Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effects of phonon interaction on the pairing in the high-T$c$
  superconductors   We study the effects of phonon interaction on the superconducting pairing in
the background of a d-wave gap, mediated by antiferromagnetic (AFM) spin
fluctuations, using coupled BCS gap equations. We found that phonon interaction
can induce a s-wave component to the d-wave gap in the (D+S) form with an
interaction anisotropy and in the (D+$i$S) form without anisotropy,
respectively. In either case, however, T$_c$ is not enhanced compared to the
pure d-wave pairing without phonon interaction. On the other hand, anisotropic
phonon interaction can dramatically enhance the d-wave pairing itself and
therefore T$_c$, together with the AFM spin fluctuation interaction. This
(D$_{AFM}$ + D$_{ph}$) type pairing exhibits strongly reduced isotope
coefficient despite the large enhancement of T$_c$ by phonon interaction.
Finally, we study the combined type of (D$_{AFM}$ + D$_{ph}$ +$i$S)) gap and
calculate the penetration depth and specific heat to be compared with the
experiments.

19
The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol