Accurate quantum–mechanical evaluation of the electric polarization of periodic solids using a multi-step method

The electric polarization of a periodic solid can be expressed as a Berry phase, and computed from the occupied Bloch state overlap matrix between neighboring wavevectors on a grid sampling the Brillouin zone. The usual discretized expression for the electric polarization leads to slow convergence with respect to the number of wavevectors on the grid. s work, we improve the integration scheme, and obtain a better accuracy without the need for a finer sampling. Our technique uses multi-step overlap matrices instead of only nearest-neighbor overlap matrices, and results in higher precision for almost no additional computation cost. t the method on AlAs, confirm the theoretical convergence rate, and observe that medium-order multi-step formulas provide superior accuracy without fluctuation problems.