The identification of the crystalline axis of anisotropic black phosphorus (BP) is key for the study of its physical properties and for its optical and electronic applications. Herein, we show that by applying an in-plane uniaxial strain and measuring the changes of Raman shifts, the crystalline axis of BP can be reliably determined. The strain effects on Raman shifts are angle-dependent, which can be expressed as a combination of Raman responses under zigzag and armchair strains. Different from previous polarized optical spectroscopic means, the proposed method does not rely on the laser polarization, the excitation wavelength, the sample thickness and the material of the stretchable substrate. Besides, the effective strain applied on BP from the stretched substrate is estimated, showing that only 20% to 40% of the strain can be effectively transferred to BP flakes from polyethylene terephthalate substrates. Our method provides not only an effective and universal approach to identify the crystalline orientation of layered BP, but also a model to extract additional information in strain-related studies, and can be extended to other 2D anisotropic materials.
In this work, we present a computational study on the possibility of strain engineering in monolayer Black Phosphorus (black P) and Blue Phosphorus (blue P) based MOSFETs. The material properties like band structure, carrier effective masses, carrier densities at band extrema are evaluated using Generalized Gradient Approximation (GGA) in Density Functional Theory (DFT).Thereafter self-consistent Non-Equilibrium Greens Function (NEGF) simulations are carried out to study the device performance metrics (such as output characteristics, ON currents, transconductance etc.) of such strained black P…
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…
The Poisson's ratio of a material characterizes its response to uniaxial strain. Materials normally possess a positive Poisson's ratio - they contract laterally when stretched, and expand laterally when compressed. A negative Poisson's ratio is theoretically permissible but has not, with few exceptions of man-made bulk structures, been experimentally observed in any natural materials. Here, we show that the negative Poisson's ratio exists in the low-dimensional natural material black phosphorus, and that our experimental observations are consistent with first principles simulations. Through ap…
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.
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 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)).
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 …
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…
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 …
Electronic structures of single crystalline black phosphorus were studied by state-of-art angleresolved photoemission spectroscopy. Through high resolution photon energy dependence measurements, the band dispersions along out-of-plane and in-plane directions are experimentally determined. The electrons were found to be more localized in the ab-plane than that is predicted in calculations. Beside the kz-dispersive bulk bands, resonant surface state is also observed in the momentum space. Our finds strongly suggest that more details need to be considered to fully understand the electronic proper…
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…
Negative Poisson's ratio (NPR) materials have attracted tremendous interest due to their unusual physical properties and potential applications. Certain two-dimensional (2D) monolayer materials have also been found to exhibit NPR and the corresponding deformation mechanism varies. In this study, we found, based on first-principles calculations, that the Poisson's ratio (PR) sign of monolayer Blue Phosphorus Oxide (BPO) can be tuned by strain: the PR is positive under uniaxial strain <= -1% but becomes negative under > 0. The deformation mechanism for BPO under strain depends on the mutual comp…
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…
The properties of metal-semiconductor junctions are often unpredictable because of non-ideal interfacial structures, such as interfacial defects or chemical reactions introduced at junctions. Black phosphorus (BP), an elemental two-dimensional (2D) semiconducting crystal, possesses the puckered atomic structure with high chemical reactivity, and the establishment of a realistic atomic-scale picture of BP's interface toward metallic contact has remained elusive. Here we examine the interfacial structures and properties of physically-deposited metals of various kinds on BP. We find that Au, Ag, …
Newly fabricated monolayer phosphorene and its few-layer structures are expected to be promising for electronic and optical applications because of their finite direct band gaps and sizable but anisotropic electronic mobility. By first-principles simulations, we show that this unique anisotropic conductance can be controlled by using simple strain conditions. With the appropriate biaxial or uniaxial strain, we can rotate the preferred conducting direction by 90 degrees. This will be of useful for exploring quantum Hall effects, and exotic electronic and mechanical applications based on phospho…
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-…
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 …
The Poisson's ratio is a fundamental mechanical property that relates the resulting lateral strain to applied axial strain. While this value can theoretically be negative, it is positive for nearly all materials, though negative values have been observed in so-called auxetic structures. However, nearly all auxetic materials are bulk materials whose microstructure has been specifically engineered to generate a negative Poisson's ratio. In the present work, we report using first principles calculations the existence of a negative Poisson's ratio in a single-layer, two-dimensional material, black…
Most recently, a brand new phosphorus allotrope called green phosphorus has been predicted, which has a direct band gap up to 2.4 eV, and its single-layer form termed green phosphorene shows high stability. Here the mechanical properties and the uniaxial strain effect on the electronic band structure of green phosphorene along two perpendicular in-plane directions are investigated. Remarkably, we find that this material can sustain a tensile strain in the armchair direction up to a threshold of 35\% which is larger than that of black phosphorene, suggesting that green phosphorene is more pucke…
Permanent magnet materials require a high uniaxial magneto-crystalline anisotropy. Exchange coupling between small crystallites with easy-plane anisotropy induces an effective uniaxial anisotropy if arranged accordingly. Nanostructuring of materials with easy-plane anisotropy is an alternative way to create hard-magnetic materials. The coercivity increases with decreasing feature size. The resulting coercive field is about 12 percent of the anisotropy field for a crystal size of 3.4 times the Bloch parameter.
As a new two-dimensional layered material, black phosphorus (BP) is a promising material for nanoelectronics and nano-optoelectronics. We use Raman spectroscopy and first-principles theory to report our findings related to low-frequency (LF) interlayer breathing modes (<100 cm-1) in few-layer BP for the first time. The breathing modes are assigned to Ag symmetry by the laser polarization dependence study and group theory analysis. Compared to the high-frequency (HF) Raman modes, the LF breathing modes are much more sensitive to interlayer coupling and thus their frequencies show much stronger …
Black phosphorus presents a very anisotropic crystal structure, making it a potential candidate for hyperbolic plasmonics, characterized by a permittivity tensor where one of the principal components is metallic and the other dielectric. Here we demonstrate that atomically thin black phosphorus can be engineered to be a hyperbolic material operating in a broad range of the electromagnetic spectrum from the entire visible spectrum to ultraviolet. With the introduction of an optical gain, a new hyperbolic region emerges in the infrared. The character of this hyperbolic plasmon depends on the int…
Black phosphorus (BP) has emerged as a direct-bandgap semiconducting material with great application potentials in electronics, photonics, and energy conversion. Experimental characterization of the anisotropic thermal properties of BP, however, is extremely challenging due to the lack of reliable and accurate measurement techniques to characterize anisotropic samples that are micrometers in size. Here, we report measurement results of the anisotropic thermal conductivity of bulk BP along three primary crystalline orientations, using the novel time-resolved magneto-optical Kerr effect (TR-MOKE…
Ferromagnetic resonance (FMR) technique has been used to study the magnetization relaxation processes and magnetic anisotropy in two different series of the Co2FeSi (CFS) Heusler alloy thin films, deposited on the Si(111) substrate by UHV sputtering. While the CFS films of fixed (50 nm) thickness, deposited at different substrate temperatures (TS) ranging from room temperature (RT) to 600^C, constitute the series-I, the CFS films with thickness t varying from 12 nm to 100 nm and deposited at 550^C make up the series-II. In series-I, the CFS films deposited at TS = RT and 200^C are completely a…
Recently, black phosphorus (BP) has joined the two dimensional material family as a promising candidate for photonic applications, due to its moderate bandgap, high carrier mobility, and compatibility with a diverse range of substrates. Photodetectors are probably the most explored BP photonic devices, however, their unique potential compared with other layered materials in the mid-infrared wavelength range has not been revealed. Here, we demonstrate BP mid infrared detectors at 3.39 um with high internal gain, resulting in an external responsivity of 82 A/W. Noise measurements show that such …
We present a theoretical survey of magnetocrystalline anisotropies in (Ga,Mn)As epilayers and compare the calculations to available experimental data. Our model is based on an envelope function description of the valence band holes and a spin representation for their kinetic-exchange interaction with localised electrons on Mn ions, treated in the mean-field approximation. For epilayers with growth induced lattice-matching strains we study in-plane to out-of-plane easy-axis reorientations as a function of Mn local-moment concentration, hole concentration, and temperature. Next we focus on the c…
The discovery of graphene and the related fascinating capabilities have triggered an unprecedented interest in inorganic two-dimensional (2D) materials. Despite the impressive impact in a variety of photonic applications, the absence of energy gap has hampered its broader applicability in many optoelectronic devices. The recent advance of novel 2D materials, such as transition-metal dichalcogenides or atomically thin elemental materials, (e.g. silicene, germanene and phosphorene) promises a revolutionary step-change. Here we devise the first room-temperature Terahertz (THz) frequency detector …
We present anisotropic thermal expansion measurements on single crystalline ErNi2B2C. All three, superconducting, antiferromagnetic and weak ferromagnetic phase transitions are unambiguously distinguished in the data. Anisotropic uniaxial pressure dependencies of the transitions are estimated based on the Ehrenfest relation, leading to a conclusion, in particular, that weak ferromagnetic state will be suppressed by small, order of several kbar, hydrostatic pressure.
Flexural thermal fluctuations in crystalline membranes affect the band structure of the carriers, which leads to an exponential density-of-states (DOS) tail beyond the unperturbed band edge. We present a theoretical description of this tail for a particular case of holes in single-layer black phosphorus, a material which exhibits an extremely anisotropic quasi-one-dimensional dispersion ($m_y/m_x\gg1$) and, as a result, an enhanced Van Hove singularity at the valence band top. The material parameters are determined by {\it ab initio} calculations and then are used for quantitative estimation o…
Quantum weight and low-loss EELS signatures of Wannier quantum geometry in black phosphorus
Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research（贾瓦哈拉尔·尼赫鲁高级科学研究中心理论科学部）；Institute of Science and Technology Austria（奥地利科学技术研究所）
Black phosphorus has attracted interest as a material for use in optoelectronic devices due to many favorable properties such as a high carrier mobility, field-effect, and a direct bandgap that can range from 0.3 eV in its bulk crystalline form to 2 eV for a single atomic layer. The low bandgap energy for bulk black phosphorus allows for direct transition photoabsorption that enables detection of light out to mid-infrared frequencies. In this work we characterize the room temperature optical response of a black phosphorus photoconductive detector at wavelengths ranging from 1.56 $μ$m to 3.75 $…
Isolation and characterization of mechanically exfoliated black phosphorus flakes with a thickness down to two single-layers is presented. A modification of the mechanical exfoliation method, which provides higher yield of atomically thin flakes than conventional mechanical exfoliation, has been developed. We present general guidelines to determine the number of layers using optical microscopy, Raman spectroscopy and transmission electron microscopy in a fast and reliable way. Moreover, we demonstrate that the exfoliated flakes are highly crystalline and that they are stable even in free-stand…
Two-dimensional crystals are emerging materials for nanoelectronics. Development of the field requires candidate systems with both a high carrier mobility and, in contrast to graphene, a sufficiently large electronic bandgap. Here we present a detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) in order to predict its electrical and optical properties. This system has a direct bandgap, tunable from 1.51 eV for a monolayer to 0.59 eV for a 5-layer sample. We predict that the mobilities are hole-dominated, rather high and highly anisotropi…
The photoinduced 3D orientational structures in the films of liquid crystalline polyester, containing azobenzene side groups, are studied both experimentally and theoretically. By using the null ellipsometry and the UV absorption methods, preferential in-plane alignment of the azobenzene fragments and in-plane reorientation under irradiation with polarized UV light are established. The uniaxial and biaxial orientational configurations of the azobenzene chromophores are detected. The biaxiality is observed in the intermediate stages of irradiation, whereas the uniaxial structure is maintained i…
Stacking two-dimensional (2D) materials into multi-layers or heterostructures, known as van der Waals (vdW) epitaxy, is an essential degree of freedom for tuning their properties on demand. Few-layer black phosphorus (FLBP), a material with high potential for nano- and optoelectronics applications, appears to have interlayer couplings much stronger than graphene and other 2D systems. Indeed, these couplings call into question whether the stacking of FLBP can be governed only by vdW interactions, which is of crucial importance for epitaxy and property refinement. Here, we perform a theoretical …
Phosphorene, a two-dimensional (2D) monolayer of black phosphorus, has attracted considerable theoretical interest, although the experimental realization of monolayer, bilayer, and few-layer flakes has been a significant challenge. Here we systematically survey conditions for liquid exfoliation to achieve the first large-scale production of monolayer, bilayer, and few-layer phosphorus, with exfoliation demonstrated at the 10-gram scale. We describe a rapid approach for quantifying the thickness of 2D phosphorus and show that monolayer and few-layer flakes produced by our approach are crystalli…
The photovoltaic effect is one of the fundamental light-matter interactions in light energy harvesting. In conventional photovoltaic solar cells, the photogenerated charge carriers are extracted by the built-in electric field of a PN junction, typically defined by ionic dopants in a semiconductor. In atomically thin semiconductors, the doping level can be controlled by the field-effect without need of implanting dopants in the lattice, which makes 2D semiconductors prospective materials to implement electrically tunable PN junctions. However, most 2D semiconducting materials do not show ambipo…
Cr2Ge2Te6 (CGT), a layered ferromagnetic insulator, has attracted a great deal of interest recently owing to its potential for integration with Dirac materials to realize the quantum anomalous Hall effect (QAHE) and to develop novel spintronics devices. Here, we study the uniaxial magnetic anisotropy energy of single-crystalline CGT and determine that the magnetic easy axis is directed along the c-axis in its ferromagnetic phase. In addition, CGT is an insulator below the Curie temperature. These properties make CGT a potentially promising candidate substrate for integration with topological i…
Anisotropic thermo-mechanical response of layered hexagonal boron nitride and black phosphorus: application as a simultaneous pressure and temperature sensor
Black phosphorus (BP) is an emerging two-dimensional semiconducting material with great potential for nanoelectronic and nanophotonic applications, especially owing to its unique anisotropic electrical and optical properties. Many theoretical studies have predicted the anisotropic optical properties of BP, but the direct experimental quantification remains challenging. The difficulties stem from the ease of BP's degradation when exposed to air in ambient conditions, and from the indirect nature of conventional approaches that are subject to large measurement uncertainties. This work reports a …
We report on a strain-induced and temperature dependent uniaxial anisotropy in V$_{2}$O$_{3}$/Ni hybrid thin films, manifested through the interfacial strain and sample microstructure, and its consequences on the angular dependent magnetization reversal. X-ray diffraction and reciprocal space maps identify the in-plane crystalline axes of the V$_{2}$O$_{3}$; atomic force and scanning electron microscopy reveal oriented rips in the film microstructure. Quasi-static magnetometry and dynamic ferromagnetic resonance measurements identify a uniaxial magnetic easy axis along the rips. Comparison wit…
Recent research works have shown that the magnetic order in some antiferromagnetic materials can be manipulated and detected electrically, due to two physical mechanisms: Neel-order spin-orbit torques and anisotropic magnetoresistance. While these observations open up opportunities to use antiferromagnets for magnetic memory devices, different physical characterization methods are required for a better understanding of those mechanisms. Here we report a magnetic field induced rotation of the antiferromagnetic Neel vector in epitaxial tetragonal CuMnAs thin films. Using soft x-ray magnetic line…
We study the effect of uniaxial strain on the band structure of ZrSe$_3$, a semiconducting material with a marked in-plane structural anisotropy. By using a modified 3-point bending test apparatus, thin ZrSe$_3$ flakes were subjected to uniaxial strain along different crystalline orientations monitoring the effect of strain on their optical properties through micro-reflectance spectroscopy. The obtained spectra showed excitonic features that blueshift upon uniaxial tension. This shift is strongly dependent on the direction along which the strain is being applied. When the flakes are strained a…
The magneto-crystalline anisotropy (MCA) of (Ga,Mn)As films has been studied on the basis of ab-initio electronic structure theory by performing magnetic torque calculations. An appreciable contribution to the in-plane uniaxial anisotropy can be attributed to an extended region adjacent to the surface. Calculations of the exchange tensor allow to ascribe a significant part to the MCA to the exchange anisotropy, caused either by a tetragonal distortion of the lattice or by the presence of the surface or interface.
Surface Phase-Field-Crystal-Helfrich model for out-of-plane deformations in thin crystalline sheets with lattice mismatch
TU Dresden（德累斯顿工业大学）；Dresden Center for Computational Materials Science, TU Dresden（德累斯顿计算材料科学中心，德累斯顿工业大学）；Cluster of Excellence - Physics of Live, TU Dresden（卓越集群-生命物理学，德累斯顿工业大学）；Center for Systems Biology Dresden (CSBD)（德累斯顿系统生物学中心）
We demonstrate strain-tuning of magnetocrystalline anisotropy over a range of more than one thousand Gauss in epitaxial Y3Fe5O12 films of excellent crystalline quality grown on lattice-mismatched Y3Al5O12 substrates. Ferromagnetic resonance (FMR) measurements reveal a linear dependence of both out-of-plane and in-plane uniaxial anisotropy on the strain-induced tetragonal distortion of Y3Fe5O12. Importantly, we find the spin mixing conductance G_r determined from inverse spin Hall effect and FMR linewidth broadening remains large: G_r = 3.33 x 10^14 Ohm^-1m^-2 in Pt/Y3Fe5O12/Y3Al5O12 heterostru…
Dopants in crystalline silicon such as phosphorus (Si:P) have electronic and nuclear spins with exceptionally long coherence times making them promising platforms for quantum computing and quantum sensing. The demonstration of single-spin single-shot readout brings these ideas closer to implementation. Progress in fabricating atomic-scale Si:P structures with scanning tunnelling microscopes offers a powerful route to scale up this work, taking advantage of techniques developed by the computing industry. The experimental and theoretical sides of this emerging quantum technology are reviewed wit…
Fourth-rank tensors of complete Voigt's symmetry, that embody the elastic properties of crystalline anisotropic substances, were constructed for all 2D crystal systems. Using them we obtained explicit expressions for inverse of Young's modulus E, inverse of shear modulus G and Poisson's ratio, which depend on components of the elastic compliances tensor S, on direction cosines of vectors n of uniaxial load and the vector m of lateral strain with crystalline symmetry axes. All 2D crystal systems are considered. Such representation yields decomposition of the above elastic characteristics to iso…
