arXiv subjects

J. P. Carbotte

Publications and source records attributed to J. P. Carbotte.

At least 127 records · Page 7Linked to original sources

arXiv2005

Optical Response for the d-density wave model

We have calculated the optical conductivity and the Raman response for the d-density wave model, proposed as a possible explanation for the pseudogap seen in high Tc cuprates. The total optical spectral weight remains approximately constant on opening of the pseudogap for fixed temperature. This occurs because there is a transfer of weight from the Drude peak to interband transitions across the pseudogap. The interband peak in the optical conductivity is prominent but becomes progressively reduced with increasing temperature, with impurity scattering, which distributes it over a larger energy range, and with ineleastic scattering which can also shift its position, making it difficult to have a direct determination of the value of the pseudogap. Corresponding structure is seen in the optical scattering rate, but not necessarily at the same energies as in the conductivity.

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arXiv2005

Theory of the critical current in two-band superconductors with application to MgB2

Using a Green's function formulation of the superfluid current j_s, where a momentum q_s is applied to the Cooper pair, we have calculated j_s as a function of q_s, temperature, and impurity scattering for a two-band superconductor. We consider both renormalized BCS and full strong-coupling Eliashberg theory. There are two peaks in the current as a function of q_s due to the two energy scales for the gaps and this can give rise to non-standard behavior for the critical current. The critical current j_c, which is given as the maximum in j_s, can exhibit a kink as a function of temperature as the maximum is transferred from one peak to other. Other temperature variations are also possible and the universal BCS behavior is violated. The details depend on the material parameters of the system, such as the amount of coupling between the bands, the gap anisotropy, the Fermi velocities, and the density of states of each band. The Ginzburg-Landau relation between j_c, the penetration depth lambda_L and thermodynamic critical field H_c, is modified. Using Eliashberg theory with the electron-phonon spectral densities given from bandstructure calculations, we have applied our calculations for j_s and j_c to the case of MgB2 and find agreement with experiment.

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arXiv2005

Properties of the superconducting state in a two-band model

Eliashberg theory is used to investigate the range of thermodynamic properties possible within a two-band model for s-wave superconductivity and to identify signatures of its two-band nature. We emphasize dimensionless BCS ratios (those for the energy gaps, the specific heat jump and the negative of its slope near Tc, the thermodynamic critical field Hc(0), and the normalized slopes of the critical field and the penetration depth near Tc), which are no longer universal even in weak coupling. We also give results for temperature-dependent quantities, such as the penetration depth and the energy gap. Results are presented both for microscopic parameters appropriate to MgB2 and for variations away from these. Strong coupling corrections are identified and found to be significant. Analytic formulas are provided which show the role played by the anisotropy in coupling in some special limits. Particular emphasis is placed on small interband coupling and on the opposite limit of no diagonal coupling. The effect of impurity scattering is considered, particularly for the interband case.

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arXiv2004

On the Relation between Optical Conductivity and Quasiparticle Dynamics: Boson Structures

An extended Drude form is often used to analyze optical data in terms of an optical scattering rate and renormalized mass corresponding, respectively, to the real and imaginary part of the memory function. We study the relationship between memory function and quasiparticle self energy for an isotropic system. We emphasize particularly boson signatures. We find it useful to introduce a new auxiliary model scattering rate and its Kramers-Kronig transform determined solely from optics which are much closer to the self energy than is the memory function itself in the normal state. In the superconducting state the simplification fails because the quasiparticle density of states acquires an essential energy dependence.

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arXiv2004

Optical conductivity in non-equilibrium d-wave superconductors

We consider the optical conductivity of a d-wave BCS superconductor in the presence of a non-equilibrium distribution of excess quasiparticles. Two different simplified models used in the past for the s-wave case are considered and results compared. In the $T^\ast$-model of Parker the excess quasiparticles are assumed to be in a thermal distribution at some temperature $T^\ast$ larger than the equilibrium sample temperature. In the $μ^\ast$- model of Owen and Scalapino a chemical potential is introduced to accommodate the excess quasiparticles. Some of the results obtained are specific to the model, most are qualitatively similar in both.

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arXiv2004

Optical spectral weight distribution in d-wave superconductors

The distribution in frequency of optical spectral weight remaining under the real part of the optical conductivity in the superconducting state of a d-wave superconductor depends on impurity concentration, on the strength of the impurity potential as well as on temperature and there is some residual absorption even at T = 0. In BCS theory the important weight is confined to the microwave region if the scattering is sufficiently weak. In an Eliashberg formulation substantial additional weight is to be found in the incoherent, boson assisted background which falls in the infrared and is not significantly depleted by the formation of the condensate, although it is shifted as a result of the opening of a superconducting gap.

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arXiv2004

Optical sum increase due to electron undressing

For a system with a fixed number of electrons, the total optical sum is a constant, independent of many-body interactions, of impurity scattering and of temperature. For a single band in a metal, such a sum rule is no longer independent of the interactions or temperature, when the dispersion and/or finite bandwidth is accounted for. We adopt such a model, with electrons coupled to a single Einstein oscillator of frequency $ω_{E}$, and study the optical spectral weight. The optical sum depends on both the strength of the coupling and on the characteristic phonon frequency, $ω_{E}$. A hardening of $ω_{E}$, due, for example, to a phase transition, leads to electron undressing and translates into a decrease in the electron kinetic energy and an increase in the total optical sum, as observed in recent experiments in the cuprate superconductors.

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arXiv2004

Microwave Conductivity of a High Purity d-wave Superconductor

The cusp-like behavior of the microwave conductivity observed in clean ortho-II YB$_{2}$Cu$_{3}$O$_{6.50}$ at low temperature and low frequency is shown to be related directly to a linear in frequency dependence of the impurity scattering rate with a negligibly small value at zero frequency. In the weak scattering limit, the conductivity decreases linearly with the frequency. In the vortex state, assuming a random (Gaussian) distribution of vortices, we show that the magnetic field profoundly alters the impurity scattering rate, which now acquires a finite zero frequency value. As a consequence, we predict a Drude-like line shape in the microwave conductivity at low frequency.

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arXiv2003

Transport in vortex state of d-wave superconductors at zero temperature: Wiedemann-Franz violation

We show that the Wiedemann-Franz law is violated at zero temperature in the vortex state of a d-wave BCS superconductor with isotropic impurity scattering. We use a semiclassical approach to include the Doppler shift experienced by the quasiparticles due to the circulating supercurrents and consider as well the Andreev scattering from an array of vortices assumed to be randomly distributed. We also show that the vertex corrections to the electric conductivity, which can be large when there is significant anisotropy in the impurity scattering, become unimportant as the magnetic field is increased. For the thermal conductivity, the corrections remain negligible as in the absence of a magnetic field.

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arXiv2003

Phase fluctuations of s-wave superconductors on a lattice

Based on an attractive $U$ Hubbard model on a lattice with up to second neighbor hopping we derive an effective Hamiltonian for phase fluctuations. The superconducting gap is assumed to have s-wave symmetry. The effective Hamiltonian we finally arrive at is of the extended XY type. While it correctly reduces to a simple XY in the continuum limit, in the general case, it contains higher neighbor interaction in spin space. An important feature of our Hamiltonian is that it gives a much larger fluctuation region between the Berezinskii-Kosterlitz-Thouless transition temperature identified with $T_{c}$ for superconducting and the mean field transition temperature identified with the pseudogap temperature.

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arXiv2003

Low Temperature Thermal Conductivity of High Purity YBa$_{2}$Cu$_{3}$O$_{6.99}$ in the Vortex State

The low temperature thermal conductivity of a d-wave superconductor is considered for arbitrary strength of the impurity potential. A random distribution of vortices is included within the usual semiclassical approach. The vortex-quasiparticle scattering is accounted for phenomenologically, in addition to impurity scattering. Application of the theory to recent data on high purity YBa$_{2}$Cu$_{3}$O$_{6.99}$ shows excellent agreement with experiment, both in zero field and in the presence of an applied magnetic field. We find that the strength of the impurity potential required to describe the data deviates qualitatively from either the unitary or Born limits.

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arXiv2003

Comparison of s- and d-wave gap symmetry in nonequilibrium superconductivity

Recent application of ultrafast pump/probe optical techniques to superconductors has renewed interest in nonequilibrium superconductivity and the predictions that would be available for novel superconductors, such as the high-Tc cuprates. We have reexamined two of the classical models which have been used in the past to interpret nonequilibrium experiments with some success: the mu* model of Owen and Scalapino and the T* model of Parker. Predictions depend on pairing symmetry. For instance, the gap suppression due to excess quasiparticle density n in the mu* model, varies as n^{3/2} in d-wave as opposed to n for s-wave. Finally, we consider these models in the context of S-I-N tunneling and optical excitation experiments. While we confirm that recent pump/probe experiments in YBCO, as presently interpreted, are in conflict with d-wave pairing, we refute the further claim that they agree with s-wave.

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arXiv2003

Wiedemann-Franz violation in the vortex state of a d-wave superconductor

We show that the Wiedemann-Franz law is violated in the vortex state of a d-wave superconductor at zero temperature. We use a semiclassical approach, which includes the Doppler shift on the quasiparticles as well as the Andreev scattering from a random distribution of vortices. We also show that the vertex corrections to the electrical conductivity due to the anisotropy of impurity scattering become unimportant in the presence of a sufficiently large magnetic field.

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arXiv2003

ARPES and optical renormalizations: phonons or spin fluctuations

Improved resolution in both, energy and momentum in ARPES-data has lead to the establishment of a definite energy scale in the dressed quasiparticle dispersion relations. The observed structure around 80 meV has been taken as evidence for coupling to phonons and has re-focused the debate about the mechanism of superconductivity in the cuprates. Here we address the relative merits of phonon as opposed to spin fluctuation mechanisms. Both possibilities are consistent with ARPES. On the other hand, when considerations are extended to infrared optical data, a spin fluctuation mechanism provides a more natural interpretation of the combined sets of data in Bi_2Sr_2CaCu_2O_{8+δ} (Bi2212).

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arXiv2003

Residual absorption at zero temperature in d-wave superconductors

In a d-wave superconductor with elastic impurity scattering, not all the available optical spectral weight goes into the condensate at zero temperature, and this leads to residual absorption. We find that for a range of impurity parameters in the intermediate coupling regime between Born (weak) and unitary (strong) limit, significant oscillator strength remains which exhibits a cusp like behavior of the real part of the optical conductivity with upward curvature as a function of frequency, as well as a quasilinear temperature dependence of the superfluid density. The calculations offer an explanation of recent data on ortho-II YBa$_2$Cu$_3$O$_{6.5}$ which has been considered anomalous.

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arXiv2002

Application of an Extended Eliashberg Theory to High-T_c Cuprates

In recent years a unified phenomenological picture for the hole doped high-T_c cuprates has emerged for a spin and charge spectroscopy. Spectral anomalies have been interpreted as evidence of charge carrier coupling to a collective spin excitation present in the optical conductivity, in ARPES (angular resolved photoemission), and in tunneling data. These anomalies can be used to derive an approximate picture of a charge carrier-exchange boson interaction spectral density I^2 chi(omega) which is then be used within an extended Eliashberg formalism to analyze normal and superconducting properties of optimally doped and overdoped cuprates. This paper reviews recent developments and demonstrates the sometimes astonishing agreement between experiment and theoretical prediction.

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arXiv2002

Transport properties in the d-density wave state: Wiedemann-Franz law

We study the Wiedemann-Franz (WF) law in the d-density wave (DDW) model. Even though the opening of the DDW gap $(W_{0})$ profoundly modifies the electronic density of states and makes it dependent on energy, the value of the WF ratio at zero temperature (T=0) remains unchanged. However, neither electrical nor thermal conductivity display universal behavior. For finite temperature, with T greater than the value of the impurity scattering rate at zero frequency $γ(0)$ i.e. $γ(0)<T\ll W_{0}$, the usual WF ratio is obtained only in the weak scattering limit. For strong scattering there are large violations of the WF law.

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arXiv2002

Changes in Optical Conductivity due to Readjustments in Electronic Density of States

Within the model of elastic impurity scattering, we study how changes in the energy dependence of the electronic density of states (EDOS) $N(ε)$ around the Fermi energy $ε_F$ are reflected in the frequency-dependent optical conductivity $σ(ω)$. While conserving the total number of states in $N(ε)$ we compute the induced changes in $σ(ω)$ as a function of $ω$ and in the corresponding optical scattering rate $1/τ_{\rm op}(ω)$. These quantities mirror some aspects of the EDOS changes but the relationship is not direct. Conservation of optical oscillator strength is found not to hold, and there is no sum rule on the optical scattering rate although one does hold for the quasiparticle scattering. Temperature as well as increases in impurity scattering lead to additional changes in optical properties not seen in the constant EDOS case. These effects have their origin in an averaging of the EDOS around the Fermi energy $ε_F$ on an energy scale set by the impurity scattering.

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