Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Possible Phononic Mechanism for $d_{x^2 - y^2}$-Superconductivity in
  the Presence of Short-Range AF Correlations   We discuss the high temperature superconductors in a regime where the
antiferromagnetic (AF) correlation length is only a couple of lattice spacings.
In the model proposed here, these short-range AF fluctuations play an essential
role in the dressing of the carriers, but the attraction needed for
superconductivity (SC) arises from a transverse phonon oxygen mode with a
finite buckling angle as it appears in ${\rm YBa_2Cu_3O_{7-\delta}}$. A simple
fermion-phonon model analog to the Holstein model is introduced to account for
this effect. We argue that the model has a $d_{x^2 - y^2}$-wave superconducting
groundstate. The critical temperature ($T_c$) and the O-isotope effect
coefficient ($\alpha_O$) vs hole density ($x$) are in qualitative agreement
with experiments for the cuprates. The minimum (maximum) of $\alpha_O$ ($T_c$)
at optimal doping is caused by a large peak in the density of states of holes
dressed by AF fluctuations, as discussed in previous van Hove scenarios.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph