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

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

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.

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

Isotope Effect in the Presence of Magnetic and Nonmagnetic Impurities

The effect of impurities on the isotope coefficient is studied theoretically in the framework of Abrikosov-Gor'kov approach generalized to account for both potential and spin-flip scattering in anisotropic superconductors. An expression for the isotope coefficient as a function of the critical temperature is obtained for a superconductor with an arbitrary contribution of spin-flip processes to the total scattering rate and an arbitrary degree of anisotropy of the superconducting order parameter, ranging from isotropic s-wave to d-wave and including anisotropic s-wave and mixed (s+d)-wave as particular cases. It is found that both magnetic and nonmagnetic impurities enhance the isotope coefficient, the enhancement due to magnetic impurities being generally greater than that due to nonmagnetic impurities. From the analysis of the experimental results on La-Sr-Cu-M-O high temperature superconductor, it is concluded that the symmetry of the pairing state in this system differs from a pure d-wave.Comment: 4 pages, 3 figure

Interlayer coupling and the c-axis quasiparticle transport in high-TcT_{c} cuprates

The c-axis quasiparticle conductivity shows different behavior depending on the nature of the interlayer coupling. For coherent coupling with a constant hopping amplitude $t_{\perp}$, the conductivity at zero frequency and zero temperature $\sigma(0,0)$ depends on the direction of the magnetic field, but it does not for angle-dependent hopping $t(\phi)$ which removes the contribution of the nodal quasiparticles. For incoherent coupling, the conductivity is also independent of field direction and changes only when paramagnetic effects are included. The conductivity sum rule can be used to determine the admixture of coherent to incoherent coupling. The value of $\sigma(0,0)$ can be dominated by $t_{\perp}$ while at the same time $t(\phi)$ dominates the temperature dependence of the superfluid density.Comment: 2 figure

Frequency dependent relaxation rate in the superconducting YBa2Cu3O{6+delta}

The submillimeter-wave 3 cm{-1} < nu < 35 cm{-1} complex conductivity of the reduced YBa2Cu3O{6+delta} film (Tc=56.5 K) was investigated for temperatures 4 K < T < 300 K and compared to the properties of the same film in the optimally doped state. The frequency dependence of the effective quasiparticle scattering rate 1/tau*(nu) was extracted from the spectra. 1/tau*(nu) is shown to be frequency independent at low frequencies and high temperatures. A gradual change to 1/tau*~nu^{1.5} law is observed as temperature decreases. In order to explain the observed temperature dependence of the low frequency spectral weight above Tc, the quasiparticle effective mass is supposed to be temperature dependent for T>Tc.Comment: 4 pages, 4 figure

Phenomenological description of the microwave surface impedance and complex conductivity of high-TcT_c single crystals

Measurements of the microwave surface impedance $Z_s(T)=R_s(T)+iX_s(T)$ and of the complex conductivity $\sigma_s(T)$ of high-quality, high-$T_c$ single crystals of YBCO, BSCCO, TBCCO, and TBCO are analyzed. Experimental data of $Z_s(T)$ and $\sigma_s(T)$ are compared with calculations based on a modified two-fluid model which includes temperature-dependent quasiparticle scattering and a unique temperature variation of the density of superconducting carriers. We elucidate agreement as well as disagreement of our analysis with the salient features of the experimental data. Existing microscopic models are reviewed which are based on unconventional symmetry types of the order parameter and on novel mechanisms of quasiparticle relaxation.Comment: 15 pages, 17 figures, 1 tabl