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In this work, the nonlinear optical response, and in particular, the highharmonic generation of semiconductors is addressed by using the Wannier gauge.One of the main problems in the time evolution of the Semiconductor Blochequations resides in the fact that the dipole couplings between different bandscan diverge and have a random phase along the reciprocal space and this leadsto numerical instability. To address this problem, we propose the use of theMaximally Localized Wannier functions that provide a framework to map ab-initiocalculations to an effective tight-binding Hamiltonian with great accuracy. Weshow that working in the Wannier gauge, the basis set in which the Blochfunctions are constructed directly from the Wannier functions, the dipolecouplings become smooth along the reciprocal space thus avoiding the problem ofrandom phases. High harmonic generation spectrum is computed for a 2D monolayerof hBN as a numerical demonstration.

High harmonic generation in crystals using Maximally Localized Wannier functions