We study the mechanical and electronic properties of heterobilayers composed of black phosphorus (BP) on hexagonal boron nitride (hBN) and of blue phosphorus (\Pblue) on hBN by means of ab-intio density functional theory. Emphasis is put on how the stress applied on the constituent layers impact their structural and electronic properties. For this purpose, we adopt a specific scheme of structural relaxation which allows us to distinguish between the energy cost of distorting each layer and the gain in stacking them together. In most cases we find that the BP tends to contract along the softer armchair direction, as already reported for similar structures. This contraction can attain up to 5\% of strain, which might deteriorate its very good transport properties along the armchair direction. To prevent this, we propose a twisted-bilayer configuration where the largest part of the stress applies on the zigzag axis, resulting in a lower impact on the transport properties of BP. We also investigated a \Pblue/hBN bilayer. A peculiar hybridization between the valence states of the two layers lets us suggest that electron-hole pairs excited in the bilayer will exhibit a mixed character, with electrons localized solely in the \Pblue{ }layer, and holes spread onto the two layers.
Based on ab initio evolutionary crystal structure search computation, we report a new phase of phosphorus called green phosphorus (λ-P), which exhibits the direct band gaps ranging from 0.7 to 2.4 eV and the strong anisotropy in optical and transport properties. Free energy calculations show that a single-layer form, termed green phosphorene, is energetically more stable than blue phosphorene and a phase transition from black to green phosphorene can occur at temperatures above 87 K. Due to its buckled structure, green phosphorene can be synthesized on corrugated metal surfaces rather than cle…
Studies of polynitrogen phases are of great interest for fundamental science and for the design of novel high energy density materials. Laser heating of pure nitrogen at 140 GPa in a diamond anvil cell led to the synthesis of a polymeric nitrogen allotrope with the black phosphorus structure, bp-N. The structure was identified in situ using synchrotron single-crystal X-ray diffraction and further studied by Raman spectroscopy and density functional theory calculations. The discovery of bp-N brings nitrogen in line with heavier pnictogen elements, resolves incongruities regarding polymeric nitr…
Elemental phosphorus nanostructures are notorious for a large number of allotropes, which limits their usefulness as semiconductors. To limit this structural diversity, we synthesize selectively quasi-1D phosphorus nanostructures inside carbon nanotubes (CNTs) that act both as stable templates and nanoreactors. Whereas zigzag phosphorus nanoribbons form preferably in CNTs with an inner diameter exceeding 1.4 nm, a previously unknown square columnar structure of phosphorus is observed to form inside narrower nanotubes. Our findings are supported by electron microscopy and Raman spectroscopy obs…
We explore the impact of strain on charge carrier mobility of monolayer $α$, $β$, $γ$ and $δ$-P, the four well known atomically thin allotropes of phosphorus, using density functional theory. Owing to the highly anisotropic band dispersion, the charge carrier mobility of the pristine allotropes is significantly higher (more than 5 times in some cases) in one of the principal directions (zigzag or armchair) as compared to the other. Uniaxial strain (upto 6% compressive/tensile) leads to bandgap alteration in each of the allotropes, especially a direct to indirect bandgap semiconductor transitio…
In this letter, we show that a new class of two-dimensional phosphorus allotropes can be constructed via assembling the previously proposed ultrathin metastable phosphorus nanotube into planar structures in different stacking orientations. Based on first-principles method, the structures, stabilities and fundamental electronic properties of these new two-dimensional phosphorus allotropes are systematically investigated. These two-dimensional phosphorus allotropes possess remarkable stabilities due to the strong inter-tube van der Waals interactions, which cause an energy release of about 30-70…
During past years, a number of reports have been published on synthesis of tetragonal allotrope of boron, t-B52 phase. However, no unambiguous characterization of the crystal structure has been performed to the present time, while remarkable variation of the a/c lattice-parameter ratio raises strong doubts about its uniqueness. Here the Rietveld refinement of the crystal structure of the high pressure - high temperature boron phase synthesized by a direct solid-state transformation of rhombohedral beta-B106 at 20 GPa and 2500 K has been reported for the first time. Although this boron allotrop…
Theoretical predictions of pressure-induced phase transformations often become long-standing enigmas because of limitations of contemporary available experimental possibilities. Hitherto the existence of a non-icosahedral boron allotrope has been one of them. Here we report on the first non-icosahedral boron allotrope, which we denoted as ζ-B, with the orthorhombic α-Ga-type structure (space group Cmce) synthesized in a diamond anvil cell at extreme high-pressure high-temperature conditions (115 GPa and 2100 K). The structure of ζ-B was solved using single-crystal synchrotron X-ray diffraction…
We study the effect of electron doping on the bonding character and stability of two-dimensional (2D) structures of elemental boron, called borophene, which is known to form many stable allotropes. Our {\em ab initio} calculations for the neutral system reveal previously unknown stable 2D $ε$-B and $ω$-B structures. We find that the chemical bonding characteristic in this and other boron structures is strongly affected by extra charge. Beyond a critical degree of electron doping, the most stable allotrope changes from $ε$-B to a buckled honeycomb structure. Additional electron doping, mimickin…
We present an ab-initio study of boron nitride as well as carbon allotropes. Their relative thermodynamic stabilities and structural phase transitions from low- to high-density phases are investigated. Pressure-temperature phase diagrams are calculated and compared to experimental findings. The calculations are performed using quantum chemical wavefunction based as well as density functional theories. Our findings reveal that predicted energy differences often depend significantly on the choice of the employed method. Comparison between calculated and experimental results allows for benchmarki…
It has been widely accepted that planar boron structures, composed of triangular and hexagonal motifs are the most stable two dimensional (2D) phases and likely precursors for boron nanostructures. Here we predict, based on ab initio evolutionary structure search, novel 2D boron structure with non-zero thickness, which is considerably, by 50 meV/atom lower in energy than the recently proposed alpha-sheet structure and its analogues. In particular, this phase is identified for the first time to have a distorted Dirac cone, after graphene and silicene the third elemental material with massless D…
We predict a new three-dimensional (3D) boron allotrope based on systematic first-principles electronic structure calculations. This allotrope can be derived by substituting each carbon atom in a hexagonal diamond lattice with a B$_{4}$ tetrahedron and possesses the same space group $P6_{3}/mmc$ as hexagonal diamond, hence it is termed as H-boron. We show that H-boron has good stability and excellent mechanical property. Remarkably, we find that H-boron is a topological metal with rich types of spin-orbit-free emergent fermions, including semi-Dirac fermion, quadratic and linear triple-point f…
The encapsulation of two-dimensional layered materials such as black phosphorus is of paramount importance for their stability in air. However, the encapsulation poses several questions, namely, how it affects, via the weak van der Waals forces, the properties of the black phosphorus and whether these properties can be tuned on demand. Prompted by these questions, we have investigated the impact of hexagonal boron nitride encapsulation on the structural and vibrational properties of few layer black phosphorus, using a first-principles method in the framework of density functional theory. We de…
The search for metallic boron allotropes has attracted great attention in the past decades and recent theoretical works predict the existence of metallicity in monolayer boron. Here, we synthesize the \b{eta}12-sheet monolayer boron on a Ag(111) surface and confirm the presence of metallic boron-derived bands using angle-resolved photoemission spectroscopy. The Fermi surface is composed of one electron pocket at the S point and a pair of hole pockets near the X point, which is supported by the first-principles calculations. The metallic boron allotrope in \b{eta}12 sheet opens the way to novel…
The allotropes of boron continue to challenge structural elucidation and solid-state theory. Here we use machine learning combined with random structure searching (RSS) algorithms to systematically construct an interatomic potential for boron. Starting from ensembles of randomized atomic configurations, we use alternating single-point quantum-mechanical energy and force computations, Gaussian approximation potential (GAP) fitting, and GAP-driven RSS to iteratively generate a representation of the element's potential-energy surface. Beyond the total energies of the very different boron allotrop…
We propose previously unknown allotropes of phosphorus carbide (PC) in the stable shape of an atomically thin layer. Different stable geometries, which result from the competition between sp2 bonding found in graphitic C and sp3 bonding found in black P, may be mapped onto 2D tiling patterns that simplify categorizing of the structures. Depending on the category, we identify 2D-PC structures that can be metallic, semi-metallic with an anisotropic Dirac cone, or direct-gap semiconductors with their gap tunable by in-layer strain.
Phosphorus is one of the most abundant elements preserved in earth, constructing with a fraction of ~0.1% of the earth crust. In general, phosphorus has several allotropes. The two most commonly seen allotropes, white and red phosphorus, are widely used in explosives and safety matches. In addition, black phosphorus, though rarely mentioned, is a layered semiconductor and have great potentials in optical and electronic applications. Remarkably, this layered material can be reduced to one single atomic layer in the vertical direction owing to the van der Waals structure, known as phosphorene, w…
Based on {\em ab initio} density functional calculations, we propose $γ$-P and $δ$-P as two additional stable structural phases of layered phosphorus besides the layered $α$-P (black) and $β$-P (blue) phosphorus allotropes. Monolayers of some of these allotropes have a wide band gap, whereas others, including $γ$-P, show a metal-insulator transition caused by in-layer strain or changing the number of layers. An unforeseen benefit is the possibility to connect different structural phases at no energy cost. This becomes particularly valuable in assembling heterostructures with well-defined metal…
Elemental phosphorous is believed to have several stable allotropes that are energetically nearly degenerate, but chemically reactive. To prevent chemical degradation under ambient conditions, these structures may be capped by monolayers of hexagonal boron nitride ({\em h}-BN) or graphene. We perform {\em ab initio} density functional calculations to simulate scanning tunneling microscopy (STM) images of different layered allotropes of phosphorus and study the effect of capping layers on these images. We find that protective monolayers of insulating {\em h}-BN allow to distinguish between the …
Ab initio calculations within the density-functional theory formalism are performed to investigate the chemical functionalization of a graphene-like monolayer of silicon - silicene - with B, N, Al or P atoms. The structural, electronic, magnetic and vibrational properties are reported. The most preferable adsorption sites are found to be valley, bridge, valley and hill site for B, N, Al and P adatoms, respectively. All the relaxed systems with adsorbed/substituted atoms exhibit metallic behaviour with strongly bonded B, N, Al, and P atoms accompanied by an appreciable electron transfer from si…
We investigate a previously unknown phase of phosphorus that shares its layered structure and high stability with the black phosphorus allotrope. We find the in-plane hexagonal structure and bulk layer stacking of this structure, which we call `blue phosphorus', to be related to graphite. Unlike graphite and black phosphorus, blue phosphorus displays a wide fundamental band gap and should exfoliate easily to form quasi-2D structures suitable for electronic applications. We study a likely transformation pathway from black to blue phosphorus and discuss possible ways to synthesize the new struct…
In this letter we propose a new methodology for crystal structure prediction, which is based on the evolutionary algorithm USPEX and the machine-learning interatomic potentials actively learning on-the-fly. Our methodology allows for an automated construction of an interatomic interaction model from scratch replacing the expensive DFT with a speedup of several orders of magnitude. Predicted low-energy structures are then tested on DFT, ensuring that our machine-learning model does not introduce any prediction error. We tested our methodology on a problem of prediction of carbon allotropes, den…
We investigate two dimensional monolayer structures of arsenic phosphorus ( AsP) by means of first principles plane wave method within density functional theory using the generalized gradient approximation. Two structures of arsenic phosphorus are taken into account which are called buckled (B-AsP) and puckered (Pu-AsP). From our numerical calculations we predicted the optimized states of a single-layer buckled and puckered honeycomb like allotropes of AsP. We demonstrate that buckled and puckered arsenic phosphorus are semiconducting single layers with band gap energies 1.858 eV and 0.924 eV,…
The elemental two-dimensional (2D) materials such as graphene, silicene, germanene, and black phosphorus have attracted considerable attention due to their fascinating physical properties. Structurally they possess the honeycomb or distorted honeycomb lattices, which are composed of six-atom rings. Here we find a new structure of 2D allotropes of group V elements composed of eight-atom rings, which we name as the octagonal tiling (OT) structure. First-principles calculations indicate that these allotropes are dynamically stable and are also thermally stable at temperatures up to 600 K. These a…
Inspired by the successful synthesis of several allotropes, boron sheets have been one of the hottest spot areas of focus in various fields. Here, we study phonon transport in three types of boron nanoribbons with zigzag and armchair edges by using a non-equilibrium Green's function combined with first principles methods. Diverse transport properties are found in the nanoribbons. At the room temperature, their highest thermal conductance can be comparable with that of graphene, while the lowest thermal conductance is less than half of graphene's. The three boron sheets exhibit different anisot…
We study the effect of boron (B) and Phosphorous (P) co-doping on electronic and optical properties of graphitic carbon nitride (g-C$_3$N$_4$ or GCN) monolayer using density functional simulations. The energy band structure indicates that the incorporation of B and P into a hexagonal lattice of GCN reduces the energy band gap from $3.1$ for pristine GCN to $1.9$ eV, thus extending light absorption toward the visible region. Moreover, on the basis of calculating absorption spectra and dielectric function, the co-doped system exhibits an improved absorption intensity in the visible region and mo…
Anisotropic thermo-mechanical response of layered hexagonal boron nitride and black phosphorus: application as a simultaneous pressure and temperature sensor
Research on black phosphorus (BP) has been experiencing a renaissance over the last few years, after the demonstration that few-layer BP exhibits high carrier mobility and a thickness-dependent band gap. For a long time, bulk BP is also known to be a superconductor under high pressure exceeding 10 GPa. The superconductivity is due to a structural transformation into another allotrope of phosphorous and accompanied by a semiconductor-metal transition. No superconductivity could be achieved for BP itself (that is, in its normal orthorhombic form) despite several attempts reported in the literatu…
In amorphous materials, acceptor and donor impurities rarely dope the system (shift the Fermi level). We find out why in a-Si:H. We report simulations on B and P doping of a-Si:H and a-Si. We analyze the Electronic Density of States (EDOS) with concentrations ranging from 1.6% to 12.5% of B or P in a-Si. The results indicate that tetrahedral B and P are effective doping configurations in a-Si, but high impurity concentrations introduce defect states. Clustered B or P also introduced mid-gap states. For a-Si:H, we report that both B(3,1) and P(3,1) (B or P atom bonded with three Si atoms and on…
First-principles calculations predicted monolayer blue phosphorus to be an alternative two-dimensional allotrope of phosphorus, like the recently discovered monolayer black phosphorus. Due to its unique crystalline and electronic structure, blue phosphorus may be a promising candidate as a BCS-superconductor after proper intercalation. In this study, using first-principles calculations, the favorable intercalation sites for some alkali metals and alkaline earths have been identified for Blue-P bilayer and the stacking configuration of bilayer is changed. Then the blue phosphorus bilayer transf…
We show that the optical and electronic properties of nanocrystalline silicon can be efficiently tuned using impurity doping. In particular, we give evidence, by means of ab-initio calculations, that by properly controlling the doping with either one or two atomic species, a significant modification of both the absorption and the emission of light can be achieved. We have considered impurities, either boron or phosphorous (doping) or both (codoping), located at different substitutional sites of silicon nanocrystals with size ranging from 1.1 nm to 1.8 nm in diameter. We have found that the cod…
Thin layers of black phosphorus present an ideal combination of a 2D material with a tunable direct bandgap and high carrier mobility. However the material suffers from degradation in ambient conditions due to an oxidation reaction which involves water, oxygen and light. We have measured the spatial profile of the conductivity on flakes of black phosphorus as a function of time using scanning microwave impedance microscopy. A microwave excitation (3 GHz) allows to image a conducting sample even when covered with a dielectric layer. We observe that on bare black phosphorus, the conductivity cha…
A review of electronic properties of insulating-, boron- and phosphorus-doped diamond is given. The main goal is, to show data in a wider context, to reveal trends and limitations with respect to carrier mobilities, conductivities, p- and n-type doping. Undoped diamond is an insulator with conductivities significantly smaller than 10^-17 Ohmcm at room temperature. Mostly, these insulating films show conductivity activation energies of 1.7 eV, an indication that small amounts of substitutional nitrogen dominates the Fermi-level. The electron and hole mobilities are very high (> 20.000 cm2/Vs at…
The complex crystal chemistry of elemental boron has led to numerous proposed structures with distinctive motifs as well as contradictory findings. Herein, evolutionary structure searches performed at 100 GPa have uncovered a series of potential new metastable phases of boron, and bonding analyses were carried out to elucidate their electronic structure. These polymorphs, dynamically stable at 100 GPa, were grouped into two families. The first was derived from the thermodynamic minimum at these conditions, $α$-Ga, whereas channels comprised the second. Two additional intergrowth structures wer…
Defects are inevitably present in two-dimensional (2D) materials and usually govern their various properties. Here a comprehensive density functional theory-based investigation of 7 kinds of point defects in a recently produced γ allotrope of 2D phosphorus carbide (γ-PC) is conducted. The defects, such as antisites, single C or P, and double C and P and C and C vacancies, are found to be stable in γ-PC, while the Stone-Wales defect is not presented in γ-PC due to its transition metal dichalcogenides-like structure. The formation energies, stability, and surface density of the considered defect…
Black phosphorus (bP) is the second known elemental allotrope with a layered crystal structure that can be mechanically exfoliated down to atomic layer thickness. We have fabricated bP naked quantum wells in a back-gated field effect transistor geometry with bP thicknesses ranging from $6\pm1$ nm to $47\pm1$ nm. Using an encapsulating polymer superstrate, we have suppressed bP oxidation and have observed field effect mobilities up to 600 cm$^2$/Vs and on/off current ratios exceeding $10^5$. Importantly, Shubnikov-de Haas (SdH) oscillations observed in magnetotransport measurements up to 35 T r…
As a way to further improve the electronic properties of group V layered semiconductors, we propose to form in-layer 2D heterostructures of black phosphorus and grey arsenic. We use \textit{ab initio} density functional theory to optimize the geometry, determine the electronic structure, and identify the most stable allotropes as a function of composition. Since pure black phosphorus and pure grey arsenic monolayers differ in their equilibrium structure, we predict a structural transition and a change in frontier states, including a change from a direct-gap to an indirect-gap semiconductor, wi…
Single layer (SL) phosphorus (phosphorene) has drawn considerable research attention recently as a two-dimensional (2D) material for application promises. It is a semiconductor showing superior transport and optical properties. Few-layer or SL black phosphorus has been successfully isolated by exfoliation from bulk crystals and extensively studied thereof for its electronic and optical properties. Blue phosphorus (blueP), an allotrope of black phosphorus where atoms are arranged in a more flat atomic configuration, has been recently suggested by theory to exist in the SL form on some substrate…
Two-dimensional (2D) layered materials with diverse properties have attracted significant interest in the past decade. The layered materials discovered so far have covered a wide, yet discontinuous electromagnetic spectral range from semimetallic graphene, insulating boron nitride, to semiconductors with bandgaps from middle infrared to visible light. Here, we introduce new layered semiconductors, black arsenic-phosphorus (b-AsP), with highly tunable chemical compositions and electronic and optical properties. Transport and infrared absorption studies demonstrate the semiconducting nature of b…
Topological metal/semimetals (TMs) have emerged as a new frontier in the field of quantum materials. A few two-dimensional (2D) boron sheets have been suggested as Dirac materials, however, to date TMs made of three-dimensional (3D) boron structures have not been found. Herein, by means of systematic first principles computations, we discovered that a rather stable 3D boron allotrope, namely 3D-alpha' boron, is a nodal-chain semimetal. In the momentum space, six nodal lines and rings contact each other and form a novel spindle nodal chain. This 3D-alpha' boron can be formed by stacking 2D wigg…
Few layer phosphorene(FLP) devices are extensively studied due to its unique electronic properties and potential applications on nano-electronics . Here we present magnetotransport studies which reveal electron-electron interactions as the dominant scattering mechanism in hexagonal boron nitride-encapsulated FLP devices. From weak localization measurements, we estimate the electron dephasing length to be 30 to 100 nm at low temperatures, which exhibits a strong dependence on carrier density n and a power-law dependence on temperature (~T-0.4). These results establish that the dominant scatteri…
Crystalline black nitrogen (BN) is an allotrope of nitrogen with the black phosphorus (BP) structure recently synthesized at high pressure by two independent research groups [Ji et al., Sci. Adv. 6, eaba9206 (2020); Laniel et al., Phys. Rev. Lett. 124, 216001 (2020)]. Here, we present a systematic study of the electronic and optical properties of BN focusing on its comparison with BP. To this end, we use the state-of-the-art quasiparticle self-consistent $GW$ approach with vertex corrections in both the electronic and optical channels. Despite many similarities, the properties of BN are found …
Two-dimensional electron gases (2DEG) have been an important source of experimental discovery and conceptual development in condensed matter physics for decades. When combined with the unique electronic properties of two-dimensional (2D) crystals, rich new physical phenomena can be probed at the quantum level. Here, we create a new 2DEG in black phosphorus, a recent member of the two-dimensional atomic crystal family, using a gate electric field. We achieve high carrier mobility in black phosphorus 2DEG by placing it on a hexagonal boron nitride substrate (h-BN). This allows us, for the first …
Schwarzites are porous structures that present negative Gaussian curvatures. Although initially proposed for carbon, in principle, schwarzites of other elements are possible. In this work, we have carried out a detailed investigation of the effect of element composition (C, Ge, Si, SiC, and BN) on the structural, electronic and optical properties of a gyroid schwarzite structure, the so-called G688. The DFT simulations were carried out using the well-known SIESTA code. Our results showed that formation energy values are in similar range of other related allotrope structures and are thermally s…
Ultrathin black phosphorus, or phosphorene, is the second known elementary two-dimensional material that can be exfoliated from a bulk van der Waals crystal. Unlike graphene it is a semiconductor with a sizeable band gap and its excellent electronic properties make it attractive for applications in transistor, logic, and optoelectronic devices. However, it is also the first widely investigated two dimensional electronic material to undergo degradation upon exposure to ambient air. Therefore a passivation method is required to study the intrinsic material properties, understand how oxidation af…
The preferred location of boron and phosphorus in oxidized free-standing Si nanoparticles was investigated using a first-principles density functional approach. The calculated formation energies indicate that P should segregate to the silicon core, whereas B is equally stable in the Si and SiO_2 regions. Our models thus suggest that, in contrast with nanocrystals with H-terminated surfaces, the efficiency of phosphorus incorporation in oxidized Si nanoparticles can be improved by thermal annealing.
Anisotropy refers to the property of a material exhibiting directionally dependent features. In this paper, we introduce black phosphorous (BP), the most stable allotrope of phosphorus in layered orthorhombic structure with a bandgap of 0.3 eV in bulk, as a unique 2D material in which electrons, phonons and their interactions with photons behave in a highly anisotropic manner within the plane of the layers. The unique anisotropic nature of BP thin films is revealed using angle-resolved Raman and infrared spectroscopies, together with angle-resolved transport study. For 15 nm thick BP, we measu…
Penta-graphene (PG) is a carbon allotrope that has recently attracted the attention of the materials science community due to its interesting properties for renewable energy applications. Although unstable in its pure form, it has been shown that functionalization may stabilize its structure. A question that arises is whether its outstanding electronic properties could also be further improved using such a procedure. As PG bilayers present both sp$^2$ and sp$^3$ carbon planes, it consists of a flexible candidate for functionalization tuning of electromagnetic properties. In this work, we perfo…
We simulate dopant profiles for phosphorus implantation into silicon using a new model for electronic stopping power. In this model, the electronic stopping power is factorized into a globally averaged effective charge Z1*, and a local charge density dependent electronic stopping power for a proton. There is only a single adjustable parameter in the model, namely the one electron radius rs0 which controls Z1*. By fine tuning this parameter, we obtain excellent agreement between simulated dopant profiles and the SIMS data over a wide range of energies for the channeling case. Our work provides …
Layered and two-dimensional (2D) materials such as graphene, boron nitride, transition metal dichalcogenides(TMDCs), and black phosphorus (BP) have intriguing fundamental physical properties and bear promise of numerous important applications in electronics and optics. Of them, BP is a novel 2D material that has been theoretically predicted to acquire plasmonic behavior for frequencies below ~0.4 eV when highly doped. The electronic properties of BP are unique due to an anisotropic structure, which could strongly influence collective electronic excitations. Advantages of BP as a material for n…
Two-dimensional materials, such as graphene, boron nitride and transition metal dichalcogenides, have attracted increased interest due to their potential applications in electronics and optoelectronics. Thermal transport in two-dimensional materials could be quite different from three-dimensional bulk materials. This article reviews the progress on experimental measurements and theoretical modeling of phonon transport and thermal conductivity in two-dimensional materials. We focus our review on a few typical two-dimensional materials, including graphene, boron nitride, silicene, transition met…
Based on variable components global optimization algorithm, we predict a stable two-dimensional (2D) phase of boron phosphide with 1:5 stoichiometry, i.e. boron pentaphosphide (BP_5) monolayer, which has a lower formation energy than that of the commonly believed graphitic phase (g-BP). BP_5 monolayer is a multiferroic material with coupled ferroelasticity and ferroelectricity. The predicted reversible strain is up to 41.41%, which is the largest among all reported ferroelastic materials. Due to the non-centrosymmetric structure and electronegativity differences between boron and phosphorus at…
