Screened hydrogen model of excitons in semiconducting nanoribbons

The optical response of quasi-one-dimensional systems is often dominated by tightly bound excitons, that significantly influence their basic electronic properties. Despite their importance for device performance, accurately predicting their excitonic effects typically requires computationally demanding many-body approaches. Here, we present a simplified model to describe the static macroscopic dielectric function, which depends only on the width of the quasi-one-dimensional system and its polarizability per unit length. We show that at certain interaction distances, the screened Coulomb potential is greater than its bare counterpart, which results from the enhanced repulsive electron-electron interactions. As a test case, we study fourteen different nanoribbons, twelve of them armchair graphene nanoribbons of different families. Initially, we devised a simplified equation to estimate the exciton binding energy and extension that provides results comparable to those from the full Bethe-Salpeter equation, albeit for a specific nanoribbon family. Then, we used our proposed screening potential to solve the 1D Wannier-Mott equation, which turn out to be broad approach, that is able to predict binding energies that match quite well the ones obtained with the Bethe-Salpeter equation, irrespective of the nanoribbon family.