Effect of van der Waals interactions on the structural and elastic properties of black phosphorus

Abstract

The structural and elastic properties of orthorhombic black phosphorus have been investigated using first-principles calculations based on density functional theory. The structural parameters have been calculated using the local density approximation (LDA), the generalized gradient approximation (GGA), and with several dispersion corrections to include van der Waals interactions. It is found that the dispersion corrections improve the lattice parameters over LDA and GGA in comparison with experimental results. The calculations reproduce well the experimental trends under pressure and show that van der Waals interactions are most important for the crystallographic b-axis, in the sense that they have the largest effect on the bonding between the phosphorus layers. The elastic constants are calculated and are found to be in good agreement with experimental values. The calculated C${}_{22}$ elastic constant is significantly larger than the C${}_{11}$ and C${}_{33}$ parameters, implying that black phosphorus is stiffer against strain along the a-axis than along the b- and c-axes. From the calculated elastic constants,the mechanical properties such as bulk modulus, shear modulus, Young's modulus and Poisson's ratio are obtained. The calculated Raman active optical phonon frequencies and their pressure variations are in excellent agreement with available experimental results.

23 pages, 7 figures

Cited by in corpus (64)

• High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus
• Electric field effect in ultrathin black phosphorus
• Liquid exfoliation of solvent-stabilised black phosphorus: applications beyond electronics
• Environmental instability of few-layer black phosphorus
• Layer-dependent Band Alignment and Work Function of Few-Layer Phosphorene
• Negative Poisson's Ratio in Single-Layer Black Phosphorus
• Black phosphorus: narrow gap, wide applications
• Solvent Exfoliation of Electronic-Grade, Two-Dimensional Black Phosphorus
• Plasma-assisted fabrication of monolayer phosphorene and its Raman characterization
• Phosphorene nanoribbons, nanotubes and van der Waals multilayers
• A black phosphorus photo-detector for multispectral, high-resolution imaging
• Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals
• Strain engineering in semiconducting two-dimensional crystals
• Strain Engineering for Phosphorene: The Potential Application as a Photocatalyst
• The Nature of the Interlayer Interaction in Bulk and Few-Layer Phosphorus
• Mechanical Properties of Single-Layer Black Phosphorus
• Strong modulation of optical properties in black phosphorus through strain-engineered rippling
• Hinge-like structure induced unusual properties of black phosphorus and new strategies to improve the thermoelectric performance
• Enhanced piezoelectricity and modified dielectric screening of 2-D group-IV monochalcogenides
• Modulation of electronic and mechanical properties of phosphorene through strain
• Remarkable effect of stacking on the electronic and optical properties of few layer black phosphorus
• A New Two-Dimensional Functional Material with Desirable Bandgap and Ultrahigh Carrier Mobility
• Black Phosphorus Nanoelectromechanical Resonators Vibrating at Very High Frequencies
• Native point defects in few-layer phosphorene
• Elastic properties of bulk and low-dimensional materials using Van der Waals density functional
• Anisotropic Ripple Deformation in Phosphorene
• Large Frequency Change with Thickness in Interlayer Breathing Mode - Significant Interlayer Interactions in Few Layer Black Phosphorus
• Electron-doped phosphorene: A potential monolayer superconductor
• Electronic Structures of Black Phosphorus Studied by Angle-resolved Photoemission Spectroscopy
• A Stillinger-Weber Potential for Single-Layer Black Phosphorus, and the Importance of Cross-Pucker Interactions for Negative Poisson's Ratio and Edge Stress-Induced Bending
• Theoretical studies of electronic transport in mono- and bi-layer phosphorene: A critical overview
• Layer-dependent surface potential of phosphorene and anisotropic/layer-dependent charge transfer in phosphorene-gold hybrid system
• Thermal Conduction in Single-Layer Black Phosphorus: Highly Anisotropic?
• Environmental Effects in Mechanical Properties of Few-layer Black Phosphorus
• Inverse Funnel Effect of Excitons in Strained Black Phosphorus
• Drastic enhancement of the Raman intensity in few-layer InSe by uniaxial strain
• Role of Interlayer Coupling on the Evolution of Band Edges in Few-Layer Phosphorene
• Anisotropic buckling of few-layer black phosphorus
• Raman anomalies as signatures of pressure induced electronic topological and structural transitions in black phosphorus: Experiments and Theory
• Electric-field tunable Dirac semimetal state in phosphorene thin films
• Effects of intrinsic strain on the structural stability and mechanical properties of phosphorene nanotubes
• Large phosphorene in-plane contraction induced by interlayer interactions in graphene-phosphorene heterostructures
• Dirac-semimetal phase diagram of two-dimensional black phosphorus
• Elastic Bending Modulus for Single-Layer Black Phosphorus
• Simulated scanning tunneling microscopy images of few-layer-phosphorus capped by graphene and hexagonal boron nitride monolayers
• Strain-induced Weyl and Dirac states and direct-indirect gap transitions in group-V materials
• Optical Properties of Anisotropic Excitons in Phosphorene
• Strength and Stability Analysis of a Single Walled Black Phosphorus Tube under Axial Compression
• Anisotropic Charge Carrier and Coherent Acoustic Phonon Dynamics of Black Phosphorus Studied by Transient Absorption Microscopy
• High temperature electron-hole superfluidity with strong anisotropic gaps in double phosphorene monolayers
• Gate induced monolayer behavior in twisted bilayer black phosphorus
• Lattice dynamics and electronic structure of energetic solids LiN3 and NaN3: A first principles study
• Stacking dependence of carrier transport properties in multilayered black phosphorous
• Lattice dynamics and elastic properties of black phosphorus
• Mono-elemental saturable absorber in mode-locked fiber laser: A review
• Investigation of structural and elastic properties of monoclinic Ba${}_2$P${}_7$X (X $=$ Cl, Br, I) Zintl Salts compounds
• Structure, elastic and dynamical properties of KN${}_3$ and RbN${}_3$: A van der Waals density functional study
• Coexistence of pressure-induced structural phases in bulk black phosphorus: a combined x-ray diffraction and Raman study up to 18 GPa
• Thermal stability of a free nanotube from single-layer black phosphorus
• Black Phosphorus and Phosphorene/Graphene Heterostructure as Alkali metal (Li, Na, and K) Ion Battery
• Bilayer Phosphorene: Effect of Stacking Order on Bandgap and its Potential Applications in Thin-Film Solar Cells
• Electronic and optical properties of crystalline nitrogen versus black phosphorus: A comparative first-principles study
• Multifield phonon spectrometrics of structured liquid and solid crystals
• Non-adiabatic suppression of 3D excitonic screening in black phosphorus by mid-infrared pulses