Truncation of periodic image interactions for confined systems

First principles methods based on periodic boundary conditions are used extensively by materials theorists. However, applying these methods to systems with confined electronic states entails the use of large unit cells in order to avoid artificial image interactions. We present a general approach for truncating the Coulomb interaction that removes image effects directly and leads to well converged results for modest-sized periodic cells. As an illustration, we find the lowest-energy quasiparticle and exciton states in two-dimensional hexagonal GaN sheets. These sheets have been proposed as parent materials for single-walled GaN nanotubes which may be of interest for optoelectronics.

Figure 1

(Color online) Static inverse dielectric constant ${ϵ}_{00}^{-1}\left(q\right)$ versus momentum transfer $q$ for GaN sheets. The periodic separation between sheets is $14\mathrm{a.u.}$ and Coulomb truncation was used. Red (dark gray) diamonds are the first-principles results using the RPA. The solid line is a fit of the form $1∕{ϵ}_{00}^{-1}\left(q\right)=1+\gamma {\mid q\mid }^2{\widehat{v}}_c^{\mathit{sh}}\left(q\right)\exp (-\alpha \mid q\mid )$ with $\gamma =2.2$ and $\alpha =2.7\mathrm{a.u.}$