Stacking sequences of black phosphorous allotropes and the corresponding few-layer phosphorenes

Abstract

Possible bulk black phosphorus (BP) allotropes are constructed based on single-layer BP with various stacking sequences. Our stacking algorithm shows that there are eight possible allotropes with two stacking layers in their unit cells possessing relatively high symmetries, and six of them are retained after structural relaxation using a van der Waals correction of optB88-vdW. The AF, AG, and AH bulk structures are presented for the first time. The structural relationship of these configurations has been explained via an interlayer slipping process. The total energy of the AF allotrope is closest to the most stable bulk BP structure (AB stacking) among all explored 2-layer stacked bulk structures. The calculated band structure of the AF allotrope using HSE06 shows a direct band gap of 0.48 eV with anisotropic electronic structures. We also presented six possible BP allotropes with three stacking layers in their unit cells. The newly reported AAF and ABC stacked structures show semiconducting and metallic features, respectively. After the bulk structures were explored, we further built the corresponding few-layer phosphorene structures and investigated their electronic properties. The results show that all the few-layer phosphorenes show semiconducting features. The AE, AAE, and AEA phosphorenes have indirect band gaps while the other explored phosphorenes possess direct band gaps located at the Γ point.

First-principles prediction of lattice coherency in van der Waals heterostructures

“…In general, the most noticeable effects are thus expected to occur in phosphorene, the softest (along the armchair direction) 2D material effectively exfoliated [40] up to date, and to be imperceptible in the case of stiffer materials like graphene. This mean-field effect also explains why the armchair lattice parameters of phosphorene are predicted to differ from its bulk counterpart [30,41,42]. Further discussions on the phosphorene-MoSe 2 interface can be found in S.M.-Sec.…”

Strain-engineered widely tunable perfect absorption angle in black phosphorus from first principles

“…We consider the same form for the incident electromagnetic field, given by Eqs. (5), in the inhomogeneously strained system as that considered in the previous section for uniformly strained BP. By incorporating the above assumptions into Eq.…”

“…Bulk black phosphorus (BP) is an anisotropic semiconductor with two types of chemical bonding. Along two principal crystal directions, the phosphorus atoms form covalent bonds with a puckered honeycomb arrangement, whereas in the third direction atoms interact relatively weakly through van der Waals forces [1][2][3][4][5][6]. The latter bonding results in a layered configuration consisting of two-dimensional phosphorus sheets.…”

“…The latter bonding results in a layered configuration consisting of two-dimensional phosphorus sheets. These weakly interacting two-dimensional layers provide a unique opportunity to create different orderings of two-dimensional layers with extremely low-cost and simple operations, including displacement and twist [5][6][7][8][9][10][11][12][13][14][15][16][17]. The ordering and number of layers, as well as their deformation, can effectively control the electronic properties of BP-based devices.…”

Comparison of Optical Response from DFT Random Phase Approximation and Low-Energy Effective Model: Strained Phosphorene

“…[5] For example, density functional theory (DFT) calculations have shown success in simulating the general band gap trend as a function of the number of layers in certain twodimensional (2D) materials, such as black phosphorus, which constitutes a designed material (with desirable key characteristics such as epsilon-near-zero response [8,9]), and observed in experiments. [10][11][12][13][14][15][16][17] Many 2D materials consist of 2D layers of strongly bonded atoms attached to each other in the third dimension by weak forces. These weakly interacting 2D layers allow for designing novel materials with controllable electronics characteristics with low-cost operations, such as layer displacement.…”