Many-Body Calculations of Excitons in Two-Dimensional GaN

We present an ab initio study on quasiparticle (QP) excitations and excitonic effects in two-dimensional (2D) GaN based on density-functional theory and many-body perturbation theory. We calculate the QP band structure using GW approximation, which generates an indirect band gap of 4.83 eV (K & RARR;& UGamma;) for 2D GaN, opening up 1.24 eV with respect to its bulk counterpart. It is shown that the success of plasmon-pole approximation in treating the 2D material benefits considerably from error cancellation. On the other hand, much better gaps, comparable to GW ones, could be obtained by correcting the Kohn-Sham gap with a derivative discontinuity of the exchange-correlation functional at much lower computational cost. To evaluate excitonic effects, we solve the Bethe-Salpeter equation (BSE) starting from Kohn-Sham eigenvalues with a scissors operator to open the single-particle gap. This approach yields an exciton binding energy of 1.23 eV in 2D GaN, which is in good agreement with the highly demanding GW-BSE results. The enhanced excitonic effects due to reduced dimensionality are discussed by comparing the optical spectra from BSE calculations with that by random-phase approximation (RPA) for both the monolayer and bulk GaN in wurtzite phase. Additionally, we find that the spin-orbit splitting of excitonic peaks is noticeable in 2D GaN but buried in the bulk crystal.