Abstract
We perform comprehensive density-functional theory calculations on strained two-dimensional phosphorus (P), arsenic (As) and antimony (Sb) in the monolayer, bilayer, and bulk α-phase, from which we compute the key mechanical and electronic properties of these materials. Specifically, we compute their electronic band structures, band gaps, and charge-carrier effective masses, and identify the qualitative electronic and structural transitions that may occur. Moreover, we compute the elastic properties such as the Young’s modulus Y; shear modulus G; bulk modulus ; and Poisson ratio ν and present their isotropic averages of as well as their dependence on the in-plane orientation, for which the relevant expressions are derived. We predict strain-induced Dirac states in the monolayers of As and Sb and the bilayers of P, As, and Sb, as well as the possible existence of Weyl states in the bulk phases of P and As. These phases are predicted to support charge velocities up to 106 m and, in some highly anisotropic cases, permit one-dimensional ballistic conductivity in the puckered direction. We also predict numerous band gap transitions for moderate in-plane stresses. Our results contribute to the mounting evidence for the utility of these materials, made possible by their broad range in tuneable properties, and facilitate the directed exploration of their potential application in next-generation electronics.
Highlights
Two-dimensional black phosphorus (BP), or phosphorene, is one of several predicted stable allotropes of few-layer phosphorus [1,2,3,4], and it has attracted considerable attention since its recent successful synthesis [5,6,7,8,9] that is possible with liquid phase exfoliation [10, 11]
We find that the lattice parameter along the puckered direction, ‘a’, shortens as the number of layers increases, which agrees with observations in other studies
We have extensively explored the mechanical and electronic properties of P, As and Sb in their few-layer and bulk phases
Summary
Two-dimensional black phosphorus (BP), or phosphorene, is one of several predicted stable allotropes of few-layer phosphorus [1,2,3,4], and it has attracted considerable attention since its recent successful synthesis [5,6,7,8,9] that is possible with liquid phase exfoliation [10, 11]. The anisotropic crystal structure of BP is responsible for its unusual electro-mechanical properties, which are predicted to be strongly directional-dependent and highly responsive to mechanically strain [11, 19]. With this renewed interest in BP, focus has quickly turned to few-layer phases of the other pnictogens, namely arsenic [28] (As), antimony [29] (Sb), bismuth [30, 31] (Bi), and their alloys [32,33,34,35,36] which are attracting steadily increasing attention. Many of the predicted straininduced properties of these materials, such as directindirect band gap transitions [13, 28, 29, 55, 56], a negative Poisson’s ratio [18, 57], as well as electronic [2, 55, 58], structural [59], and topological [51, 60,61,62] transitions, are already spurring their incorporation in emergent technologies such as field-effect transistors [8, 20], gas-sensors [63, 64], optical switches [65, 66], solar-cells [34], next-generation batteries [67,68,69],
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