Using the Tight Binding (TB) parameters extracted from Density Functional Theory (DFT) and Recursive Green's Function method, it is shown that skewed-zigzag black phosphorous (phosphorene) nanoribbons obtain large and tuneable bandgap in response to vertical and transverse electric fields. Depending on the direction of the applied field the mid-gap states could possess the localized or metallic nature i.e. non-zero mid-gap density of states. Adjustability of the bandgap and optical dipole transition matrix elements are explained based on the symmetry of involved band edge states. This promises new electronic and optical devices based on phosphorene nanoribbons.
By the means of screened exchange density functional theory, we find that the phosphorene nanoribbons with bare zigzag edges that undergo Peierls distortion is a antiferromagnetic semiconductor in which the polarized states are mainly localized at the edges. Under application of external electric fields, the phosphorene nanoribbons present exotic electronic structure transitions including semiconducting, half-metallic, and metallic states.
Edge-induced gap states in finite phosphorene layers are examined using analytical models and density functional theory. The nature of such gap states depends on the direction of the cut. Armchair nanoribbons are insulating, whereas nanoribbons cut in the perpendicular direction (with zigzag and cliff-type edges) are metallic, unless they undergo a reconstruction or distortion with cell doubling, which opens a gap. All stable nanoribbons with unsaturated edges have gap states that can be removed by hydrogen passivation. Armchair nanoribbon edge states decay exponentially with the distance to t…
In this work, the electronic properties of phosphorene nanoribbons with different width and edge configurations are studied by using density functional theory. It is found that the armchair phosphorene nanoribbons are semiconducting while the zigzag nanoribbons are metallic. The band gaps of armchair nanoribbons decrease monotonically with increasing ribbon width. By passivating the edge phosphorus atoms with hydrogen, the zigzag series also become semiconducting, while the armchair series exhibit a larger band gap than their pristine counterpart. The electronic transport properties of these p…
Using the tight-binding (TB) approximation with inclusion of the spin-orbit interaction, we predict a topological phase transition in the electronic band structure of phosphorene in the presence of axial strains. We derive a low-energy TB Hamiltonian that includes the spin-orbit interaction for bulk phosphorene. Applying a compressive biaxial in-plane strain and perpendicular tensile strain in ranges where the structure is still stable leads to a topological phase transition. We also examine the influence of strain on zigzag phosphorene nanoribbons (zPNRs) and the formation of the correspondin…
The success of graphene for nanopore DNA sequencing has shown that it is possible to explore other potential single-atom and few-atom thick layers of elemental 2D materials beyond graphene (e.g., phosphorene and silicene). Using density functional theory, we studied the interaction of DNA bases with nanopores created in finite-size nanoribbons from graphene, phosphorene, and silicene. We observe that binding energies of DNA bases using nanopores from phosphorene and silicene are generally smaller compared to graphene. The band gaps of phosphorene and silicene are significantly altered due to i…
We perform a comprehensive first-principles study of the electronic properties of phosphorene nanoribbons, phosphorene nanotubes, multilayer phosphorene, and heterobilayers of phosphorene and two-dimensional (2D) transition metal dichalcogenide (TMDC) monolayer. The tensile strain and electric-field effects on electronic properties of low-dimensional phosphorene nanostructures are also investigated. Our calculations show that zigzag phosphorene nanoribbons (z-PNRs) are metals, regardless of the ribbon width while armchair phosphorene nanoribbons (a-PNRs) are semiconductors with indirect bandga…
The graphene and phosphorene nanostructures have a big potential application in a large area of actuals research in physics. However, their methods of synthesis still do not allow the production of perfect materials with an intact molecular structure. In this paper, the occurrence of atomic vacancies was considered in the edge structure of the zigzag phosphorene and graphene nanoribbons. For different concentrations of these edge vacancies, their influence on the metallic properties was investigated. The calculations were performed for different sizes of the unit cell. Furthermore, for a small…
Using Density Functional Theory (DFT) method we compute linear optical absorption spectra and nonlinear optical susceptibilities of hydrogen passivated armchair and zigzag Phosphorous Nanoribbons (aPNR and zPNR) as well as α-phase phosphorous monolayer. We observe that: (a) Crystallographic direction has a strong effect on the band edge absorption which causes optical anisotropy as well as a red shift of absorption spectra by increasing the nanoribbon width. (b) The absorption values are in the order of $10^{5} cm^{-1}$ which are similar to the experimentally measured values. (c) There is two …
In this study, we analyze the band structure, the state characterization, and electronic transport of monolayer black phosphorus (phosphorene) zigzag nanoribbons (zPNRs) and armchair nanoribbons (aPNRs), using five-parameter tight-binding (TB) approximation. In zPNRs, the ratio of the two dominant hopping parameters indicates the possibility of a relativistic dispersion relation and the existence of a pair of separate quasi-flat bands at the Fermi level. Moreover, the corresponding states are edge localized if their bands are well separated from the valence and conduction bands. We also invest…
Zigzag phosphorene nanoribbons are metallic owing to the edge states, whose energies are inside the gap and far from the bulk bands. We show that -- through electrical manipulation of edge states -- electron propagation can be restricted to one of the ribbon edges or, in case of bilayer phosphorene nanoribbons, to one of the layers. This finding implies that edge and layer can be regarded as tunable equivalents of the spin-one-half degree of freedom, i.e., the pseudospin. In both layer- and edge-pseudospin schemes, we propose and characterize a pseudospin field-effect transistor, which can gen…
We investigate the energy spectrum of single layer black phosphorene nanoribbons (BPN) by means of a low-energy expansion of a recently proposed tight-binding model that describes electron and hole bands close to the Fermi energy level. Using the continuum approach, we propose boundary conditions based on sublattice symmetries for BPN with zigzag and armchair edges and show that our results for the energy spectra exhibit good agreement with those obtained by using the five-parameter tight-binding model. We also explore the behaviour of the energy gap versus the nanoribbon width $W$. Our findin…
Armchair phosphorene nanoribbons (APNRs) are known to be semiconductors with an indirect bandgap. Here, we propose to introduce new states in the gap of APNRs by creating a periodic structure of vacancies (antidots). Based on the tight-binding model, we show that a periodic array of vacancies or nanopores leads to the formation of an impurity band inside the gap region. We first present an analytical expression for the dispersion relation of an impurity band induced by hybridization of bound states associated with each single vacancy defect. Then, we increase the size of vacancy defects to inc…
Double-level quantum systems are good candidates for revealing coherent quantum transport properties. Here, we consider quantum interference effects due to the formation of a two-level system (TLS) coupled to the edge channel of a zigzag Phosphorene nanoribbon (ZPNR). Using the tight-binding approach, we first demonstrate the formation of a TLS in bulk Phosphorene sheet due to the existence of two nearby vacancy impurities. Then, we show that such a TLS can couple to the quasi-one-dimensional continuum of the edge states in a ZPNR which results in the the appearance of two-dip Fano-type line s…
By combining density functional theory and nonequilibrium Green's function, we study the electronic and transport properties of monolayer black phosphorus nanoribbons (PNRs). First, we investigate the band-gap of PNRs and its modulation by the ribbon width and an external transverse electric feld. Our calculations indicate a giant Stark effect in PNRs, which can switch on transport channels of semiconducting PNRs under low bias, inducing an insulator-metal-transition. Next, we study the transport channels in PNRs via the calculations of the current density and local electron transmission pathw…
The ability to detect and discriminate DNA bases by reading it directly using simple and cost-effective methods is an important problem whose solution can produce significant value for areas such as cancer and human genetic disorders. Two-dimensional (2D) materials have emerged as revolutionary materials for electronic DNA sequencing with strong potentials for fast, single-nucleotide direct-read DNA sequencing with a minimum amount of consumables. Among 2D materials, graphene is the most explored for DNA sequencing. This is due to its commercial availability. The major hindrance of graphene is…
We study exchange interaction in zigzag bilayer phosphorene nanoribbons (ZBLPNRs) under a perpendicular electric field. We evaluate the spatial and electric field dependency of static spin susceptibility in real space in various configurations of magnetic impurities at zero temperature. The electronic properties of ZBLPNR in the presence of a gate voltage is also obtained. In comparison to the other two-dimensional (2D) materials such as graphene and silicene, ZBLPNR has two nearly degenerated quasiflat edge modes at the Fermi level, isolated from the bulk states. The band gap modulation of ZB…
The energy spectrum and eigenstates of single-layer black phosphorous nanoribbons in the presence of perpendicular magnetic field and in-plane transverse electric field are investigated by means of a tight-binding method and the effect of different types of edges is analytically examined. A description based on a new continuous model is proposed by expansion of the tight-binding model in the long-wavelength approximation. The wavefunctions corresponding to the flatband part of the spectrum are obtained analytically and are shown to approach agree well with the numerical results from the tight-…
We study the effects of a vertical electric field on the electronic band structure and transport in multilayer phosphorene and its nanoribbons. In phosphorene, at a critical value of the vertical electric field ($E_c$), the band gap closes and the band structure undergoes a massive-to-massless Dirac fermion transition along the armchair direction. This transition is observable in quantum Hall measurements, as the power-law dependence of the Landau-level energy on the magnetic field $B$ goes from $\sim (n+1/2)B$ below $E_c$, to $\sim [(n+1/2)B]^{2/3}$ at $E_c$, to $\sim [(n+1/2)B]^{1/2}$ above …
Searching for room temperature ferromagnetic semiconductors has evolved into a broad field of material science and spintronics for decades, nevertheless, these novel states remain rare. Phosphorene, a monolayer black phosphorus with a puckered honeycomb lattice structure possessing a finite band gap and high carrier mobility, has been synthesized recently. Here we show, by means of two different large scale quantum Monte-Carlo methods, that relatively weak interactions can lead to remarkable edge magnetism in the phosphorene nanoribbons. The ground state constrained path quantum Monte-Carlo si…
On the basis of many-body {\it ab-initio} calculations, using single-shot G$_0$W$_0$ method and Bethe-Salpeter equation, we study phosphorene nanoribbons (PNRs) in the two typical zigzag and armchair directions. The electronic structure, optical absorption, electron-hole (exciton) binding energy, exciton exchange splitting, and exciton wave functions are calculated for different size of PNRs. The typically strong splitting between singlet and triplet excitonic states make PNRs favorable systems for application in optoelectronic. Quantum confinement occurs in both kinds of PNRs, and it is stron…
We theoretically investigate the thermoelectric properties of zigzag bilayer phosphorene nanoribbons (ZBPNR). We first, draw an analogy between the extended Su-Schrieffer-Heeger (SSH) ladder and ZBPNR edge states and obtain their corresponding band structure and wave functions analytically. Then, by applying the energy filtering method, we show that the electric power and thermoelectric efficiency of the ZBPNRs can be improved remarkably in the presence of mid-gap edge states. We also argue how to engineer the edge modes to further optimize thermoelectric power and efficiency of the system by …
We numerically study the effect of the edge states on the conductance and thermopower in zigzag phosphorene nanoribbons (ZPNRs) based on the tight-binding model and the scattering-matrix method. It is interesting to find that the band dispersion, conductance, and thermopower can be modulated by applying a bias voltage and boundary potentials to the two layers of the ZPNRs. Under the certain bias voltage, the two-fold degenerate quasi-flat edge bands split perfectly. The conductance can be switched off, and the thermopower around zero energy increases. In addition, when only the boundary potent…
We investigate the effects of a perpendicular electric field applied to multilayer phosphorene nanoribbons with zigzag and armchair edges. Within the context of the tight-binding model, we explore the electronic properties of these systems giving emphasis to the appearance of Dirac-like spectra, a transition that occurs when the gate density associated with the applied displacement field is greater than the critical value $n_c$. We show that the confinement properties and the screening effects in such systems play an important role on the determination of $n_c$, suggesting a scheme to determin…
Phosphorene is an anisotropic puckered two-dimensional ($2$D) hexagonal lattice of phosphorus atoms. The edge modes in a zigzag phosphorene nanoribbon (ZPNR) are quasi-flat in nature and fully isolated from the bulk states, which are unique in comparison to the other hexagonal lattices like graphene, silicene etc. We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between two magnetic impurities placed on the nanoribbon, and extract the signatures of the flat edge states via the behavior of it. Due to the complete separation of the edge states from the b…
An antiferromagnetic insulating state has been found in the zigzag phosphorene nanoribbons (ZPNRs) from a comprehensive density functional theory calculations. Comparing with other one-dimensional systems, the magnetism in ZPNRs display several surprising characteristics: (i) the magnetic moments are antiparallel arranged at each zigzag edge; (ii) the magnetism is quite stable in energy (about 29 meV/magnetic-ion) and the band gap is big (about 0.7 eV); (iii) a moderate compressive strain will induce a magnetic to nonmagnetic as well as semiconductor to metal transition. All of these phenomena…
Transport of the edge-state electrons along zigzag phosphorene nanoribbons in presence of two impurities/vacancies is analytically investigated. Considering the places of the defects, a number of different situations are examined. When both defects are placed on the edge zigzag chain, as is expected, with changing the energy of the traveling electrons the electrical conductance exhibits a resonance behavior. In this case, for two vacancies the observed resonant peaks become extremely sharp. An amazing behavior is seen when the second vacancy is located along an armchair chain while the first i…
We report the electronic structure and optical absorption spectra of monolayer black phosphorus (phosphorene) nanoribbons (PNRs) via first-principles simulations. The band gap of PNRs is strongly enhanced by quantum confinement. However, differently orientated PNRs exhibit distinct scaling laws for the band gap vs the ribbon width (w). The band gaps of armchair PNRs scale as 1/(w^2), while zigzag PNRs exhibit a 1/w behavior. These distinct scaling laws reflect a significant implication of the band dispersion of phosphorene: electrons and holes behave as classical particles along the zigzag dir…
The effects of lattice distortion and chemical disorder on charge transport properties of two-terminal zigzag phosphorene nanoribbons (zPNRs), which shows resonant tunneling behavior under an electrical applied bias, are studied. Our comprehensive study is based on an {\it ab~initio} quantum transport calculations on the basis of the Landauer theory. We use nitrogen and silicon substitutional dopant atoms, and employ different physical quantities such as $I-V$ curve, voltage drop behavior, transmission spectrum, transmission pathway, and atomic current, to explore the transport mechanism of zP…
Motivated by recent scanning tunneling microscopy/spectroscopy experiments on probing single vacancies in black phosphorus, we present a theory for Fano antiresonances induced by coupling between vacancy states and edge states of zigzag phosphorene nanoribbons (zPNRs). To this end, in the first step, using the tight-binding Hamiltonian, we obtain an analytic solution on the lattice for the state associated to a single vacancy located in the bulk phosphorene which shows a highly anisotropic localization in real space. For a finite zigzag ribbon, in the absence of particle-hole symmetry, the loc…
Zigzag phosphorene nanoribbons have quasi-flat band edge modes entirely detached from the bulk states. We analytically study the electronic transport through such edge states in the presence of a localized defect for semi-infinite and finite ribbons. Using the tight-binding model, we derive analytical expressions for the Green's function and transmission amplitude of both pristine and defective nanoribbons. We find that the transmission of both semi-infinite and finite ribbons is sensitive to the location of a single impurity defect with respect to the edge. By the presence of an impurity on t…
First principles density-functional theory calculations were performed to investigate quantum confinement and edge effects on the electronic properties of zigzag green phosphorene nanoribbons (ZGPNRs) with edge chemical species including H, OH, F, Cl, O, and S for the ribbons width in the range of 0.5 \~{} 3.7 nm. The ZGPNRs were obtained from the relaxed two-dimensional (2D) green phosphorene monolayer with different cutting strategies and the most energetically favorable ribbon configuration was selected for further exploration of the size and edge effects. It was found that the electronic p…
Phosphorene, a honeycomb structure of black phosphorus, was isolated recently. We investigate electric properties of phosphorene nanoribbons based on the tight-binding model. A prominent feature is the presence of quasi-flat edge bands entirely detached from the bulk band. We explore the mechanism of the emergence of the quasi-flat bands analytically and numerically from the flat bands well known in graphene by a continuous deformation of a honeycomb lattice. The quasi-flat bands can be controlled by applying in-plane electric field perpendicular to the ribbon direction. The conductance is swi…
In recent years, single element two-dimensional atom crystal materials have aroused extensive interest in many applications. Blue phosphorus, successfully synthesized on Au substrate by molecular beam epitaxy not long ago, shows unusual geometrical and electronic structures. We investigate the electronic structures and transport properties of zigzag blue phosphorene nanoribbons by using a first-principles method, which can be obviously tuned via different groups passivation on the both edges. The ZBPNRs-H and ZBPNRs-OH present a wide gap semiconductor property. While the ZBPNRs-O are metallic.…
We propose a new type of edges, arising due to the anisotropy inherent in the puckered structure of a honeycomb system such as in phosphorene. Skewed-zigzag and skewed-armchair nanoribbons are semiconducting and metallic, respectively, in contrast to their normal edge counterparts. Their band structures are tunable, and a metal-insulator transition is induced by an electric field. We predict a field-effect transistor based on the edge states in skewed-armchair nanoribbons, where the edge state is gapped by applying arbitrary small electric field $E_z$. A topological argument is presented, reve…
It is known that there is a wide class of quasi-two-dimensional graphenelike nanomaterials which in many respects can outperform graphene. So, here in addition to graphene, the attention is directed to stanene (buckled honeycomb structure) and phosphorene (puckered honeycomb structure). It is shown that, depending on the doping, these materials can have magnetically ordered edges. Computed diagrams of magnetic phases illustrate that, on the one hand, n-type doped narrow zigzag nanoribbons of graphene and stanene have antiferromagnetically aligned magnetic moments between the edges. On the othe…
In this work, we present a systematic first-principles density-functional theory based study of geometry, electronic structure, and optical properties of armchair phosphorene nanoribbons (APNRs), with the aim of understanding the influence of edge passivation. Ribbons of width ranging from 0.33 nm to 3.8 nm were considered, with their edges functionalized with the groups H, OH, F, Cl, S, and Se. The geometries of various APNRs were optimized, and the stability was checked by calculating their formation energies. Using the relaxed geometries, calculations of their band structure and optical pro…
For the pristine phosphorene nanoribbons (PNRs) with edge states, there exist two categories of edge bands near the Fermi energy (EF), i.e., the shuttle-shaped twofold-degenerate and the near-flat simple degenerate edge bands. However, the usual experimental measurement may not distinguish the difference between the two categories of edge bands. Here we study the varying rule for the edge bands of PNRs under an external electrostatic field. By using the KWANT code based on the tight-binding approach, we find that the twofold-degenerate edge bands can be divided into two separated shuttles unti…
Electronic DNA sequencing using two-dimensional (2D) materials such as graphene has recently emerged as the next-generation of DNA sequencing technology. Owing to its commercial availability and remarkable physical and conductive properties, graphene has been widely investigated for DNA sequencing by several theoretical and experimental groups. Despite this progress, sequencing using graphene remains a major challenge. This is due to the hydrophobic nature of graphene, which causes DNA bases to stick to its surface via strong π-π interactions, reducing translocation speed and increasing error …
We theoretically study emergent edge and corner states in monolayer blue phosphorus (blue phosphorene) using the first-principles calculation and tight-binding model. We show that the existence of the Wannier orbitals at every bond center yields edge states both in zigzag and armchair nanoribbons. The properties of the edge states can be well described by a simple effective Hamiltonian for uncoupled edge orbitals, where the structural relaxation near the boundary significantly affects the edge band structure. For corner states, we examine two types of corner structures consisting of zigzag and…
Spectral and transport properties of electrons in confined phosphorene systems are investigated in a five hopping parameter tight-binding model, using analytical and numerical techniques. The main emphasis is on the properties of the topological edge states accommodated by the quasi-flat band that characterizes the phosphorene energy spectrum. We show, in the particular case of phosphorene, how the breaking of the bipartite lattice structure gives rise to the electron-hole asymmetry of the energy spectrum. The properties of the topological edge states in the zig-zag nanoribbons are analyzed un…
We investigate theoretically the Landau levels (LLs) and magneto-transport properties of phosphorene under a perpendicular magnetic field within the framework of the effective \textbf{\emph{k$\cdot$p}} Hamiltonian and tight-binding (TB) model. At low field regime, we find that the LLs linearly depend both on the LL index $n$ and magnetic field $B$, which is similar with that of conventional semiconductor two-dimensional electron gas. The Landau splittings of conduction and valence band are different and the wavefunctions corresponding to the LLs are strongly anisotropic due to the different an…
The central question in the field of 2D materials is how a material behaves when it is patterned at nanometer scale with different edge geometries. Due to the anisotropy inherent in the puckered structure, black phosphorene nanostructures may have more varieties of edge geometries. Here, we present a comprehensive 2D planar crystallographic characterization of phosphorene uniformly by a chiral vector (angle), from which a new type of edge atomic configuration, the slope edge geometry is discovered. The phosphorene nanoribbons (PNRs) with slope edges, like previously noticed zigzag and skewed-a…
Here we comprehensively investigate Landau levels, Hofstadter butterfly and transport properties of a semi-Dirac nanoribbon in a perpendicular magnetic field using a recently developed real-space implementation of the Kubo formula based on Kernel Polynomial Method. A Dirac ribbon is considered to compare and contrast our results for a semi-Dirac system. We find that the Landau levels being non-equidistant from each other for the semi-Dirac case (true for a Dirac as well), the flatness of the energy bands vanishes in the bulk and becomes dispersive for a semi-Dirac ribbon in contrast to a Dirac…
We analytically study the electronic structures and optical properties of zigzag-edged black phosphorene nanoribbons (ZPNRs) utilizing the tight-binding (TB) Hamiltonian and Kubo formula. By solving the discrete Schordinger equation directly, we obtain the energy spectra and wavefunctions for a $N$-ZPNR with $N$ number of transverse zigzag atomic chains, and classify the eigenstates according to the lattice symmetry. We then obtain the optical transition selection rule of ZPNRs based on the symmetry analysis and the analytical expressions of the optical transition matrix elements. Under an inc…
Two-dimensional (2D) crystals' edge structures not only influence their overall properties but also dictate their formation due to edge-mediated synthesis and etching processes. Edges must be carefully examined because they often display complex, unexpected features at the atomic scale, such as reconstruction, functionalization, and uncontrolled contamination. Here, we examine atomic-scale edge structures and uncover reconstruction behavior in bilayer phosphorene. We use in situ transmission electron microscopy (TEM) of phosphorene/graphene specimens at elevated temperatures to minimize surfac…
