Phosphorene is a graphene-like material with an intermediate band gap, in contrast to zero-gap graphene and large-gap dichalcogenides or hexagonal boron nitride (hBN), which makes it more suitable for nanoelectronic devices. However, inducing band-gap modulation in freestanding phosphorene nanoribbons (PNRs) is problematic, as high in-plane electric fields are necessary to close the gap. We perform here a detailed investigation concerning the substrate influence on the electric-field control exerted by an external gate, using the density functional theory–non-equilibrium Green’s functions (DFT-NEGF) framework. It is established that the interaction with a hexagonal boron nitride supporting layer significantly enhances the gap modulation. Furthermore, we address the issue of contacting the PNRs, by using conducting graphene nanoribbons embedded in the support hBN layer. Within this setup, a measurable spin polarization is achieved owing to the anti-ferromagnetic coupling between the edges of the graphene nanoribbons.

Accurate and efficient tools for calculating the ground state properties of interacting quantum systems are essential in the design of nanoelectronic devices. The exact diagonalization method fully accounts for the Coulomb interaction beyond mean field approximations and it is regarded as the gold-standard for few electron systems. However, by increasing the number of instances to be solved, the computational costs become prohibitive and new approaches based on machine learning techniques can provide a significant reduction in computational time and resources, maintaining a reasonable accuracy. Here, we employ pix2pix, a general-purpose image-to-image translation method based on conditional generative adversarial network (cGAN), for predicting ground state densities from randomly generated confinement potentials. Other mappings were also investigated, like potentials to non-interacting densities and the translation from non-interacting to interacting densities. The architecture of the cGAN was optimized with respect to the internal parameters of the generator and discriminator. Moreover, the inverse problem of finding the confinement potential given the interacting density can also be approached by the pix2pix mapping, which is an important step in finding near-optimal solutions for confinement potentials.

Accurate and efficient tools for calculating the ground state properties of interacting quantum systems are essential in the design of nanoelectronic devices. The exact diagonalization method fully accounts for the Coulomb interaction beyond mean field approximations and it is regarded as the gold-standard for few electron systems. However, by increasing the number of instances to be solved, the computational costs become prohibitive and new approaches based on machine learning techniques can provide a significant reduction in computational time and resources, maintaining a reasonable accuracy. Here, we employ pix2pix, a general-purpose image-to-image translation method based on conditional generative adversarial network (cGAN), for predicting ground state densities from randomly generated confinement potentials. Other mappings were also investigated, like potentials to non-interacting densities and the translation from non-interacting to interacting densities. The architecture of the cGAN was optimized with respect to the internal parameters of the generator and discriminator. Moreover, the inverse problem of finding the confinement potential given the interacting density can also be approached by the pix2pix mapping, which is an important step in finding near-optimal solutions for confinement potentials.