Optimizing second harmonic generation in inorganic crystals: dimensionality effects and structural metrics

To be employed in laser applications, an ideal nonlinear optical crystal exhibiting second harmonic generation needs to maximize both its nonlinear susceptibility and bandgap. However, the two metrics are related by a tradeoff relation. Here, we propose a bandgap-independent measure of nonlinearity – a material's structural anharmonicity – related to the so-called Miller's index. We computed Miller's index across >400 materials, where Miller indices vary across three orders of magnitude in all materials considered, independent of bandgap. This is in stark contrast to standard texts arguing that Miller indices are close to a constant. We further computationally determined the dimensions of all structures considered and observe that, contrary to what has been speculated in literature, there is no trend that lower dimensional structures carry larger nonlinearities. This conclusion motivates future efforts to explore a materials space unbiased in its choice of structural dimensionality.