, the gap is particularly large for ``magic numbers'' of electrons for a given system size or of atoms for a fixed electron density. These features are in accordance with the exact solutions, but are essentially missed in the grand canonical results.

cond-mat.supr-con↗

arXiv1999

New Solutions of the T-Matrix Theory of the Attractive Hubbard Model

This short paper summarizes a calculational method for obtaining the dynamical properties of many-body theories formulated in terms of (unrenormalized) bare propagators (and more generally, in terms of meromorphic functions, or convolutions over meromorphic functions) to a very high accuracy. We demonstrate the method by applying it to a T-matrix theory of the attractive Hubbard model in two dimensions. We expand the pair propagator using a partial fraction decomposition, and then solve for the residues and pole locations of such a decomposition using a computer algebra system to an arbitrarily high accuracy (we used MapleV and obtained these quantities to a relative error of 10^(-80)). Thus, this method allows us to bypass all inaccuracies associated with the traditional analytical continuation problem. Our results for the density of states make clear the pronounced development of a pseudogap as the temperature is lowered in this formulation of the attractive Hubbard model.

cond-mat.str-el↗

arXiv1999

A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm

We critique a Pade analytic continuation method whereby a rational polynomial function is fit to a set of input points by means of a single matrix inversion. This procedure is accomplished to an extremely high accuracy using a novel symbolic computation algorithm. As an example of this method in action we apply it to the problem of determining the spectral function of a one-particle thermal Green's function known only at a finite number of Matsubara frequencies with two example self energies drawn from the T-matrix theory of the Hubbard model. We present a systematic analysis of the effects of error in the input points on the analytic continuation, and this leads us to propose a procedure to test quantitatively the reliability of the resulting continuation, thus eliminating the black magic label frequently attached to this procedure.

cond-mat.str-el↗

arXiv1999

Where is 99% of the condensation energy of Tl_2Ba_2CuO_y coming from?

Anderson's interlayer tunneling model can account for up to 1% of the condensation energy of Tl_2Ba_2CuO_y. Here we account for the remaining 99%. We predict an in-plane kinetic energy gain of 1 to 3 meV per planar oxygen in the optimally doped material when it goes superconducting. It is suggested that the effect may be most easily detected in underdoped dirty samples.

cond-mat.supr-con↗

arXiv1999

Electronic Shell Structure of Nanoscale Superconductors

Motivated by recent experiments on Al nanoparticles, we have studied the effects of fixed electron number and small size in nanoscale superconductors, by applying the canonical BCS theory for the attractive Hubbard model in two and three dimensions. A negative ``gap'' in particles with an odd number of electrons as observed in the experiments is obtained in our canonical scheme. For particles with an even number of electrons, the energy gap exhibits shell structure as a function of electron density or system size in the weak-coupling regime: the gap is particularly large for ``magic numbers'' of electrons for a given system size or of atoms for a fixed electron density. The grand canonical BCS method essentially misses this feature. Possible experimental methods for observing such shell effects are discussed.

cond-mat.supr-con↗

arXiv1999

Self-consistent treatment of dynamical correlation functions using a spectral representation technique

A system of equations resulting from an approximation of the equation of motion of Green functions for correlated electron systems is usually solved using Matsubara technique. In this work we propose an alternative method which works entirely along the real frequency axis. Using the example of the attractive Hubbard model studied in the T-matrix approximation both self-consistently and non-self-consistently we demonstrate how powerful such a treatment is especially when dynamic quantities are calculated.

cond-mat.str-el↗

arXiv1999

Canonical BCS Approximation for the Attractive Hubbard Model

We test the canonical BCS wave functions for fixed number of electrons for the attractive Hubbard model. We present results in one dimension for various chain lengths, electron densities, and coupling strengths. The ground-state energy and energy gap to the first excited state are compared with the exact solutions obtained by the Bethe ansatz as well as with the results from the conventional grand-canonical BCS approximations. While the canonical and grand-canonical BCS results are both in very good agreement with the exact results for the ground state energies, improvements due to conserving the electron number in finite systems are manifest in the energy gap. As the system size is increased, the canonical results converge to the grand-canonical ones. The ``parity'' effect that arises from the number parity (even or odd) of electrons are studied with our canonical scheme.

cond-mat.supr-con↗