# High harmonic generation in crystals using Maximally Localized Wannier functions

## TL;DR

This paper introduces a Wannier gauge approach using Maximally Localized Wannier functions to improve the numerical stability of high harmonic generation calculations in semiconductors, demonstrated on a 2D hBN monolayer.

## Contribution

It proposes a novel Wannier gauge method that stabilizes the computation of high harmonic generation in semiconductors by smoothing dipole couplings in reciprocal space.

## Key findings

- Dipole couplings become smooth along reciprocal space in Wannier gauge.
- The method successfully computes high harmonic spectra for 2D hBN.
- The approach enhances numerical stability in nonlinear optical response simulations.

## Abstract

In this work, the nonlinear optical response, and in particular, the high harmonic generation of semiconductors is addressed by using the Wannier gauge. One of the main problems in the time evolution of the Semiconductor Bloch equations resides in the fact that the dipole couplings between different bands can diverge and have a random phase along the reciprocal space and this leads to numerical instability. To address this problem, we propose the use of the Maximally Localized Wannier functions that provide a framework to map ab-initio calculations to an effective tight-binding Hamiltonian with great accuracy. We show that working in the Wannier gauge, the basis set in which the Bloch functions are constructed directly from the Wannier functions, the dipole couplings become smooth along the reciprocal space thus avoiding the problem of random phases. High harmonic generation spectrum is computed for a 2D monolayer of hBN as a numerical demonstration.