Black phosphorus (BP) has emerged as a promising material candidate for next generation electronic and optoelectronic devices due to its high mobility, tunable band gap and highly anisotropic properties. In this work, polarization resolved ultrafast mid-infrared transient reflection spectroscopy measurements are performed to study the dynamical anisotropic optical properties of BP under magnetic fields up to 9 T. The relaxation dynamics of photoexcited carrier is found to be insensitive to the applied magnetic field due to the broadening of the Landau levels and large effective mass of carriers. While the anisotropic optical response of BP decreases with increasing magnetic field, its enhancement due to the excitation of hot carriers is similar to that without magnetic field. These experimental results can be well interpreted by the magneto-optical conductivity of the Landau levels of BP thin film, based on an effective k*p Hamiltonian and linear response theory. These findings suggest attractive possibilities of multi-dimensional controls of anisotropic response (AR) of BP with light, electric and magnetic field, which further introduces BP to the fantastic magnetic field sensitive applications.
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.
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)).
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…
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…
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…
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 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…
To date, the intrinsic thermal conductivity tensor of bulk black phosphorus (BP), an important 2D material, is still unknown, since recent studies focus on BP flakes not on bulk BP. Here we report the anisotropic thermal conductivity tensor of bulk BP, for temperature range 80 - 300 K. Our measurements are similar to prior measurements on submicron BP flakes along zigzag and armchair axes, but are >25% higher in the through-plane axis, suggesting that phonon mean-free-paths are substantially longer in the through-plane direction. We find that despite the anisotropy in thermal conductivity, pho…
As an emerging single elemental layered material with a low symmetry in-plane crystal lattice, black phosphorus (BP) has attracted significant research interest owing to its unique electronic and optoelectronic properties, including its widely tunable bandgap, polarization dependent photoresponse and highly anisotropic in-plane charge transport. Despite extensive study of the steady-state charge transport in BP, there has not been direct characterization and visualization of the hot carriers dynamics in BP immediately after photoexcitation, which is crucial to understanding the performance of …
Black phosphorus has recently emerged as a promising material for high performance electronic and optoelectronic device for its high mobility, tunable mid-infrared bandgap and anisotropic electronic properties. Dynamical evolution of photo excited carriers and its induced change of transient electronic properties are critical for materials' high field performance, but remains to be explored for black phosphorus. In this work, we perform angle resolved transient reflection spectroscopy to study the dynamical evolution of anisotropic properties of black phosphorus under photo excitation. We find…
Black phosphorus (BP) has emerged as a promising candidate for next generation electronics and optoelectronics among the 2D family materials due to its extraordinary electrical/optical/optoelectronic properties. Interestingly, BP shows strong anisotropic transport behaviour because of its puckered honeycomb structure. Previous studies have demonstrated the thermal transport anisotropy of BP and theoretically attribute this to the anisotropy in both phonon dispersion relation and phonon relaxation time. However, the exact origin of such strong anisotropy lacks clarity and has yet to be proven e…
Black phosphorus has been revisited recently as a new two-dimensional material showing potential applications in electronics and optoelectronics. Here we report the anisotropic in-plane thermal conductivity of suspended few-layer black phosphorus measured by micro-Raman spectroscopy. The armchair and zigzag thermal conductivities are ~20 and ~40 W m$^{-1}$ K$^{-1}$ for black phosphorus films thicker than 15 nm, respectively, and decrease to ~10 and ~20 W m$^{-1}$ K$^{-1}$ as the film thickness is reduced, exhibiting significant anisotropy. The thermal conductivity anisotropic ratio is found to…
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…
Black phosphorus consists of stacked layers of phosphorene, a two-dimensional semiconductor with promising device characteristics. We report the realization of a widely tunable bandgap in few-layer black phosphorus doped with potassium using an in-situ surface doping technique. Through band-structure measurements and calculations, we demonstrate that a vertical electric field from dopants modulates the bandgap owing to the giant Stark effect and tunes the material from a moderate-gap semiconductor to a band-inverted semimetal. At the critical field of this band inversion, the material becomes …
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…
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 about the energy and momentum resolved optical response of black phosphorus (BP) in its bulk form. Along the armchair direction of the puckered layers we find a highly dispersive mode that is trongly suppressed in the perpendicular (zig-zag) direction. This mode emerges out of the single-particle continuum for finite values of momentum and is therefore interpreted as an exciton. We argue that this exciton, which has already been predicted theoretically for phosphorene -- the monolayer form of BP -- can be detected by conventional optical spectroscopy in the two-dimensional case and m…
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…
When a two-dimensional material, adhered onto a compliant substrate, is subjected to compression it can undertake a buckling instability yielding to a periodic rippling. Interestingly, when black phosphorus flakes are compressed along the zig-zag crystal direction the flake buckles forming ripples with a 40% longer period than that obtained when the compression is applied along the armchair direction. This anisotropic buckling stems from the puckered honeycomb crystal structure of black phosphorus and a quantitative analysis of the ripple period allows us to determine the Youngs's modulus of f…
In this work, \b{eta}-phosphorus carbide 1D nano-wires (PCNWs) are investigated in the framework of density functional theory. The dynamical stability of the considered \b{eta}-PCNWs at 300 K is verified using ab initio molecular dynamics calculations. According to the results on the band structure calculations, \b{eta}-PCNWs can be semiconductors, semimetals or metals depending on their size and form. Thus, owning to their unique shape and high tunability of electronic properties \b{eta}-PCNWs may be used in optical and photovoltaic nanodevices.
We report the quasiparticle band gap, excitons, and highly anisotropic optical responses of few-layer black phosphorous (phosphorene). It is shown that these new materials exhibit unique many-electron effects; the electronic structures are dispersive essentially along one dimension, leading to particularly enhanced self-energy corrections and excitonic effects. Additionally, within a wide energy range, including infrared light and part of visible light, few-layer black phosphorous absorbs light polarized along the structure's armchair direction and is transparent to light polarized along the z…
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.
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.
Resistivity measurements of a few-layer black phosphorus (bP) crystal in parallel magnetic fields up to 45 T are reported as a function of the angle between the in-plane field and the source-drain (S-D) axis of the device. The crystallographic directions of the bP crystal were determined by Raman spectroscopy, with the zigzag axis found within 5° of the S-D axis, and the armchair axis in the orthogonal planar direction. A transverse magneto-resistance (TMR) as well as a classically-forbidden longitudinal magneto-resistance (LMR) are observed. Both are found to be strongly anisotropic and non-m…
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…
Black phosphorus has been the subject of growing interest due to its unique band structure that is both layer dependent and anisotropic. While many have studied the linear optical response of black phosphorus, the nonlinear response has remained relatively unexplored. Here we report on the observation of third-harmonic generation in black phosphorus using an ultrafast near-IR laser and measure Chi(3) experimentally for the first time. It was found that the third-harmonic emission is highly anisotropic, dependent on the incident polarization, and varies strongly with the number of layers presen…
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…
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…
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…
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.
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 pola…
Anisotropic thermo-mechanical response of layered hexagonal boron nitride and black phosphorus: application as a simultaneous pressure and temperature sensor
Synapses are functional links between neurons, through which "information" flows in the neural network. These connections vary significantly in strength, typically resulting from the intrinsic heterogeneity in their chemical and biological properties. Such heterogeneity is fundamental to the diversity of neural activities, which together with other features of the brain enables functions ranging from perception and recognition, to memory and reasoning. Realizing such heterogeneity in synaptic electronics is critical towards building artificial neural network with the potential for achieving th…
Transient electron-hole pairs generated in semiconductors can exhibit unconventional excitonic condensation. Anisotropy in the carrier mass is considered as the key to elongate the life time of the pairs, and hence to stabilize the condensation. Here we employ time- and angle-resolved photoemission spectroscopy to explore the dynamics of photo-generated carriers in black phosphorus. The electronic structure above the Fermi level has been successfully observed, and a massive-and-anisotropic Dirac-type dispersions are confirmed; more importantly, we directly observe that the photo-carriers gener…
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 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 …
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 report the anisotropic magneto-transport measurement on a non-compound band semiconductor black phosphorus (BP) with magnetic field B up to 16 Tesla applied in both perpendicular and parallel to electric current I under hydrostatic pressures. The BP undergoes a topological Lifshitz transition from band semiconductor to a zero-gap Dirac semimetal state, characterized by a weak localization-weak antilocaliation transition at low magnetic fields and the emergence of a nontrivial Berry Phase of detected by SdH magneto-oscillations in magnetoresistance curves. In the transition region, we observ…
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 …
The electronic properties of the layered black phosphorus (black-P) and its monolayer counterpart phosphorene are investigated by using the first-principles calculations based on the density functional theory (DFT). The room-temperature electronic transport coefficients are evaluated within the semi-classical Boltzmann theory. The electrical conductivity exhibits anisotropic behavior while the Seebeck coefficient is almost isotropic. At the optimal doping level and room temperature, bulk black-P and phosphorene are found to have large thermoelectric power factors of 118.4 and 138.9 μWcm-1K-2, …
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…
Black phosphorus (BP) is a layered material with anisotropic properties. We study interfaces formed by a pentacene monolayer adsorbed on monolayer BP, a prototypical system for BP surface passivation. We place the pentacene monolayer along the zigzag and armchair directions of the BP substrate, respectively, to examine the anisotropy of the heterogeneous interfaces. We perform first-principles $GW$ plus Bethe-Salpeter equation ($GW$-BSE) calculations to determine the quasiparticle and optical properties. To quantitatively analyze the anisotropy of the optical properties, we develop a general c…
Two-dimensional materials supporting deep-subwavelength plasmonic modes can also exhibit strong magneto-optical responses. Here, we theoretically investigate magnetoplasmons (MPs) in monolayer black phosphorus (BP) structures under moderate static magnetic fields. We consider three different structures, namely, a continuous BP monolayer, an edge formed by a semi-infinite sheet, and finally, a triangular wedge configuration. Each of these structures shows strongly anisotropic magneto-optical responses induced both by the external magnetic field and by the intrinsic anisotropy of the BP lattice.…
We use an atomistic approach to study the electronic properties of monolayer and bilayer black phosphorus in the vicinity of a charged defect. In particular, we combine screened defect potentials obtained from first-principles linear response theory with large-scale tight-binding simulations to calculate the wavefunctions and energies of bound acceptor and donor states. As a consequence of the anisotropic band structure, the defect states in these systems form distorted hydrogenic orbitals with a different ordering than in isotropic materials. For the monolayer, we study the dependence of the …
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 thin films might offer attractive alternatives to narrow gap compound semiconductors for optoelectronics across mid- to near-infrared frequencies. In this work, we calculate the optical conductivity tensor of multilayer black phosphorus thin films using the Kubo formula within an effective low-energy Hamiltonian. The optical absorption spectra of multilayer black phosphorus are shown to vary sensitively with thickness, doping, and light polarization. In conjunction with experimental spectra obtained from infrared absorption spectroscopy, we also discuss the role of interband c…
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…
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…
Black Phosphorus (BP) has gained renewed attention due to its singular anisotropic electronic and optical properties that might be exploited for a wide range of technological applications. In this respect, the thermal properties are particularly important both to predict its room temperature operation and to determine its thermoelectric potential. From this point of view, one of the most spectacular and poorly understood phenomena is, indeed, the BP temperature-induced band-gap opening: when temperature is increased the fundamental band-gap increases instead of decreasing. This anomalous therm…
Recently fabricated two dimensional (2D) phosphorene crystal structures have demonstrated great potential in applications of electronics. Mechanical strain was demonstrated to be able to significantly modify the electronic properties of phosphorene and few-layer black phosphorus. In this work, we employed first principles density functional theory calculations to explore the mechanical properties of phosphorene, including ideal tensile strength and critical strain. It was found that a monolayer phosphorene can sustain tensile strain up to 27% and 30% in the zigzag and armchair directions, resp…
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…
We report analytic results on quantum capacitance (C$_{q}$) measurements and their optical tuning in dual-gated device with potassium-doped multi-layered black phosphorous (BP) as the channel material. The two-dimensional (2D) layered BP is highly anisotropic with a semi-Dirac dispersion marked by linear and quadratic contributions. The C$_{q}$ calculations mirror this asymmetric arrangement. A further increase to the asymmetry and consequently C$_{q}$ is predicted by photon-dressing the BP dispersion. To achieve this and tune C$_{q}$ in a field-effect transistor (FET), we suggest a configurat…
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 …
We examine the electronic properties of 2D electron gas in black phosphorus multilayers in the presence of a perpendicular magnetic field, highlighting the role of in-plane anisotropy on various experimental quantities such as ac magneto-conductivity, screening, and magneto-plasmons. We find that resonant structures in the ac conductivity exhibits a red-shift with increasing doping due to inter-band coupling, $γ$. This arises from an extra correction term in the Landau energy spectrum proportional to $n^2γ^2$ ($n$ is Landau index), up to second order in $γ$. We found also that Coulomb interact…
One hundred years after its first successful synthesis in the bulk form in 1914, black phosphorus (black P) was recently rediscovered from the perspective of a two-dimensional (2D) layered material, attracting tremendous interest from condensed matter physicists, chemists, semiconductor device engineers and material scientists. Similar to graphite and transition metal dichalcogenides (TMDs), black P has a layered structure but with a unique puckered single layer geometry. Because the direct electronic band gap of thin film black P can be varied from 0.3 to around 2 eV, depending on its film th…
We present polarization-resolved transient transmission measurements on multi-layer black phosphorus. Background free two-color pump-probe spectroscopy measurements are carried out on mechanically exfoliated black phosphorus flakes that have been transferred to a large-bandgap, silicon carbide substrate. The blue-shifted pump pulse (780 nm) induces an increased transmission of the probe pulse (1560 nm) over a time scale commensurate with the measurement resolution (hundreds of fs). After the initial pump-induced transparency, the sign of the transient flips and a slower enhanced absorption is …
We present a theory for single- and two-phonon charge carrier scattering in anisotropic two-dimensional semiconductors applied to single-layer black phosphorus (BP). We show that in contrast to graphene, where two-phonon processes due to the scattering by flexural phonons dominate at any practically relevant temperatures and are independent of the carrier concentration $n$, two-phonon scattering in BP is less important and can be considered negligible at $n\gtrsim10^{13}$ cm$^{-2}$. At smaller $n$, however, phonons enter in the essentially anharmonic regime. Compared to the hole mobility, whic…
