Strain and the optoelectronic properties of nonplanar phosphorene monolayers

Significance Phosphorene is a new 2D atomic material, and we document a drastic reduction of its electronic gap when under a conical shape. Furthermore, geometry determines the properties of 2D materials, and we introduce discrete differential geometry to study them. This geometry arises from particle/atomic positions; it is not based on a parametric continuum, and it applies across broad disciplinary lines. Lattice kirigami, ultralight metamaterials, polydisperse aggregates, ceramic nanolattices, and 2D atomic materials share an inherent structural discreteness, and their material properties evolve with their shape. To exemplify the intimate relation among material properties and the local geometry, we explore the properties of phosphorene––a new 2D atomic material––in a conical structure, and document a decrease of the semiconducting gap that is directly linked to its nonplanar shape. This geometrical effect occurs regardless of phosphorene allotrope considered, and it provides a unique optical vehicle to single out local structural defects on this 2D material. We also classify other 2D atomic materials in terms of their crystalline unit cells, and propose means to obtain the local geometry directly from their diverse 2D structures while bypassing common descriptions of shape that are based from a parametric continuum.

• Publication year

  2015

• Venue

  Proceedings of the National Academy of Sciences of the United States of America

• Publication date

  2015-04-27

• Fields of study

  Medicine, Materials Science, Physics

• Identifiers
  DOI 10.1073/pnas.1500633112arXiv 1504.07275PMID 25918413PMCID 4434758
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Black phosphorus field-effect transistors.

  2014cited by this paper
• Strong, lightweight, and recoverable three-dimensional ceramic nanolattices

  2014cited by this paper
• Strain-Engineering Anisotropic Electrical Conductance of Phosphorene

  2014cited by this paper
• Strain-induced gap modification in black phosphorus.

  2014cited by this paper
• Quantitative chemistry and the discrete geometry of conformal atom-thin crystals.

  2014cited by this paper
• Tunable Phonon Polaritons in Atomically Thin van der Waals Crystals of Boron Nitride

  2014cited by this paper
• Tuning of the electronic and optical properties of single-layer black phosphorus by strain

  2014cited by this paper
• Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus

  2014cited by this paper
• Transition-metal dichalcogenide bilayers: Switching materials for spintronic and valleytronic applications

  2014cited by this paper
• Graphene's morphology and electronic properties from discrete differential geometry

  2014cited by this paper
• Phosphorene: an unexplored 2D semiconductor with a high hole mobility.

  2014cited by this paper
• Making the cut: lattice kirigami rules.

  2014cited by this paper
• Simulated scanning tunneling microscopy images of few-layer phosphorus capped by graphene and hexagonal boron nitride monolayers

  2014cited by this paper
• Stability and properties of high-buckled two-dimensional tin and lead

  2014cited by this paper
• Phosphorene: An Unexplored 2D Semiconductor with a High Hole

  2014cited by this paper
• Phase coexistence and metal-insulator transition in few-layer phosphorene: a computational study.

  2014cited by this paper
• Polydispersity-driven topological defects as order-restoring excitations

  2014cited by this paper
• Semiconducting layered blue phosphorus: a computational study.

  2014cited by this paper
• Two-dimensional mono-elemental semiconductor with electronically inactive defects: the case of phosphorus.

  2014influential reference
• Local curvature and stability of two-dimensional systems

  2014cited by this paper
• Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus.

  2014influential reference
• Tiling phosphorene.

  2014cited by this paper
• Dislocation reactions, grain boundaries, and irreversibility in two-dimensional lattices using topological tweezers

  2013cited by this paper
• Mechanical model of blebbing in nuclear lamin meshworks

  2013cited by this paper
• Large-gap quantum spin Hall insulators in tin films.

  2013cited by this paper
• Observation time scale, free-energy landscapes, and molecular symmetry

  2013cited by this paper
• Universal collapse of stress and wrinkle-to-scar transition in spherically confined crystalline sheets

  2013cited by this paper
• Local strain engineering in atomically thin MoS2.

  2013cited by this paper
• High-Strength Chemical-Vapor–Deposited Graphene and Grain Boundaries

  2013cited by this paper
• Topologically protected quantum transport in locally exfoliated bismuth at room temperature.

  2013cited by this paper
• Defect motifs for constant mean curvature surfaces.

  2013cited by this paper
• Computational discovery of single-layer III-V materials

  2013cited by this paper
• The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets.

  2013cited by this paper
• Extraordinary room-temperature photoluminescence in WS$_{2}$ monolayers

  2013cited by this paper
• Electronics and optoelectronics of two-dimensional transition metal dichalcogenides.

  2012cited by this paper
• Extraordinary room-temperature photoluminescence in triangular WS2 monolayers.

  2012cited by this paper
• Optical materials: Inspired by strain

  2012cited by this paper
• Construction of discrete shell models by geometric finite differences

  2012cited by this paper
• Graphene: Carbon in Two Dimensions

  2012influential reference
• Designer Dirac fermions and topological phases in molecular graphene

  2012cited by this paper
• Platonic and Archimedean geometries in multicomponent elastic membranes

  2011cited by this paper
• Gauge fields in graphene

  2010cited by this paper
• Pleats in crystals on curved surfaces

  2010cited by this paper
• Crossover of the three-dimensional topological insulator Bi 2 Se 3 to the two-dimensional limit

  2009cited by this paper
• Fabrication of a freestanding boron nitride single layer and its defect assignments.

  2009cited by this paper
• Two- and one-dimensional honeycomb structures of silicon and germanium.

  2008cited by this paper
• Discrete differential geometry : An applied introduction

  2008cited by this paper
• Discrete Differential Geometry

  2008cited by this paper
• Crystallography on curved surfaces

  2006cited by this paper
• Two-dimensional gas of massless Dirac fermions in graphene

  2005cited by this paper
• Two-dimensional atomic crystals.

  2005cited by this paper
• Quantum spin Hall effect in graphene.

  2004cited by this paper
• Energy Landscapes by David Wales

  2004cited by this paper
• Grain Boundary Scars and Spherical Crystallography

  2003cited by this paper
• The Geometry of Soft Materials: A Primer

  2002cited by this paper
• The SIESTA method for ab initio order-N materials simulation

  2001cited by this paper
• Generalized Gradient Approximation Made Simple.

  1996cited by this paper
• Chemistry of the Fullerenes: The Manifestation of Strain in a Class of Continuous Aromatic Molecules

  1993cited by this paper
• Unified approach for molecular dynamics and density-functional theory.

  1985cited by this paper
• Computers and Mathematics with Applications Discrete Schemes for Gaussian Curvature and Their Convergence

  year unknowncited by this paper

• Predicting photovoltaic efficiency of two-dimensional Janus materials for applications in solar energy harvesting: A combined first-principles and machine learning study

  2026cites this paper
• Strain driven modulations in electronic, optical properties and photovoltaic efficiencies of 2D AH (A = Si, Ge) monolayers: An account from first-principles study

  2025cites this paper
• First-principles study on structural, electronic, optical and photovoltaic properties of Sc2C-based Janus MXenes for solar cell applications

  2025cites this paper
• Insights into the auxetic behavior of graphene: A study on the temperature dependence of Poisson's ratio and in-plane moduli

  2023cites this paper
• Rippled blue phosphorene with tunable energy band structures and negative Poisson’s ratio

  2023cites this paper
• Highly stable electronic properties of rippled antimonene under compressive deformation

  2022cites this paper
• Effect of stacking order on the vibration properties of bilayer black phosphorus

  2022cites this paper
• Tunneling effect in phosphorene through double barriers

  2021cites this paper
• Enhanced photocatalytic activity of phosphorene under different pH values using density functional theory (DFT)

  2021cites this paper
• Energy spectrum for charge carriers in graphene with folded deformations or with flexural modes with Gaussian and Lévy distributed random pseudo-magnetic fields

  2021cites this paper
• Two-Dimensional Black Phosphorus Nanomaterials: Emerging Advances in Electrochemical Energy Storage Science

  2020cites this paper
• Graphene gets bent

  2020cites this paper
• Optoelectronic properties of pristine antimonene, phosphorene and their binary compound

  2020cites this paper
• Tunable charge density wave in a lateral black/blue phosphorene heterostructure: A first-principles calculation

  2020cites this paper
• Electronic properties of two-dimensional materials

  2020cites this paper
• Excellent Thermoelectric and Piezoelectric Properties of Differently Stacked Layers of Two-Dimensional Transition Metal Dinitride HfN2

  2020cites this paper
• Supreme enhancement of ferromagnetism in a spontaneous-symmetry-broken 2D nanomagnet

  2020cites this paper
• Property-Activity Relationship of Black Phosphorus at the Nano-Bio Interface: From Molecules to Organisms.

  2020cites this paper
• Bandgap tuning of two-dimensional materials by sphere diameter engineering

  2020cites this paper
• Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities

  2020cites this paper
• The effect of strain on the zigzag and armchair phosphorene nanoribbon

  2020cites this paper
• Phosphorene pnp junctions as perfect electron waveguides

  2020cites this paper
• Junye Cheng1,3, Lingfeng Gao2, Tian Li3, Shan Mei4, Cong Wang2, Bo Wen2, Weichun Huang5, Chao Li2, Guangping Zheng3, Hao Wang1 *, Han Zhang2 *

  2020cites this paper
• Electron optics in phosphorene pn junctions: Negative reflection and anti-super-Klein tunneling.

  2019cites this paper
• Metastable interlayer Frenkel pair defects in black phosphorus

  2019cites this paper
• Group-IV monochalcogenide monolayers: Two-dimensional ferroelectrics with weak intralayer bonds and a phosphorenelike monolayer dissociation energy

  2019cites this paper
• First-principles Study of Structural and Optical Properties of Novel Materials

  2019cites this paper
• Ultrafast diffusive cross-sheet motion of lithium through antimonene with 2 + 1 dimensional kinetics

  2019cites this paper
• Applications of Phosphorene and Black Phosphorus in Energy Conversion and Storage Devices

  2018cites this paper
• A Perspective on Recent Advances in Phosphorene Functionalization and Its Applications in Devices

  2018cites this paper
• Extracting the Energy Sensitivity of Charge Carrier Transport and Scattering

  2018cites this paper
• Metal-insulator transition in 8−Pmmn borophene under normal incidence of electromagnetic radiation

  2018cites this paper
• Optical transitions and localized edge states in skewed zigzag phosphorene nanoribbons

  2018cites this paper
• Strain Modulation of Electronic Properties of Monolayer Black Phosphorus

  2017cites this paper
• Tuning the ferroelectric-to-paraelectric transition temperature and dipole orientation of group-IV monochalcogenide monolayers

  2017cites this paper
• Quasiparticle band gaps and optical spectra of strained monolayer transition-metal dichalcogenides

  2017cites this paper
• Recent advances in black phosphorus-based photonics, electronics, sensors and energy devices

  2017cites this paper
• Recent Advances in the Study of Phosphorene and its Nanostructures

  2017cites this paper
• Electronic and optical properties of strained graphene and other strained 2D materials: a review

  2016cites this paper
• Molecular Structure and Dynamics of Water on Pristine and Strained Phosphorene: Wetting and Diffusion at Nanoscale

  2016cites this paper
• First-principles study of the defected phosphorene under tensile strain

  2016cites this paper
• Atomic structures and electronic properties of phosphorene grain boundaries

  2016cites this paper
• Bending Two-Dimensional Materials To Control Charge Localization and Fermi-Level Shift.

  2016cites this paper
• Light-Matter Interactions in Phosphorene.

  2016cites this paper
• Strong Modulation of Optical Properties in Black Phosphorus through Strain-Engineered Rippling.

  2015cites this paper
• Geometry and bandgaps

  2015cites this paper
• Mechanical properties of phosphorene nanoribbons and oxides

  2015cites this paper
• Quasiparticle energies, excitons, and optical spectra of few-layer black phosphorus

  2015cites this paper
• Quantum confinement in black phosphorus through strain-engineered rippling

  2015cites this paper
• Wetting and Diffusion of Water on Pristine and Strained Phosphorene

  2015cites this paper
• Discrete differential geometry and the properties of conformal two-dimensional materials

  2015cites this paper
• Thermal conductivity of armchair black phosphorus nanotubes: a molecular dynamics study

  2015cites this paper
• Out-of-plane structural flexibility of phosphorene

  2015cites this paper
• Strain engineering in semiconducting two-dimensional crystals

  2015cites this paper
• Intrinsic Defects, Fluctuations of the Local Shape, and the Photo-Oxidation of Black Phosphorus

  2015cites this paper