Capturing the full momentum dependency in diagrammatic calculations

The study of disorder in Condensed Matter Physics is as old as the field itself. Disorder can suppress desirable material properties such as the conductivity but it can play a fundamental role in quantum phase transitions and can even be shown to enhance superconductivity. The requirement of a realistic quantum description of disorder led to the development of diagrammatic techniques which are able to deal with disorder in a controlled way. Several approximation schemes may be employed in order to resum an infinite subseries of diagrams, such as the self-consistent T-matrix approximation and the self-consistent Born approximation. While nonperturbative, these approaches typically fail to capture any momentum dependency of the disorder-averaged Green's function coming from disorder. Here, we present an exact method to capture the momentum dependency due to disorder in the disorder-averaged Green's function, effectively summing a larger subset of diagrams. We use KITE to apply this method to several 2D systems such as the square lattice subject to Anderson disorder, graphene with vacancies and SrRuO3. Our method is valid for any amount of disorder and is in complete agreement with diagrammatic calculations in both the limit of very low and very high concentration of impurities.