Strong disorder in nodal semimetals: Schwinger-Dyson–Ward approach

Abstract

The self-consistent Born approximation quantitatively fails to capture disorder effects in semimetals. We present an alternative, simple-to-use nonperturbative approach to calculate the disorder-induced self-energy. It requires a sufficient broadening of the quasiparticle pole and the solution of a differential equation on the imaginary frequency axis. We demonstrate the performance of our method for various paradigmatic semimetal Hamiltonians and compare our results to exact numerical reference data. For intermediate and strong disorder, our approach yields quantitatively correct momentum-resolved results. It is thus complementary to existing renormalization group treatments of weak disorder in semimetals.