Interplay between interactions and disorder in nested fermionic systems: Angle-resolved renormalization group theory

We solve the problem of weakly disordered interacting fermions near the flat two-dimensional Fermi surface. For this problem we develop a new angle resolved renormalization group theory that takes into account both the interactions and the disorder as functions of angular position of the electrons near the Fermi surface. The model is treated by the $N$-patch renormalization group procedure upon the effective action for the partition function for M replicas. The flow equation for the effective interaction and for the effective diffusion function (of three angles) is integrated numerically and the phase diagram is constructed. The low temperature phase is associated to the dominant eigenvalue of the diverging susceptibility. The angular dependence of the corresponding eigenvectors determines the form and the symmetry of the order parameter. The simultaneously diverging diffusion function $D$ provides information about the effects of disorder to the low-temperature state. Keywords. Non-conventional superconductivity, disordered systems, functional renormalization