Screened potential in one-dimensional systems: Application to electron-hole interaction and Wannier-Mott-like excitons in atomic wires

The geometry and electronic properties of nanostructures such as chains, wires, and ribbons, which are restricted in two dimensions, give rise to novel and unexpected physical phenomena. We derive the screened Coulomb potential in one-dimensional (1D) systems by solving the Poisson equation for different spatial distributions of the responding electron gas across the cross section, characterized by a 1D static electronic polarizability alpha 1D. Both local and nonlocal screening responses are examined. Starting from three different bare soft-core or truncated potentials of the 1D hydrogen atom, we construct seven corresponding models for the screened interaction. These screened model potentials are then applied to describe exciton binding energies using a variational approach with a trial function based on the ground-state wave function of the 1D hydrogen atom. We explicitly study atomic wires composed of MgN2, S3, Te3, As2S3, and Bi2Te3. The required parameters, including wire geometry, static electronic polarizability, and effective electron and hole masses, are computed within density functional theory. We find that reduced screening at short distances and antiscreening at longer distances lead to extraordinarily large exciton binding energies in the range of 1-4 eV. For extremely thin atomic wires, binding energies even larger than the values without screening are predicted. The exciton binding energy EB and radius rB obtained from the variational treatment are compared with ab initio results from many-body perturbation theory using the GW approximation and solutions of the Bethe-Salpeter equation. Chemical trends are traced back to material parameters such as electronic polarizability and effective interband masses. From the comparison with the first-principles results, we identify the most accurate screening model for 1D systems.