Jha, Sudhanshu S. ; Rajagopal, A. K.
(1997)
*Intralayer and interlayer spin-singlet pairing and
energy gap functions with different possible symmetries in
high-T _{c} layered superconductors*
Physical Review B, 55
(22).
pp. 15248-15260.
ISSN 0163-1829

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Official URL: http://link.aps.org/doi/10.1103/PhysRevB.55.15248

Related URL: http://dx.doi.org/10.1103/PhysRevB.55.15248

## Abstract

Anisotropy and the wave-vector dependence of the
energy gap function determine many important properties of a
superconductor. Starting from first principles, we present
here a complete analysis of possible symmetries of the
superconducting gap function E_{g}(k) at the Fermi
surface in high-T_{c} layered superconductors with
either a simple orthorhombic or a tetragonal unit cell. This
is done within the framework of Gorkov's mean-field theory of
superconductivity in the so-called 'layer representation'
introduced by us earlier. For N conducting cuprate layers,
J=1,2,...,N, in each unit cell, the spin-singlet order
parameters Δ_{JJ'}(k) can be expanded in terms
of possible basis functions of all the irreducible
representations relevant to layered crystals, which are
obtained here. In layered materials, the symmetry is
restricted to the translational lattice periodicity in the
direction perpendicular to the layers and the residual point
group and translational symmetries for the two-dimensional
unit cell in each layer of the three-dimensional unit cell.
We derive an exact general relation to determine different
branches of the energy gap function E_{g}(k) at the
Fermi surface in terms of Δ_{JJ'}(k), which
include both intralayer and interlayer order parameters. For
N=2, we also obtain an exact expression for quasiparticle
energies E_{p}(k), p=1,2, in the superconducting
state in the presence of intralayer and complex interlayer
order parameters as well as complex tunneling matrix elements
between the two layers in the unit cell, which need not be
equivalent. The form of the possible basis functions are also
listed in terms of cylindrical coordinates
k_{t},φ,k_{z} to take advantage of the
orthogonality of functions with respect to φ
integrations. In layered materials, with open Fermi surfaces
in the k_{z} direction, there is orthogonality of
basis functions with respect to k_{z} also
(-πk_{z}dπ).m. Our results show that in
orthorhombic systems, planar
d_{k}_{x}^{2}_{-k}_{y}^{2}-like (B_{1g}) and
d_{kx}k_{y}-like (B_{2g}) symmetries
are always mixed, respectively, with the planar s-wave-like
(A_{1g}) and A_{2g}-like symmetries of the
corresponding tetragonal system. There is also the
possibility of a weak modulation of E_{g}(k) as a
function of k_{z}(~cos k_{z}d). In addition,
in the presence of interlayer pairings which may or may not
have the same symmetry as the intralayer order parameters,
even in tetragonal systems the nodes of the
d_{k}_{x}^{2}-k_{y}_{2}-like intralayer gap function will be shifted. In view of
this, some suggestions for analyzing experimental data are
also presented.

Item Type: | Article |
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Source: | Copyright of this article belongs to American Physical Society. |

ID Code: | 13888 |

Deposited On: | 12 Nov 2010 14:32 |

Last Modified: | 02 Jun 2011 15:31 |

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