Higher-Order Trotter–Suzuki Implementation on Tight Binding Propagation Method for Calculating the Density of States and Optical Conductivity of Disordered Graphene

We employ a novel numerical method combining the second-order Trotter Suzuki (TS) approximation with the tight-binding propagation method (TBPM) to study disorder in 2D materials. This approach improves the accuracy of solving the time-dependent Schrödinger equation (TDSE) for calculating the density of states (DOS) using the Fourier transform of correlation functions. By embedding the Tight Binding Hamiltonian in the time evolution operator, the method achieves efficient computations. For optical conductivity, we apply the TS approximation within the Kubo formula, utilizing a similar numerical framework. Our results show that the second-order TS approximation enhances the precision of key quantities, with a 20% improvement in the full width at half maximum (FWHM) of the DOS peak and a 43% improvement in the van Hove singularity (vHS) peak. This approach also provides accurate optical conductivity calculations for large-scale 2D systems (1 000 000 atoms), considering disorder from carbon vacancies and hydrogen adatoms.