Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
  • Editors' Suggestion

Microwave conductivity and superfluid density in strongly overdoped Tl2Ba2CuO6+δ

D. Deepwell, D. C. Peets, C. J. S. Truncik, N. C. Murphy, M. P. Kennett, W. A. Huttema, Ruixing Liang, D. A. Bonn, W. N. Hardy, and D. M. Broun
Phys. Rev. B 88, 214509 – Published 12 December 2013
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • EXPERIMENTAL METHODS
  • RESULTS
  • DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    We present measurements of the microwave surface impedance of the single-layer cuprate Tl2Ba2CuO6+δ, deep in the overdoped regime, with Tc≈25 K. Measurements have been made using cavity perturbation of a dielectric resonator at 17 discrete frequencies ranging from 2.50 to 19.16 GHz, and at temperatures from 0.12 to 27.5 K. From the surface impedance we obtain the microwave conductivity, penetration depth, and superfluid density. The superfluid density displays a strong linear temperature dependence from 2 to 14 K, indicative of line nodes in the energy gap. The microwave data are compared with theoretical predictions for a d-wave superconductor with pointlike impurities, with the conclusion that disorder in Tl2Ba2CuO6+δ acts predominantly in the weak-to-intermediate-strength scattering regime, and that small-angle scattering is important.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    2 More
    • Received 8 November 2013

    DOI:https://doi.org/10.1103/PhysRevB.88.214509

    ©2013 American Physical Society

    Authors & Affiliations

    D. Deepwell1, D. C. Peets2,3, C. J. S. Truncik1, N. C. Murphy1, M. P. Kennett1, W. A. Huttema1, Ruixing Liang2,4, D. A. Bonn2,4, W. N. Hardy2,4, and D. M. Broun1,*

    • 1Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
    • 2Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
    • 3Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
    • 4Canadian Institute for Advanced Research, Toronto, Ontario, Canada MG5 1Z8

    • *dbroun@sfu.ca

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 88, Iss. 21 — 1 December 2013

    Reuse & Permissions
    Access Options
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1
      Surface resistance of Tl2Ba2CuO6+δ at a set of 17 frequencies ranging from 2.50 to 19.16 GHz, as indicated in the legend. Rs(T) decreases monotonically with temperature, with a rounded transition near Tc. The frequency dependence of Rs becomes stronger at low temperatures, as the material transitions from the Rs∝ω behavior of a metal to the Rs∝ω2 regime of a superconductor.Reuse & Permissions
    • Figure 2
      Figure 2
      Surface reactance of Tl2Ba2CuO6+δ at the same set of frequencies as in Fig. 1, from 2.50 GHz (bottom) to 19.16 GHz (top). At the onset of superconductivity, there is a small rise in Xs(T) due to the kinetic inductance of the superconducting electrons. As the electrons condense further, the penetration depth shrinks, causing Xs(T) to decrease at lower temperatures.Reuse & Permissions
    • Figure 3
      Figure 3
      Real part of the microwave conductivity σ1(T) at fixed frequencies from 2.50 GHz (top) to 19.16 GHz (bottom). σ1(T) rises substantially on cooling through Tc, before peaking at 15 to 16 K, then decreasing to a residual low-temperature value comparable to that in the normal state. σ00 denotes the bare universal conductivity expected for a d-wave conductor. Inset: the microwave conductivity expected for an s-wave superconductor, calculated using Mattis-Bardeen theory (Ref. 61) for the same set of reduced frequencies used in the Tl2Ba2CuO6+δ experiment. In contrast to what is seen in Tl2Ba2CuO6+δ, the initial rise in σ1(T) on cooling is almost vertical, before peaking then becoming exponentially small at low temperature.Reuse & Permissions
    • Figure 4
      Figure 4
      Microwave conductivity spectra σ1(ω) plotted at discrete temperatures. The strong variation of σ1(ω) in the low-GHz range indicates charge excitations relaxing on microwave time scales. σ1 decreases, and its frequency dependence weakens, on cooling to the lowest temperatures. The strong frequency dependence observed below Tc weakens then disappears on warming into the normal state. [The perfectly flat behavior at 27 K reflects the normalization condition σ1(T=27.5K)=1/ρdc, used to determine the resonator constant at each frequency.] σ00 denotes the bare universal conductivity expected for a d-wave conductor.Reuse & Permissions
    • Figure 5
      Figure 5
      Frequency-dependent superfluid density 1/λ2(T) from 2.50 GHz (bottom) to 19.16 GHz (top). Over most of the temperature range, 1/λ2(T) shows a strong linear temperature dependence, the expected behavior of a d-wave superconductor with line nodes in the energy gap. 1/λ2(T) develops upward curvature on the approach to Tc: this, and the presence of fine structure in 1/λ2(T), suggests some inhomogeneity of Tc across the sample. At all temperatures, 1/λ2 is an increasing function of frequency, with the frequency dependence strongest on the approach to Tc. Below a temperature T*=2.3 K, 1/λ2(T) crosses over to a quadratic temperature dependence, the characteristic behavior of d-wave superconductivity in the presence of disorder. Inset: 1/λ2(T) at 2.50 GHz, plotted vs T2.Reuse & Permissions
    • Figure 6
      Figure 6
      The suppression of zero-temperature superfluid density by strong-, intermediate-, and weak-scattering disorder. The suppression fraction is λ002/λ02, where λ00 is the zero-temperature penetration depth with no disorder, and λ0 is the zero-temperature penetration depth in the presence of disorder. Data are shown for strong- (c=0, long dashes), intermediate- (c=1, solid line), and weak- (c≫1, short dashes) scattering regimes, as a function of the corresponding normal-state scattering rate Γn. The degree of suppression relevant to overdoped Tl2Ba2CuO6+δ is indicated by the shaded bands, one based on an estimate of λ00 from the ARPES energy dispersion, the other from dHvA data.Reuse & Permissions
    • Figure 7
      Figure 7
      Dependence of the superfluid-density disorder crossover temperature T* on the normal-state scattering rate Γn for strong- (c=0, long dashes), intermediate- (c=1, solid line), and weak- (c≫1, short dashes) scattering disorder. Note that the horizontal scale has been expanded (Γn has been multiplied by a factor of 100) for the strong-scattering, unitarity-limit curve. The parameter regime relevant to overdoped Tl2Ba2CuO6+δ (T*≈0.1Tc) is indicated by the shaded band. Only for weak-to-intermediate-strength scattering does the implied value of Γn agree with that obtained from normal-state transport.Reuse & Permissions
    • Figure 8
      Figure 8
      Effect of strong- and weak-scattering disorder on superfluid density ρs in a d-wave superconductor, from SCTMA theory. In the absence of disorder, ρs has linear T dependence at low T (clean limit, solid curve). The pair-breaking effects of strong-scattering disorder (unitarity limit, long dashes) are confined to low temperatures, with Δρs(T)∝T2 below a crossover temperature T*. Weak-scattering disorder (Born limit, short dashes) can drive a similar crossover to quadratic T dependence, but only at such a high density of scatterers that the ρs(T) is suppressed from its clean-limit form over the entire temperature range. For both unitarity-limit (c=0,Γ=0.01Tc) and Born-limit curves (c=30,Γ=1200Tc), the level of disorder has been adjusted so that T*≈0.1Tc, the regime relevant to overdoped Tl2Ba2CuO6+δ.Reuse & Permissions
    • Figure 9
      Figure 9
      The normalized density of states N(ω) of a d-wave superconductor at T=0, in the presence of weak- and strong-scattering disorder. SCTMA results have been evaluated for clean-limit (solid line), unitarity-limit (long dashes), and Born-limit (short dashes) cases, for the same set of scattering parameters as in Fig. 8. The pair-breaking effects of strong-scattering disorder are confined to a narrow range of energies near ω=0. For the Born limit, which is most appropriate to Tl2Ba2CuO6+δ, the density of states bears little resemblance to that of a clean-limit superconductor, with no coherence peak at ω=Δ0.Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review B

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×