# Thermal conductivity of YBa2Cu3−xZnxO7−y

TL;DR: In this paper, the phonon part of the thermal conductivity of a series of well characterized samples of YBa 2 Cu 3−x Zn x O 7−y has been measured.

Abstract: Thermal conductivity of a series of well characterized samples of YBa 2 Cu 3−x Zn x O 7−y has been measured. The phonon part of the thermal conductivity has been fitted to a modified BRT type expression. The fit parameters, among other things, indicate that the gap parameter 2/k B Tc and the electron-phonon coupling strength decrease with increasing zinc concentration in the sample.

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TL;DR: In this article, a theory of the thermal conductivity of superconductors is presented, based on the theory of super conductivity due to Bardeen, Cooper, and Schrieffer, which is treated as quasi-particles, allowing a Boltzmann equation to be set up.

Abstract: A theory of the thermal conductivity of superconductors is presented, based on the theory of superconductivity due to Bardeen, Cooper, and Schrieffer. The excited states of the system are treated as quasi-particles, allowing a Boltzmann equation to be set up. The electronic contribution to the thermal conductivity when the dominant scatterers are impurities has been calculated exactly. The result is very close to that of the Heisenberg-Koppe theory which is in fair agreement with experiment. The variational principle of Wilson has been used to find the electronic conductivity when the dominant scatterers are lattice waves. It is concluded that the theory fails to predict the sharp drop in the ratio $\frac{{\ensuremath{\kappa}}_{\mathrm{es}}}{{\ensuremath{\kappa}}_{\mathrm{en}}}$ as the temperature is lowered below ${T}_{c}$, a feature which is characteristic of the experimental results. The effect of the electrons on the lattice conductivity has also been calculated. The theoretical values may be too large.

362 citations

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TL;DR: In this paper, the contribution of longitudinal acoustic phonons to the electron-phonon coupling constant λ was estimated to lie within the weak coupling range, taking into account scattering of phonons by structural defects like boundaries, point defects, and sheetlike faults.

Abstract: The observed peak below T c in the thermal conductivity К of YBa 2 Cu 3 O 7 can be explained fairly well by applying the BCS theory for lattice thermal conductivity limited by electron scattering. The contribution of longitudinal acoustic phonons to the electron-phonon coupling constant λ is estimated to lie within the weak coupling range. In addition to phonon-electron scattering we have taken into account scattering of phonons by structural defects like boundaries, point defects, and sheetlike faults. More detailed information about the strength of the phonon-electron scattering and the nature of the gap (weak or strong coupling) could be obtained from measurements of the anisotropy of К in single crystals.

155 citations

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TL;DR: In this paper, the authors derived the analog to the Bloch equation for the case of thermal conduction in a superconductor limited by phonon scattering by introducing an appropriate general form for the nonequilibrium part of the distribution function into the corresponding Boltzmann equation.

Abstract: The analog to the Bloch equation for the case of thermal conduction in a superconductor limited by phonon scattering is derived by introducing an appropriate general form for the nonequilibrium part of the distribution function into the corresponding Boltzmann equation. This integral equation for the deviation function is solved numerically for different temperatures $T$ by replacing it by sets of simultaneous linear equations with dimensions up to 39. The limiting curve for the deviation function when $T$ approaches the transition temperature ${T}_{c}$ from below turns out to be identical to the curve which has been reported by Klemens for the normal state. With $T$ decreasing below ${T}_{c}$ the maximum of the deviation function rises and shifts to higher energies. The ratio of the thermal conductivity in the superconducting state to that in the normal state, $\frac{{\ensuremath{\kappa}}_{s}}{{\ensuremath{\kappa}}_{n}}$, plotted against $\frac{T}{{T}_{c}}$ is found to increase monotonically and to have a limiting slope of about 1.62 at ${T}_{c}$. Consideration of the energy dependence of the energy gap in the case of lead yields a sizable effect on the plot of $\frac{{\ensuremath{\kappa}}_{s}}{{\ensuremath{\kappa}}_{n}}$ vs $\frac{T}{{T}_{c}}$.

29 citations

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TL;DR: In this article, the authors analyze the thermal conductivity of both ceramic and single crystal samples of high temperature superconductors and find that phonons are the main heat carriers in these materials.

Abstract: We review and analyze the data on the thermal conductivity of both ceramic and single crystal samples of high temperature superconductors. A universal pattern can be extracted and interpreted in the following way: phonons are the main heat carriers in these materials, and in the high temperature range the thermal conductivity κ is almost constant due to phonon scattering against disorder; below the superconducting transition temperature κ increases as phonon scattering against carriers condensing into the superconducting state decreases and at still lower temperatures there is a region in which a T2 law is obeyed that most probably is due to resonant phonon scattering against low energy excitations, i.e. tunneling systems similar to those found in disordered materials. The origin of the relevant disorder is discussed.

13 citations

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TL;DR: In this paper, thermal conductivity of YBa2Cu3O7 was measured on samples of a few mm thickness and the experimental set up was described and results discussed, pointing towards a contribution to thermal resistivity from three-phonon Umklapp processes.

Abstract: Thermal conductivity of YBa2Cu3O7 has been measured on samples of a few mm thickness. AboveT
c thermal conductivity is found to decrease with increase in temperature, pointing towards a contribution to thermal resistivity from three-phonon Umklapp processes. BelowT
c thermal conductivity increases rapidly before reaching a maximum at about 50 K and then falls towards zero at lower temperatures. The experimental set up is described and results discussed.

10 citations