We systematically investigate the structural and electronic properties of twisted $h$-BN bilayers to understand the role of the twisting angle. Using first-principles methods with relaxation taken into account, we simulate $h$-BN bilayers with commensurate supercells with the smallest angle being $2.{88}^{\circ }$ until ${60}^{\circ }$. We find that the interlayer separation is not constant throughout each bilayer because of the various stacking patterns throughout the layers, which also plays a significant role in their interlayer charge redistribution. The calculations for the 110 generated structures show the existence of flat bands in several twisted $h$-BN bilayers, as well as the emergence of different trends in their properties as a function of the twist angle. These results are useful for establishing a systematic base line of registry-dependent relations for the development of more advanced computational methods to access incommensurate $h$-BN bilayers.

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• Electronic structure
• 2-dimensional systems
• Hexagonal boron nitride
• Twisted heterostructures
• Density functional theory