In the second scenario, we assume Δ$_{A}$ ≪ t$_{⊥}$ ≪ Δ$_{B}$. In this case t$_{⊥}$ wipes out the effects of interactions on the A-bands. Coupling them together then gives us an anisotropic two dimensional Fermi liquid. But as t$_{⊥}$ is much smaller than Δ$_{B}$, the Cooperons on the outer bands at zeroth order remain unperturbed. The coupling then between the anisotropic Fermi liquid and the B-Cooperons induces superconductivity in the system as a whole. This superconductivity is d-wave in nature. We now elaborate on these two scenarios. We treat the interladder hopping through a random phase approximation (RPA) analysis of the interladder hopping. The form of the hopping is taken to be long range where a, b = 1 , ..., 4 run over the legs of an individual ladder and n and m mark the n ’th and m ’th ladders. By particle-hole symmetry the hopping is assumed to have peaks both near k$_{⊥}$ = 0 and k = G/ 2 where G = (0 , π/ 2) is the inverse lattice vector perpendicular to the ladders. In particular the hopping takes the form where f$_{ab}$ ( m − n ) = f$_{ba}$ ( n − m ) and f$_{ab}$ (0) = 0 (i.e. no (additional) hopping within a ladder). By treating H$_{interladder}$ in an RPA approach, we find that the single particle Green’s function takes the form where 7 t eff 1 ( k$_{y}$ ) = 2 ∑ n> 0 cos(4 k$_{y}$ ) $_{×}$( 2( s 2 1 + s 2 $_{2}$) t n, 0 1 , 1 + (2 s$_{1}$s$_{2}$ − s 2 $_{1}$)( t n, 0 1 , 2 + t n, 0 2 , $_{1}$) − 2 s$_{1}$s$_{2}$ ( t n, 0 3 , 1 + t n, 0 1 , $_{3}$) − s 2 $_{2}$( t n, 0 1 , 4 + t n, 0 4 , $_{1}$) ) ; t n,m a,b = (1 − ( − 1) n − $^{m}$) f$_{ab}$ ( m − n ) (3.2) H$_{interladder}$ = − ∑ n = m,a,b t n,m a,b c † $_{n,a}$c$_{m,b}$ , (3.1) G 2D RPA ret ( ω, k$_{x}$, k$_{y}$ ) = Γ$_{1}$( k$_{y}$ ) G 2D A $_{1}$( ω, k$_{x}$, k$_{y}$ ) + Γ$_{2}$( k$_{y}$ ) G 2D A $_{2}$( ω, k$_{x}$, k$_{y}$ ); G 2D $_{A$_{i}$}$( ω, k$_{x}$, k$_{y}$ ) = G$_{A}$$_{i}$ ( ω, k$_{x}$ ) 1 + G$_{A}$$_{i}$ ( ω, k$_{x}$ ) t eff i ( k$_{y}$ ) , (3.3) A. Scenario I