The Effect of Disorder on the Superconducting Gap in 2d Systems

The effect of disorder on superconductivity has been a tempting avenue of study for scientists for many years. However, direct numerical computation of characteristic quantities such as the superconducting gap is traditionally limited by the large dimensions that are required for the system to have true disorder. We apply the recently developed Kernel Polynomial method as an approximate diagonalization technique to 2 dimensional superconducting Hamiltonians which improves the size of systems that can be studied from D = 10⁵ to D=10⁹. We present a scheme to extract the superconducting gap from the approximate density of states and benchmark our method with well understood simple systems. Lastly, we apply this method to disordered systems with the disorder coming from impurity-based perturbations added to homogeneous materialistic Hamiltonians.