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.Comment: 22 pages, 7 figures accepted for publication by Phys. Rev.

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.Comment: Accepted for publication by Phys. Rev. B 7 Pages and 4 Figure

Angle-dependent magnetothermal conductivity in d-wave superconductors

We analyse the behavior of the thermal conductivity, $\kappa(H)$, in the vortex state of a quasi-two-dimensional d-wave superconductor when both the heat current and the applied magnetic field are in the basal plane. At low temperature the effect of the field is accounted for in a semiclassical approximation, via a Doppler shift in the spectrum of the nodal quasiparticles. In that regime $\kappa(H)$ exhibits twofold oscillations as a function of the angle between the direction of the field in the plane and the direction of the heat current, in agreement with experiment.Comment: 2 pages, submitted to proceedings of M2S-HTSC-VI (Houston

Optical conductivity in superconductors with mixed symmetry order parameters

The real and imaginary part of the optical conductivity and the derived optical scattering rate of superconductors with mixed s + d or s + id symmetry order parameter is calculated for different mixing and for moderate impurity concentrations in two limiting cases, namely the Born (weak) and the resonant (unitary) scattering limit. There are pronounced differences in the optical conductivity between impurity limits and with the symmetry of the order parameter. Theoretical predictions are compared to experimental data.Розраховані дійсна і уявна складові частини оптичної провідності та інтенсивність оптичного розсіяння у надпровідниках з параметром порядку змішаної s + d та s + id симетрії для різної величини змішування і для помірних концентрацій домішок у двох граничних випадках борнівського (слабого) та резонансного (одноразого) розсіяння. Спостерігаються значні відмінності оптичної провідності між граничними випадками для розсіяння на домішках та зі зміною симетрії параметра порядку. Передбачення теорії порівнюються з експериментальними даними

Constraints on possible mechanisms for high-Tc superconductivity

This paper discusses a phenomenological model used to describe various properties of a dx²−y² superconductor in its temperature as well as frequency dependence, namely, the London penetration depth, the optical conductivity, the microwave conductivity, and the electronic thermal conductivity. We assume the CuO₂ planes to be the dominant feature for superconductivity and develop a 2D-formalism in which inelastic scattering is modelled explicitly by a spectral density which describes a fluctuation spectrum responsible for the superconducting transition and also for the large inelastic scattering observed in the normal state above the critical temperature Tc . The feedback effect of superconductivity on the spectral density is modelled by a temperature dependent low frequency cutoff. Theoretical results are compared with the experimental data and the fact that such a model allows a consistent description of a variety of phenomena is then used to formulate constraints on possible mechanisms of superconductivity in oxides.Дана стаття розглядає феноменологічну модель, що використовується для опису різноманітних властивостей dx²−y²–надпровідників в залежності як від температури, так і від частоти, а саме глибини проникнення Лондона, оптичної провідності, мікрохвильової провідності та електронної термічної провідності. Ми вважаємо, що саме площини CuO₂ є основним чинником для виникнення надпровідності, і тому розвиваємо двомірний формалізм, в якому процеси непружного розсіяння моделюються точно через спектральну густину, що описує флуктуаційний спектр, який є відповідальним за виникнення надпровідного переходу, а також за велике непружне розсіяння, що спостерігається в нормальному стані вище критичної температури Tc . Зворотній вплив надпровідності на спектральну густину моделюється температурнозалежним низькочастотним обрізанням. Теоретичні результати порівнюються з експериментальними даними і, виходячи з того, що дана модель дає змогу зробити послідовний опис цілого ряду явищ, формулюються обмеження на можливі механізми виникнення надпровідності в оксидах

Optical Sum Rule in Finite Bands

In a single finite electronic band the total optical spectral weight or optical sum carries information on the interactions involved between the charge carriers as well as on their band structure. It varies with temperature as well as with impurity scattering. The single band optical sum also bears some relationship to the charge carrier kinetic energy and, thus, can potentially provide useful information, particularly on its change as the charge carriers go from normal to superconducting state. Here we review the considerable advances that have recently been made in the context of high $T_c$ oxides, both theoretical and experimental.Comment: Review article accepted for publication in J. Low Temp. Phys. 29 pages, 33 figure

Electron-phonon renormalization in small Fermi energy systems

The puzzling features of recent photoemission data in cuprates have been object of several analysis in order to identity the nature of the underlying electron-boson interaction. In this paper we point out that many basilar assumptions of the conventional analysis as expected to fail in small Fermi energy systems when, as the cuprates, the Fermi energy $E_{\rm F}$ is comparable with the boson energy scale. We discuss in details the novel features appearing in the self-energy of small Fermi energy systems and the possible implications on the ARPES data in cuprates.Comment: 4 pages, 5 eps figures include

Magnetic field effects on the density of states of orthorhombic superconductors

The quasiparticle density of states in a two-dimensional d-wave superconductor depends on the orientation of the in-plane external magnetic field H. This is because. in the region of the gap nodes, the Doppler shift due to the circulating supercurrents around a vortex depend on the direction of H. For a tetragonal system the induced pattern is four-fold symmetric and, at zero energy, the density of states exhibits minima along the node directions. But YBa_2C_3O_{6.95} is orthorhombic because of the chains and the pattern becomes two-fold symmetric with the position of the minima occuring when H is oriented along the Fermi velocity at a node on the Fermi surface. The effect of impurity scattering in the Born and unitary limit is discussed.Comment: 24 pages, 11 Figure

Phenomenology of the normal state in-plane transport properties of high-TcT_c cuprates

In this article, I review progress towards an understanding of the normal state (in-plane) transport properties of high-$T_c$ cuprates in the light of recent developments in both spectroscopic and transport measurement techniques. Against a backdrop of mounting evidence for anisotropic single-particle lifetimes in cuprate superconductors, new results have emerged that advocate similar momentum dependence in the transport decay rate $\Gamma$({\bf k}). In addition, enhancement of the energy scale (up to the bare bandwidth) over which spectroscopic information on the quasiparticle response can be obtained has led to the discovery of new, unforeseen features that surprisingly, may have a significant bearing on the transport properties at the dc limit. With these two key developments in mind, I consider here whether all the ingredients necessary for a complete phenomenological description of the anomalous normal state transport properties of high-$T_c$ cuprates are now in place.Comment: 31 pages, 10 figure

Angular dependence of the penetration depth in unconventional superconductors

We examine the Meissner state nonlinear electrodynamic effects on the field and angular dependence of the low temperature penetration depth, $\lambda$, of superconductors in several kinds of unconventional pairing states, with nodes or deep minima (``quasinodes'') in the energy gap. Our calculations are prompted by the fact that, for typical unconventional superconducting material parameters, the predicted size of these effects for $\lambda$ exceeds the available experimental precision for this quantity by a much larger factor than for others. We obtain expressions for the nonlinear component of the penetration depth, $\Delta\lambda$, for different two- and three- dimensional nodal or quasinodal structures. Each case has a characteristic signature as to its dependence on the size and orientation of the applied magnetic field. This shows that $\Delta\lambda$ measurements can be used to elucidate the nodal or quasinodal structure of the energy gap. For nodal lines we find that $\Delta\lambda$ is linear in the applied field, while the dependence is quadratic for point nodes. For layered materials with $\rm{YBa_2Cu_3O_{7-\delta}}$ (YBCO) type anisotropy, our results for the angular dependence of $\Delta\lambda$ differ greatly from those for tetragonal materials and are in agreement with experiment. For the two- and three- dimensional quasinodal cases, $\Delta\lambda$ is no longer proportional to a power of the field and the field and angular dependences are not separable, with a suppression of the overall signal as the node is filled in.Comment: 16 pages plus nine figure