Heterostructures include a layer of a two-dimensional material placed on a multiferroic layer. An ordered array of differing polarization domains in the multiferroic layer produces corresponding domains having differing properties in the two-dimensional material. When the multiferroic layer is ferroelectric, the ferroelectric polarization domains in the layer produce local electric fields that penetrate the two-dimensional material. The local electric fields modulate the charge carriers and carrier density on a nanometer length scale, resulting in the formation of lateral p-n or p-i-n junctions, and variations thereof appropriate for device functions.