The mechanical properties of single-layer black phosphrous under uniaxial deformation are investigated using first-principles calculations. Both Young's modulus and the ultimate strain are found to be highly anisotropic and nonlinear as a result of its quasi-two-dimensional puckered structure. Specifically, the in-plane Young's modulus is 44.0 GPa in the direction perpendicular to the pucker, and 92.7 GPa in the parallel direction. The ultimate strain is 0.48 and 0.20 in the perpendicular and parallel directions, respectively.
It is of critical importance to understand the mechanical properties change of electrode materials during lithium intercalation in the mechanical design of Li-ion batteries, for the purpose of the high reliability and safety in their applications. Here, we investigated the mechanical properties of both bulk and single layer phosphorus during the lithium intercalation process by using the first-principles calculations. Our results show that the Young's modulus of bulk and layered phosphorus strongly depends on the lithium intercalation. The mechanical bearing capacities, such as critical strain…
Two-dimensional black phosphorus has been configured as field-effect transistors, showing an intrinsic symmetric ambipolar transport characteristic. Here, we demonstrate the strongly modulated ambipolar characteristics of few-layer black phosphorus in oxygen. Pure oxygen exposure can dramatically decrease the electron mobility of black phosphorus without degrading the hole transport. The transport characteristics can be nearly recovered upon annealing in Argon. This reveals that oxygen molecules are physisorbed on black phosphorus. In contrast, oxygen exposure upon light illumination exhibits …
We perform classical molecular dynamics to investigate the effects of mechanical strain on single-layer black phosphorus nanoresonators at different temperatures. We find that the resonant frequency is highly anisotropic in black phosphorus due to its intrinsic puckered configuration, and that the quality factor in the armchair direction is higher than in the zigzag direction at room temperature. The quality factors are also found to be intrinsically larger than graphene and MoS2 nanoresonators. The quality factors can be increased by more than a factor of two by applying tensile strain, with …
We report on the mechanical properties of few-layer black phosphorus (BP) nanosheets, in high vacuum and as a function of time of exposure to atmospheric conditions [1]. BP flakes with thicknesses ranging from 4 to 30 nm suspended over circular holes are characterized by nanoindentations using an atomic force microscope tip. From measurements in high vacuum an elastic modulus of 46+/-10 GPa and breaking strength of 2.4+/-1 GPa are estimated. Both magnitudes are independent of the thickness of the flakes. Our results show that the exposure to air has substantial influence in the mechanical resp…
Phosphorus atomic chains, the utmost-narrow nanostructures of black phosphorus (BP), are highly relevant to the in-depth development of BP into one-dimensional (1D) regime. In this contribution, we report a top-down route to prepare atomic chains of BP via electron beam sculpting inside a transmission electron microscope (TEM). The growth and dynamics (i.e. rupture and edge migration) of 1D phosphorus chains are experimentally captured for the first time. Furthermore, the dynamic behaviors and associated energetics of the as-formed phosphorus chains are further corroborated by density function…
Energy bandgap largely determines the optical and electronic properties of a semiconductor. Variable bandgap therefore makes versatile functionality possible in a single material. In layered material black phosphorus, the bandgap can be modulated by the number of layers; as a result, few-layer black phosphorus has discrete bandgap values that are relevant for opto-electronic applications in the spectral range from red, in monolayer, to mid-infrared in the bulk limit. Here, we further demonstrate continuous bandgap modulation by mechanical strain applied through flexible substrates. The strain-…
We show that black phosphorus has room-temperature charge mobilities on the order of 10$^4$ cm$^2$V$^{-1}$s$^{-1}$, which are about one order of magnitude larger than silicon. We also demonstrate strong anisotropic transport in black phosphorus, where the mobilities along the armchair direction are about one order of magnitude larger than zigzag direction. A photocarrier lifetime as long as 100 ps is also determined. These results illustrate that black phosphorus is a promising candidate for future electronic and optoelectronic applications.
Functionalization of atomically thin nanomaterials enables the tailoring of their chemical, optical, and electronic properties. Exfoliated black phosphorus, a layered two-dimensional semiconductor exhibiting favorable charge carrier mobility, tunable bandgap, and highly anisotropic properties, is chemically reactive and degrades rapidly in ambient conditions. In contrast, here we show that covalent aryl diazonium functionalization suppresses the chemical degradation of exfoliated black phosphorus even following weeks of ambient exposure. This chemical modification scheme spontaneously forms ph…
This paper reports a few-layer black phosphorus thickness pattern fabricated by a top-down nanofabrication approach. This was achieved by a new wet etching process that can etch selected regions of few-layer black phosphorus with an atomic layer accuracy. This method is deep-UV and e-beam lithography process compatible,and is free of oxygen and other common doping sources. It provides a feasible patterning approach for largescale manufacturing of few-layer BP materials and devices.
An investigation of the mechanical, electronic, and optical properties of the recently reported material K4 phosphorus was made in this work. The K4 phosphorus has been proved to be mechanically and dynamically stable up to 7 GPa under hydrostatic pressure. We compared the elastic anisotropy, average acoustic velocity and Debye temperature of K4 phosphorus at 0 and 7 GPa. The ideal tensile at large strains of K4 phosphorus was also examined, with the results showing that it would cleave under the tensile strength of 8.5 GPa with the strain of 0.3. In addition, the effect of tensile strain and …
Black phosphorene is not stable at ambient conditions, so atomic defects and oxidation effects are unavoidable in black phosphorus samples in the experiment. The effects of these defects on the performance of the black phosphorus nanoresonators are still unclear. Here, we perform classical molecular dynamics to investigate the effects of the vacancy and oxidation on single-layer black phosphorus nanoresonators at different temperatures. We find that the vacancy causes strong reduction in the quality factor of the nanoresonators, while the oxidation has weaker effect on the nanoresonators. More…
Black phosphorus (BP) nanostructures enable a new strategy to tune the electronic and optical properties of this atomically thin material. In this paper we show, via density functional theory calculations, the possibility to modify the optical properties of BP quantum dots via covalent functionalization. The quantum dot selected in this study has chemical formula P24H12 and has been covalent functionalized with one or more benzene rings or anthracene. The effect of functionalization is highlighted in the absorption spectra, where a red shift of the absorption is noticeable. The shift can be as…
The single-layer black phosphorus is characteristic for its puckered configuration that possesses the hinge-like mechanism, which leads to the highly anisotropic in-plane Poisson's ratios and the negative out-of-plane Poisson's ratio. We reveal that the hinge-like mechanism can be attributed to the angle-angle cross interaction, which, combined with the bond stretching and angle bending interactions, is able to provide a good description of the mechanical properties in the single-layer black phosphorus. We also propose a nonlinear angle-angle cross interaction, which follows the form of the St…
The success of black phosphorus in fast electronic and photonic devices is hindered by its rapid degradation in presence of oxygen. Orthorhombic tin selenide is a representative of group IV-VI binary compounds that are robust, isoelectronic, and share the same structure with black phosphorus. We measured the band structure of SnSe and found highly anisotropic valence bands that form several valleys having fast dispersion within the layers and negligible dispersion across. This is exactly the band structure desired for efficient thermoelectric generation where SnSe has shown a great promise.
Utilizing a combination of low-temperature scanning tunneling microscopy/spectroscopy (STM/STS) and electronic structure calculations, we characterize the structural and electronic properties of single atomic vacancies within several monolayers of the surface of black phosphorus. We illustrate, with experimental analysis and tight-binding calculations, that we can depth profile these vacancies and assign them to specific sublattices within the unit cell. Measurements reveal that the single vacancies exhibit strongly anisotropic and highly delocalized charge density, laterally extended up to 20…
Atomic structure of single-crystalline black phosphorus was studied by high resolution synchrotron-based photoelectron diffraction (XPD). The results show that the topmost phosphorene layer in the black phosphorus is slightly displaced compared to the bulk structure and presents a small contraction in the direction perpendicular to the surface. Furthermore, the XPD results show the presence of a small buckling among the surface atoms, in agreement with previously reported scanning tunneling microscopy results. The contraction of the surface layer added to the presence of the buckling indicates…
Twisted stacked few layer black phosphorus heterostructures were successfully fabricated in this work. Abnormal blue shifts in their Ag1 and Ag2 Raman peaks and unique optical reflections were observed in these samples. The phonon behavior difference can be explained by our density functional theory calculations, which suggest that interlayer coupling has a significant effect in twisted bilayer black phosphorus. According to the calculations, the interlayer interactions are not simply van der Waals interactions. Additional interactions, such as weak valence bonding between the top and bottom f…
The single-layer black phosphorus is characteristic for its puckered structure, which has leaded to highly anisotropy in its optical, electronic, and mechanical properties. We report, using the non-equilibrium Green's function approach and the first-principles method, that the anisotropy in the thermal conduction is very weak in the single-layer black phosphorus -- the difference between two in-plane directions is less than 4%. Our phonon calculations disclose that the two in-plane acoustic phonon branches have lower group velocities in the direction perpendicular to the pucker, as the black p…
The interlayer breathing and shear modes in few-layer black phosphorus are investigated for their symmetry and lattice dynamical properties. The symmetry groups for the even-layer and odd-layer few-layer black phosphorus are utilized to determine the irreducible representation and the infrared and Raman activity for the interlayer modes. The valence force field model is applied to calculate the eigenvectorw and frequencies for the interlayer breathing and shear modes, which are explained using the atomic chain model. The anisotropic puckered configuration for black phosphorus leads to a highly…
We ascertain the anisotropic thermal conductivity of alumina passivated black phosphorus (BP), a reactive 2D nanomaterial with strong in-plane anisotropy. We measure the room temperature thermal conductivity by time-domain thermoreflectance for the three crystalline axes of exfoliated BP. The thermal conductivity along the zigzag direction (86 +/- 8 W/(m*K)) is ~2.5 times higher than that of the armchair direction (34 +/- 4 W/(m*K)).
The distinguishing structural feature of single-layer black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layer black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the lon…
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…
Few-layer black phosphorus has recently emerged as a promising candidate for novel electronic and optoelectronic device. Here we demonstrate by first-principles calculations and Boltzmann theory that, black phosphorus could also have potential thermoelectric applications and a fair ZT value of 1.1 can be achieved at elevated temperature. Moreover, such value can be further increased to 5.4 by substituting P atom with Sb atom, giving nominal formula of P0.75Sb0.25. Our theoretical work suggests that high thermoelectric performance can be achieved without using complicated crystal structure or s…
In this work, we reported uniform layer-by-layer sublimation of black phosphorus under heating below 600 K. The uniformity and crystallinity of BP samples after thermal thinning were confirmed by Raman spectra and 2D Raman imaging. A uniform and crystalline bilayer black phosphorus flake with an area of 180 um^2 was prepared with this method. No micron scale defects were observed. The sublimation rate of BP was around 0.18 nm / min at 500 K and 1.5 nm / min at 550 K. Both room and high temperature Raman peak intensity ratio Si/A2g vs. BP thickness relations were established for in-situ thickne…
Intercalation is an effective method to improve and modulate properties of two-dimensional materials. Even so, spatially controlled intercalation at atomic scale, which is important to introduce and modulated properties, has not been successful due to difficulties in controlling the diffusion of intercalants. Here, we show formation of angstrom-wide conductive channels (~4.3 A) in black phosphorus by Cu intercalation. The atomic structure, resultant microstructural effects, intercalation mechanism, and local variations of electronic properties modulated in black phosphorus by Cu intercalation …
We report operating temperatures and heating coefficients measured in a multi-layer black phosphorus device as a function of injected electrical power. By combining micro-Raman spectroscopy and electrical transport measurements, we have observed a linear temperature increase up to 600K at a power dissipation rate of 0.896Kμm^3/mW. By further increasing the bias voltage, we determined the threshold power and temperature for electrical breakdown and analyzed the fracture in the black phosphorus layer that caused the device failure by means of scanning electron microscopy and atomic force microsc…
We study the charged impurity limited mobility in black phosphorus, a highly anisotropic layered material. We compute the mobility within the Boltzmann transport equation under detailed balance condition, and taking into account the anisotropy in transport and electronic structure. For carrier densities accessible in experiments, we obtained an anisotropy ratio of 3 ~ 4 at zero temperature, two-folds larger than that observed in experiments on multilayers samples. We discuss also how the anisotropy depends on carrier density and impurity distribution.
Black phosphorus is not stable when it is exposed to air. When covered or terminated by single layer carbon atoms, such as graphene carbon nanotube, it is more strongly protected in the rapid degradation than the bare black phosphorus. Moreover, due to weak interaction between phosphorus atoms in black phosphorene, the nanotube obtained by curling single layer black phosphorus is not as stable as a carbon nanotube at finite temperature. In present work, we recommend a new 1D material, i.e., composite double wall nanotubes from a black phosphorus nanotube with a CNT. The dynamic response of the…
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…
We derive an analytic formula for the Young's modulus in single-layer black phosphorus using the valence force field model. By analyzing the directional dependence for the Young's modulus, we explore the third principle direction with direction angle phi_tp = 0.268pi besides armchair and zigzag directions. The maximum Young's modulus value is in the third principle direction. More specifically, the Young's modulus is 52.2 N/m, 85.4 N/m, and 111.4 N/m in the armchair direction, zigzag direction, and the third principle direction, respectively. This new principle direction is of significance for…
Graphene, as a passivation layer, can be used to protect the black phosphorus from the chemical reaction with surrounding oxygen and water. However, black phosphorus and graphene heterostructures have low efficiency of heat dissipation due to its intrinsic high thermal resistance at the interfaces. The accumulated energy from Joule heat has to be removed efficiently to avoid the malfunction of the devices. Therefore, it is of significance to investigate the interfacial thermal dissipation properties and manipulate the properties by interfacial engineering on demand. In this work, the interfaci…
We derive an analytic formula for the elastic bending modulus of single-layer black phosphorus (SLBP) based on the valence force field model. The obtained elastic bending modulus is 4.8028 eV and 7.9905 eV along the armchair and zigzag directions in the SLBP, respectively. These values are obviously larger than the bending modulus of 1.4 eV in graphene due to the intrinsic finite thickness for SLBP. Our derivation analytically illustrates that the elastic bending modulus of the SLBP is proportional to the square of the intrinsic thickness of the SLBP.
Exfoliated black phosphorus has recently emerged as a new two-dimensional crystal that, due to its peculiar and anisotropic crystalline and electronic band structures, may have potentially important applications in electronics, optoelectronics and photonics. Despite the fact that the edges of layered crystals host a range of singular properties whose characterization and exploitation are of utmost importance for device development, the edges of black phosphorus remain poorly characterized. In this work, the atomic structure and the behavior of phonons near different black phosphorus edges are …
We are reporting a new synthetic strategy to grow large size black phosphorus (Black-P) crystals through a ternary clathrate Sn$_{24}$P$_{22-x}$I$_8$, under lower synthetic temperature and pressure. The Black-P crystals are found grown in situ at the site where the solid clathrate originally resides, which suggests chemical vapor mineralizer does not play a critical role for the Black-P formation. More detailed systematical studies has indicated the P vacancies in the framework of ternary clathrate Sn$_{24}$P$_{22-x}$I$_8$ is important for the subsequent Black-P from phosphorus vapors, and a l…
Black phosphorus has recently attracted significant attention for its highly anisotropic properties. A variety of ultrafast optical spectroscopies has been applied to probe the carrier response to photoexcitation, but the complementary lattice response has remained unaddressed. Here we employ femtosecond electron diffraction to explore how the structural anisotropy impacts the lattice dynamics after photoexcitation. We observe two timescales in the lattice response, which we attribute to electron-phonon and phonon-phonon thermalization. Pronounced differences between armchair and zigzag direct…
The effects of size, strain, and vacancies on thermal properties of armchair black phosphorus nanotubes are investigated based on qualitative analysis from molecular dynamics simulations. It is found that the thermal conductivity has a remarkable size effect because of the restricted paths for phonon transport, strongly depending on the diameter and length of nanotube. Owing to the intensified low-frequency phonons, axial tensile strain can facilitate thermal transport. On the contrary, compressive strain weakens thermal transport due to the enhanced phonon scattering around the buckling of na…
We study the carrier relaxation dynamics in thin black phosphorus (bP) using time-resolved differential transmission measurements. The inter-band and intra-band transitions, relaxation, and carrier recombination lifetimes are revealed by tuning the mid-infrared probe wavelength above and below the bandgap of black phosphorus. When the probe energy exceeds the bandgap, Pauli blocked inter-band transitions are observed. The differential transmission signal changes sign from positive to negative when the probe energy is below the bandgap, due to the absence of inter-band transitions and enhanceme…
We report a scalable approach to synthesize a large-area (up to 4 mm) thin black phosphorus (BP) film on a flexible substrate. We first deposited a red phosphorus (RP) thin-film on a flexible polyester substrate, followed by its conversion to BP in a high-pressure multi-anvil cell at room temperature. Raman spectroscopy and transmission electron microscopy measurements confirmed the formation of a nano-crystalline BP thin-film with a thickness of around 40 nm. Optical characterization indicates a bandgap of around 0.28 eV in the converted BP, similar to the bandgap measured in exfoliated thin-…
Contrary to empirical observations, lowest-order $k\cdot\hat{p}$ theory predicts that monolayer black phosphorus ("phosphorene") is completely immune to zigzag-polarized optical excitation at the bandgap energy. Using symmetry arguments, we derive a $2\times2$ Hamiltonian under the $k\cdot\hat{p}$ formalism including higher-order corrections, which is used to show that the experimentally-measured band-gap transition with zigzag polarization is dominated by the third order $k\cdot\hat{p}$ perturbation in the interband optical matrix element, whereas the effects of spin-orbit interaction are neg…
In this work, we correlated the angular dependence of the Raman response of black phosphorus to its crystallographic orientation by using transmission electron microscopy and Raman spectroscopy. It was found that the intensity of the A2g mode reached a maximum when the polarization direction of the incident light was parallel to the zigzag crystallographic orientation. Notably, it was further confirmed that the zigzag crystallographic direction exhibited superior conductance and carrier mobility. Because of the lattice extension along the armchair direction, an intensification of the anisotrop…
We study theoretically the structural and electronic response of layered bulk black phosphorus to in-layer strain. Ab initio density functional theory (DFT) calculations reveal that the strain energy and interlayer spacing display a strong anisotropy with respect to the uniaxial strain direction. To correctly describe the dependence of the fundamental band gap on strain, we used the computationally more involved GW quasiparticle approach that is free of parameters and superior to DFT studies, which are known to underestimate gap energies. We find that the band gap depends sensitively on the in…
We report ambipolar transport properties in black phosphorus using an electric-double-layer transistor (EDLT) configuration. The transfer curve clearly exhibits ambipolar transistor behavior with an ON-OFF ratio of 5*10^3. The band gap was determined as = 0.35 eV from the transfer curve, and Hall-effect measurements revealed that the hole mobility was ~ 190 cm^2/Vs at 170 K, which is one order of magnitude larger than the electron mobility. By inducing an ultra-high carrier density of ~ 10^14 cm^-2, an electric-field-induced transition from the insulating state to the metallic state was realiz…
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…
We report a study of the structural phase transitions induced by pressure in bulk black phosphorus by using both synchrotron x-ray diffraction for pressures up to 12.2 GPa and Raman spectroscopy up to 18.2 GPa. Very recently black phosphorus attracted large attention because of the unique properties of fewlayers samples (phosphorene), but some basic questions are still open in the case of the bulk system. As concerning the presence of a Raman spectrum above 10 GPa, which should not be observed in an elemental simple cubic system, we propose a new explanation by attributing a key role to the no…
The low formation energy of atomic vacancies in black phosphorus allows it to serve as an ideal prototypical system for exploring the dynamics of interlayer interstitial-vacancy (I-V) pairs (i.e. Frenkel defects) which account for Wigner energy release. Based on a few-layer model of black phosphorus, we conduct discrete geometry analysis and investigate the structural dynamics of intimate interlayer Frenkel pairs from first-principles calculations. We reveal a highly metastable I-V pair state driven by anisotropic dipole-like strain fields which can build strong connections between neighbourin…
Artificial lattices have been employed in many two-dimensional systems, including those of electrons, atoms and photons, in a quest for massless Dirac particles with flexibility and controllability. Periodically patterned molecule assembly and electrostatic gating as well as moiré pattern induced by substrate, have produced electronic states with linear dispersions from isotropic two-dimensional electron gas (2DEG). Here we demonstrate that massless Dirac fermions with tunable anisotropic characteristics can, in general, be generated in highly anisotropic 2DEG under slowly varying external per…
Black phosphorus is a very promising material for telecommunication due to its direct bandgap and strong resonant absorption in near-infrared wavelength range. However, ultrafast nonlinear photonic applications relying on the ultrafast photo-carrier dynamics as well as optical nonlinearity in black phosphorus remain unexplored. In this work, we investigate nonlinear optical properties of solution exfoliated BP and demonstrate the usage of BP as a new saturable absorber for high energy pulse generation in fiber laser. In order to avoid the oxidization and degradation of BP, we encapsulated BP b…
Black phosphorus is a quasi-two-dimensional layered semiconductor with a narrow direct band gap of 0.3 eV. A giant surface Stark effect can be produced by the potassium doping of black phosphorus, leading to a semiconductor to semimetal phase transition originating from the creation of a strong surface dipole and associated band bending. By using time- and angle-resolved photoemission spectroscopy, we report the partial photoinduced screening of this band bending by the creation of a compensating surface photovoltage. We further resolve the detailed dynamics of this effect at the pertinent tim…
Thermal conductivity of single layer black phosphorus (BP) is investigated by combining density functional calculations and Peierls-Boltzmann transport equation. Differing from isotropic and divergent thermal conductivities in two-dimensional graphene and MoS$_2$, an compelling co-existence of size-dependent and size-independent thermal conductivities are discovered for single layer BP along zigzag (ZZ) and armchair (AM) direction, respectively. Besides, thermal conductivities in single layer BP are found to be highly anisotropic because of orientation dependent group velocities, e.g., thermal…
We present an analytic study, based on the tight-binding approximation, of strain effects on the electronic bandgap in single-layer black phosphorus. We obtain an expression for the variation of the bandgap induced by a general strain type that includes both tension in and out of the plane and shear, and use this to determine the most efficient strain direction for different strain types, along which the strongest bandgap manipulation can be achieved. We find that the strain direction that enables the maximum manipulation of the bandgap is not necessarily in the armchair or zigzag direction. I…
The competition between the electron-hole Coulomb attraction and the three-dimensional dielectric screening dictates the optical properties of layered semiconductors. In low-dimensional materials, the equilibrium dielectric environment can be significantly altered by the ultrafast excitation of photo-carriers, leading to renormalized band gap and exciton binding energies. Recently, black phosphorus emerged as a 2D material with strongly layer-dependent electronic properties. Here, we resolve the coherent response of screening to sub-gap photo-excitation in bulk black phosphorus and find that m…
The Lennard-Jones potential is widely used to describe the interlayer interactions within layered materials like graphene. However, it is also widely known that this potential strongly underestimates the frictional properties for layered materials. Here we propose to supplement the Lennard-Jones potential by a Gaussian-type potential, which enables more accurate calculations of the frictional properties of two-dimensional layered materials. Furthermore, the Gaussian potential is computationally simple as it introduces only one additional potential parameter that is determined by the interlayer…
Black Phosphorus (BP) is unique among layered materials owing to its homonuclear lattice and strong structural anisotropy. While recent investigations on few layers BP have extensively explored the in-plane (a,c) anisotropy, much less attention has been given to the out-of-plane direction (b). Here, the optical response from bulk BP is probed using polarization-resolved photoluminescence (PL), photoluminescence excitation (PLE) and resonant Raman scattering along the zigzag, out-of-plane, and armchair directions. PL reveals an unexpected b-polarized emission occurring in the visible at 1.75 eV…
