The model consists of two conducting layers in a unit cell with identical two-dimen-
sional band structures and interlayer hopping strengths J1 and J2. The quasiparticles
within the same layer interact via a phenomenological pairing interaction of the BCS type
so that the total Hamiltonian has the form H = Ho + V, where the band energy term is
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Ho =     E (k)Oj,,(k)t5j,(k)
jk, n=1
+ E[J1# 1,(k)Oj2,(k) + J20 2,(k)-'j,,o(k) + H.c.],        (1)
jk,
where Wo(k) = k2/2mo - Ep, k = (kZ, ky), a is the spin index, n = 1,2.is the layer index
within a unit cell, and the sum on j is over all unit cells normal to the planes. The units
are chosen such that h = kB = 1. The interaction term is
V =   -       1AonOI n(k)4jn, (-k) jno. (-k') jn,(k'),          (2)
jn k, k','
where we assume two unequal pair coupling strengths AOn, both are cut off at a common
energy w1j. The condition a' = -a will be imposed, since the pair coupling mechanism
only allows singlet pairs. The model has been generalized to two layers with different
two-dimensional band structures and different Fermi surfaces [7], but the simpler model
considered here gives a clearer physical picture.
The quasiparticle Green's function matrix elements are defined in the familiar way:
G   ,(k,  -') =
F-n(k, -T') = (T{kf,(k,r)V,-,(-k,r')]),                (3)
where k = (k, kz), kz is the crystal momentum in the c-direction, < - - > denotes thermal
average, and
O(k = ..         4',,(k  jeikUTs+(n-1)j.              (4)

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