“…Note, however, that interactions among impurities in neighboring supercells will affect the results if N is not sufficiently large. 12,13 The resulting matrix problem reads (H 0 + H 1 ) · c n, k = E n, k S · c n, k , where n and k label band and k-vector, respectively, S is the overlap matrix, and E n, k and c n, k denote eigenvalues and eigenvectors. If a total of N k k-points in the irreducible Brillouin zone are sampled, the local density of states L(ω) on the impurity site is evaluated numerically as…”