We calculate the microwave conductivity of a d x i_ y i superconductor in the presence of elastic impurity scattering and inelastic scattering due to antiferromagnetic spin fluctuations. The low-temperature conductivity does not simply reflect the linear temperature dependence of the number of quasiparticles in a d-wave system, as often supposed. We compare with recent data on high-quality YBa2Cu306.95 single crystals.PACS numbers: 74.25.Fy, 72.10.Di, 74.25.Nf Microwave surface impedance measurements of the cuprate superconductors provide information on the real and imaginary parts of the long wavelength (q-> 0) conductivity. The imaginary part of the conductivity is proportional to the square of the inverse penetration depth, and its low frequency limit determines the superfluid density. Recent experiments [1] on high purity crystals of YBa2Cu3C>6.95 have found that the superfluid density n s appears to decrease linearly with T at low temperatures, in contrast to measurements on samples of apparently poorer quality which exhibit a T 2 variation at the lowest temperatures [2]. The linear-JT variation of n s has been interpreted in terms of an unconventional superconducting state with lines of order parameter nodes on the Fermi surface [1,3].Several authors [4-6] have attempted to account for the measured T 2 dependence of the penetration depth in other samples by postulating the existence of resonant potential scatterers acting as strong pair breakers in the unconventional state. While this model appears to describe several aspects of the penetration depth experiments consistently, it is natural to ask whether a similar approach can be used to understand the frequency and temperature dependence of the real part of the conductivity cr(7\fl). In this Letter, we examine the consequences of the joint assumptions of */-wave pairing and strong impurity scattering for the conductivity, and compare our results with the experimental data of Bonn et al. [7][8][9].Conductivity and phenomenological model.-Bonn et al. [7,8] use measurements of the surface resistance R s ^(S^fl^^/c 4 at microwave frequency ft, together with the penetration depth A,, to determine the conductivity a. These authors then propose that the real part of the conductivity can be represented by a Drude-like form associated with the excited quasiparticles, cr(TM)=-n qp (T) m qp i + n 2 r 2 (r)where n is the electron density, n qp {T) = \ -n s (T) is the relative number of quasiparticles excited at temperature T, and r(T) is the relaxation time in the superconducting state. Bonn et al. find that in high purity single crystals, there is a large increase in r(T) below T c , interpreted in terms of a collapse of the inelastic scattering due to the decrease in the spin fluctuation spectral weight as the superconducting gap opens [10]. The increase continues down to a temperature To of order 0.47V, where r(70, which has increased by almost 10 2 , reaches an impuritydominated limit where r appears to saturate at a constant value. Associated with the initial ...
The phase diagram of the 2D t-J model is investigated using high-temperature expansions. Series for the Heimholtz free energy, the inverse compressibility, the chemical potential, and the uniform spin susceptibility through tenth order are calculated and analyzed. A region of phase separation is found at 7=0 for Jit lying above a line extending from Jit =3.8 at zero filling to Jit = 1.2 at half filling. For very small Jit near half filling where the Nagaoka effect is possible, we find a region of divergent uniform magnetic susceptibility at T-0.
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