Since the advent of single layer graphene, two dimensional materials have been the system of interest to the entire scientific community. Increase in computation power has allowed to study materials using tools such as Density Functional Theory. In DFT, plane wave basis sets are used to solve Poisson equation to calculate the potential. This method works very well to simulate materials with neutral defects in bulk, surfaces or two dimensional materials. However, this creates a problem when it comes to charged defects. The plane wave basis set uses periodic boundary condition in which when the material is charged, the periodic images interact with each other. The materials and mathematics communities have tried to solve this problem using various methods such as Coloumb cutoff and compensating charge methods using plane wave basis sets or mixed basis set. However, the methods have slow convergence. Thus, the challenges to study point defect are real and opportunities are immense.
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