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1
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84927865064
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Z. X. Shen et al., Phys. Rev. Lett. bf 70, 1553 (1993).
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2
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84927865063
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D.Wollman et al. (to be published).
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6
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84927865059
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Phenomenological studies of a dx2-y2 pairing mechanism have been performed by P. Monthoux and D. Pines, Phys. Rev. Lett. bf 69, 961 (1992); and by S. Lenck, J.P. Carbotte, and R.C. Dynes (to be published).
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7
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84927865058
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The present work uses a slightly different version of the FLEX approximation from that in Refs., Ref. 4, Ref. 5, Specifically, the exchange of s wave singlet pairs is omitted here. For this reason, the transition temperatures reported below are roughly 20 in, Ref. 5
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8
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84927865057
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Zh. Eksp. Teor. Fiz. bf 34, 1438 (1958) [Sov. Phys. JETP bf 7, 996 (1958)].
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Migdal, A.B.1
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11
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84927865055
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A familiar semiquantitative construction of this type is the Coulomb pseudopotential in electron phonon strong coupling theory.
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12
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0001227357
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An alternate approach, useful in approximations which contain convolution integrals, is the fast Fourier transform technique [J.W. Serene and D.W. Hess
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bf 44
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An alternate approach, useful in approximations which contain convolution integrals, is the fast Fourier transform technique [J.W. Serene and D.W. Hess, Phys. Rev. B bf 44, 3391 (1991)].
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(1991)
Phys. Rev. B
, vol.3391
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13
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84927865053
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For a detailed description of this division see, Ref. 10
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14
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84927865052
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Vertex renormalizations have already been carried out in a full parquet approximation for the Anderson impurity model, see, Ref. 9
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15
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0542424381
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The FLEX equations for the superconducting phase were written down in the context of a BCS like treatment by Chien Hua Pao and N.E. Bickers
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bf 44
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The FLEX equations for the superconducting phase were written down in the context of a BCS like treatment by Chien Hua Pao and N.E. Bickers, Phys. Rev. B bf 44, 10270 (1991).
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(1991)
Phys. Rev. B
, vol.10270
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16
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84927865051
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Our solution for φ(k) retains dx2-y2 symmetry at all temperatures below Tc. In principle, other solutions may exist which mix different representations at sufficiently low temperature, even though only the dx2-y2 solution is allowed for T→ Tc. We have not performed a search for more general solutions.
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17
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84927865050
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We have not yet studied the effect of a momentum space RG on calculations in the superconducting state. Such an RG is highly successful in the normal state (Ref. 10) and would allow additional flexibility in treating the superconducting state (e.g., in performing precise integrations near the gap nodes).
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18
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84927865049
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Using Ω6 rather than Ω0 is analogous to using the phonon Debye frequency, rather than a multiple of the bandwidth, in electron phonon treatments. Note, however, that the effective action used with Ω6 is determined quantitatively by the RG.
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20
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84927865048
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The detailed frequency dependence of the pairing interaction is strongly affected by the opening of the gap. This dependence is not reflected directly by the integrated weight.
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21
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84927865047
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For the dx2-y2 state, the full spin susceptibility chis (not calculated here) is expected to vanish linearly at low T for Q = 0, ω = 0. This is not a required property of bar{ chi}s (which contains no vertex corrections).
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22
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84927865046
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The gap was extracted directly from the imaginary part of the diagonal real frequency Green's function using a Padé approximant continuation. Note that due to the presence of the frequency dependent quantity ξk the gap Δ(ω) is not simply φ (ω)/Z(ω) as in the electron phonon problem.
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24
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84927865045
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See, e.g., S. W. Cheong et al., Phys. Rev. Lett. bf 67, 1791 (1991).
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