Band gap control in phosphorene/BN structures from first principles calculations Lukas Eugen Marsoner Steinkasserer, 1, * Simon Suhr, 1 and Beate Paulus 1 1 Institut f¨ ur Chemie und Biochemie, Freie Universit¨ at Berlin, Takustraße 3, D-14195 Berlin, Germany (Dated: July 27, 2016) Using both DFT as well as G0W0 calculations, we investigate static and dynamic effects on the phosphorene band gap upon deposition and encapsulation on/in BN multilayers. We demonstrate how competing long- and short-range effects cause the phosphorene band gap to increase at low P - BN interlayer spacings, while the band gap is found to drop below that of isolated phosphorene in the BN/P bilayer at intermediate distances around 4 ˚ A. Subsequent stacking of BN layers, i.e. BN/BN/P and BN/BN/BN/P is found to have a negligible effect at the DFT level while at the G0W0 increased screening lowers the band gap as compared to the BN/P bilayer. Encapsulation between two BN layer is found to increase the phosphorene band gap by a value approximately twice that observed when going from freestanding phosphorene to BN/P. We further investigate the use of the GLLB-SC functional as a starting point for G0W0 calculations showing it to, in the case of phosphorene, yield results close to those obtained from GW0@PBE calculations. I. INTRODUCTION In 2014 a new type of material consisting of a black- phosphorus monolayer (phosphorene) was first synthe- sized [1–4]. Phosphorene has quickly become the subject of considerable research interest due to its attractive op- tical gap between 1.3 eV [5], 1.45 eV [2], 1.75 eV [6] and 1.73 eV [7] as well as high charge-carrier mobility [8]. The material is further made appealing by the anisotropy of its transport properties, with electrons and holes possess- ing notably different effective masses along the phospho- rene armchair and zig-zag direction. While being extremely attractive as an object of study, pristine phosphorene unfortunately suffers from rapid degradation by oxygen under ambient conditions [9]. A natural remedy for this problem consists in protecting the phosphorene layer by capping or encapsulating it with/in more environmentally stable materials. BN has been pro- posed as the natural candidate for this application and BN/phosphorene heterostructures have been studied in a number of recent theoretical works at the DFT level [10–13]. It is well known though from other 2D-materials that adsorption, even on materials possessing low dielectric constants such as BN, can have a significant impact on their electronic properties [14]. As these effects are often attributable to long-range screening effects not accounted for within DFT, many-body electronic structure methods such as GW are necessary to study them from a theoret- ical point of view. Herein, we consider in detail the effects of the interac- tion of phosphorene with BN on the phosphorene elec- tronic structure employing recently developed methods for the accurate computation of electron-correlation ef- fects within 2D-materials [15]. The effects of screening are investigated for different numbers of layers of BN on both sides of phosphorene with particular emphasis be- * marsoner@zedat.fu-berlin.de ing placed on the effects of the P/BN interlayer spacing as well as different P/BN stacking sequences. II. COMPUTATIONAL DETAILS The lattice parameters for phosphorene and BN were obtained using the PBE0 [16] functional combined with Grimme’s D2 dispersion correction [17]. We chose this combination of methods as it was shown by Sansone et al. [18] to yield lattice parameters very close to those ob- tained from high-level ab-initio calculations. Relaxation of the monolayer was performed using the CRYSTAL14 program [19, 20] together with a POB-triple-ζ basis set as described by Peintinger et al. [21]. d int FIG. 1. The left-hand figure shows a top-on view of the phos- phorene/BN bilayer supercell used for all multilayer calcula- tions throughout this work, while the right-hand site shows a site-on view of the same structure where the definition of the interlayer spacing has also been indicated. Heterostructures were modeled via a unit cell consist- ing of a 1 × 3 phosphorene supercell and a 1 × 4 supercell of the primitive orthorhombic cell of BN. The resulting cell is shown in figure 1. The maximum resulting strain within the BN layers is ≈ 4.7 %. Note that we have tested the robustness of our conclusions against a con- sistent change in the lattice constant of the phosphorene monolayer and the P/BN heterostructure and found the effect to be that of a rigid shift of the band gap with only a small (≈ 0.03 eV) difference in the change of the band gap upon formation of the bilayer. Plane-wave DFT calculations were performed using the GPAW code [22–25] and employed an energy cutoff of arXiv:1607.08059v1 [cond-mat.mtrl-sci] 27 Jul 2016