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 potential of the top layer or bottom layer is adjusted, only one edge band bends and merges into the bulk band. The first conductance plateau is strongly decreased to $e^2/h$ around zero energy. Particularly, when the two boundary potentials are adjusted, all the edge bands bend and fully merge into the bulk band, and the bulk energy gap is maximized. More interestingly, a pronounced conductance plateau with $G=0$ is found around zero energy, which is attributable to the opening of the bulk energy gap between the valence and conduction bands. Meanwhile, the thermopower can be enhanced more than twice, compared to that of the perfect ZPNRs. The large magnitude of thermopower is ascribed to the appearance of the bulk energy gap around zero energy. Our results show that the modulated ZPNRs are more reliable in thermoelectric application.
We numerically study the electrical and thermoelectric transport properties in phosphorene in the presence of both a magnetic field and disorder. The quantized Hall conductivity is similar to that of a conventional two-dimensional electron gas, but the positions of all the Hall plateaus shift to the left due to the spectral asymmetry, in agreement with the experimental observations. The thermoelectric conductivity and Nernst signal exhibit remarkable anisotropy, and the thermopower is nearly isotropic. When a bias voltage is applied between top and bottom layers of phosphorene, both thermopowe…
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…
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…
We investigate, based on the tight-binding model and in the linear deformation regime, the strain dependence of the electronic band structure of phosphorene, exposed to a uniaxial strain in one of its principle directions, the normal, the armchair and the zigzag directions. We show that the electronic band structure of strained phosphorene, for experimentally accessible carrier densities and uniaxial strains, is well described by a strain-dependent decoupled electron-hole Hamiltonian. Then, employing the decoupled Hamiltonian, we consider the strain dependence of the charged-impurity-limited c…
Using first-principles calculations and non-equilibrium Green's function method, we investigate the ballistic thermal transport in single-layer phosphorene. A significant crystallographic orientation dependence of thermal conductance is observed, with room temperature thermal conductance along zigzag direction being 40 percent higher than that along armchair direction. Furthermore, we find that the thermal conductance anisotropy with the orientation can be tuned by applying strain. In particular, the zigzag-oriented thermal conductance is enhanced when a zigzag-oriented strain is applied but d…
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 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…
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 …
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…
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.
Density functional theory calculations are performed on phosphorene quantum dots having different shapes and edge terminations to investigate their structure stability, electronic properties, and gas sensing ability. All the selected phosphorene dots, namely hexagonal and triangular flakes with armchair and zigzag terminations, have positive binding energies which insure their stability even though the bond lengths are much longer than those in the infinite phosphorene layer. It is found that all the selected hydrogen passivated quantum dots have a wide energy gap. In contrast, the partial pas…
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…
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…
We studied the electronic structure and optic absorption of phosphorene (monolayer of black phosphorus) under strain. Strain was found to be a powerful tool for the band structure engineering. The in-plane strain in armchair or zigzag direction changes the effective masse components along both directions, while the vertical strain only has significant effect on the effective mass in the armchair direction. The band gap is narrowed by compressive in-plane strain and tensile vertical strain. Under certain strain configurations, the gap is closed and the energy band evolutes to the semi-Dirac typ…
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…
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…
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…
This work presents theoretical demonstration of Aharonov-Bohm (AB) effect in monolayer phosphorene nanorings (PNR). Atomistic quantum transport simulations of PNR are employed to investigate the impact of multiple modulation sources on the sample conductance. In presence of a perpendicular magnetic field, we find that the conductance of both armchair and zigzag PNR oscillate periodically in a low-energy window as a manifestation of the AB effect. Our numerical results have revealed a giant magnetoresistance (MR) in zigzag PNR (with a maximum magnitude approaching two thousand percent). It is a…
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…
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…
We theoretically investigate phosphorene zigzag nanorribons as a platform for constriction engineering. In the presence of a constriction at the upper edge, quantum confinement of edge protected states reveals resonant tunnelling Breit-Wigner transmission peaks, if the upper edge is uncoupled to the lower edge. Coupling between edges in thin constrictions gives rise to Fano-like and anti-resonances in the transmission spectrum of the system.
We study the anisotropic electronic properties of 2D SnS, an analogue of phosphorene, grown by physical vapor transport. With transmission electron microscope and polarized Raman spectroscopy, we identify the zigzag and armchair directions of the as-grown 2D crystals. 2D SnS field-effect transistors with a cross-Hall-bar structure are fabricated. They show heavily hole-doped (~10$^{19}$ cm$^{-3}$) conductivity with strong in-plane anisotropy. At room temperature the mobility along the zigzag direction exceeds 20 cm$^{2}$V$^{-1}$s$^{-1}$, which can be up to 1.7 times of that in the armchair dir…
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…
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.…
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…
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…
Insights into electronic and transport properties of phosphorene nanorings in two perpendicular directions: Effects of circular and elliptical external potentials
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…
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…
The anisotropy in resonant tunneling transport through an electrostatic barrier in mono layer black phosphorus either in presence or in absence of an oscillating potential is studied. Non-perturbative Floquet theory is applied to solve the time dependent problem and the results obtained are discussed thoroughly. The resonance spectra in field free transmission are Lorentzian in nature although the width of the resonance for the barrier along the zigzag direction is too thinner than that for the armchair one. Resonant transmission is suppressed for both the cases by the application of oscillati…
Using a simple LCAO model by Harrison, we have qualitatively studied the edge state of bilayer phosphorene, which is a unit structure of the layered crystal of black phosphorus. This model successfully reproduces the isolated edge state in the bulk gap in monolayer phosphorene. In bilayer phosphorene, however, it shows that edge states are almost buried in the valence band and there is no isolated midgap edge state at the zigzag edge. Since the buried edge state works as acceptor, holes are doped from the edge state into the bulk. This gives a possible explanation for p-type conduction in undo…
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…
The newly emerging monolayer phosphorene was recently predicted to be a promising thermoelectric material. In this work, we propose to further enhance the thermoelectric performance of phosphorene by the strain-induced band convergence. The effect of the uniaxial strain on the thermoelectric properties of phosphorene was investigated by using the first-principles calculations combined with the semi-classical Boltzmann theory. When the zigzag-direction strain is applied, the Seebeck coefficient and electrical conductivity in zigzag direction can be greatly enhanced simultaneously at the critica…
We consider states localized by electrostatic potentials in phosphorene using an atomistic tight binding approach. From the results of the tight-binding calculations of the confined states we extract effective masses for the conduction band electrons in the armchair and zigzag directions. The masses derived in this way are used for a simple single-band effective mass model which, as we find, reproduces very well the tight-binding energy spectrum in external magnetic field, the probability densities and the interaction effects. Both methods produce Wigner crystallization for the ground-state of…
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…
We compute binding energies, Stark shifts, electric-field-induced dissociation rates, and the Franz-Keldysh effect for excitons in phosphorene in various dielectric surroundings. All three effects show a pronounced dependence on the direction of the in-plane electric field, with the dissociation rates in particular decreasing by several orders of magnitude upon rotating the electric field from the armchair to the zigzag axis. To better understand the numerical dissociation rates, we derive an analytical approximation to the anisotropic rates induced by weak electric fields, thereby generalizin…
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…
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…
Recently fabricated two dimensional (2D) phosphorene crystal structures have demonstrated great potential in applications of electronics. In this work, strain effect on the electronic band structure of phosphorene was studied using first principles methods. It was found that phosphorene can withstand a surface tension and tensile strain up to 10 N/m and 30%, respectively. The band gap of phosphorene experiences a direct-indirect-direct transition when axial strain is applied. A moderate -2% compression in the zigzag direction can trigger this gap transition. With sufficient expansion (+11.3%) …
We apply the generalized Boltzmann theory to describe thermoelectric transport properties of monolayer phosphorene in the presence of short- and long-range charged impurity interactions. First, we propose a low-energy Hamiltonian to explore the accurate electronic band structure of phosphorene in comparison with those results obtained by density-functional simulations. We explain the effect of the coupling between the conduction and valence bands on the thermoelectric properties. We show that the electric conductivity of phosphorene is highly anisotropic, while the Seebeck coefficient and figu…
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…
Phosphorene, a monolayer of black phosphorus (BP), is an elemental two-dimensional material with interesting physical properties, such as high charge carrier mobility and exotic anisotropic in-plane properties. To fundamentally understand these various physical properties, it is critically important to conduct an atomic-scale structural investigation of phosphorene, particularly regarding various defects and preferred edge configurations. However, it has been challenging to investigate mono- and few-layer phosphorene because of technical difficulties arising in the preparation of a high-qualit…
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 …
As a canonical response to the applied magnetic field, the electronic states of a metal are fundamentally reorganized into Landau levels. In Dirac metals, Landau levels can be expected without magnetic fields, provided that an inhomogeneous strain is applied to spatially modulate electron hoppings in a similar way as the Aharonov-Bohm phase. We here predict that a twisted zigzag nanoribbon of graphene exhibits strain-induced pseudo Landau levels of unexplored but analytically solvable dispersions at low energies. The presence of such dispersive pseudo Landau levels results in a negative strain…
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…
Phosphorene, a single layer of black phosphorus, is a direct-band gap two-dimensional semiconductor with promising charge and spin transport properties. The electronic band structure of phosphorene is strongly affected by the structural anisotropy of the underlying crystal lattice. We describe the relevant conduction and valence bands close to the $Γ$ point by four- and six-band (with spin) $k \cdot p$ models, including the previously overlooked interband spin-orbit coupling which is essential for studying anisotropic crystals. All the $k \cdot p$ parameters are obtained by a robust fit to {\i…
We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in two-dimensional black phosphorus, phosphorene. The RKKY interaction enhances significantly for the low levels of hole doping owing to the nearly valence flat band. Remarkably, for the hole-doped phosphorene, the highest RKKY interaction occurs when two impurities are located along the zigzag direction and it tends to a minimum value with changing the direction from the zigzag to the armchair direction. We show that the interaction is highly anisotropic and the magnetic ground-state of two magnetic adatoms can be tun…
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…
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 study the effects of an applied in-plane uniaxial strain on the plasmon dispersions of monolayer, bilayer and double-layer phosphorene structures in the long-wavelength limit within the linear elasticity theory. In the low energy limit, these effects can be modeled through the change in the curvature of the anisotropic energy band along the armchair and zigzag directions. We derive analytical relations for the plasmon modes under uniaxial strain and show that the direction of the applied strain is important. Moreover, we observe that along the armchair direction, the changes of the plasmon …
In this article, we explore the anisotropic electron energy loss spectrum (EELS) in monolayer phosphorene based on ab-initio time dependent density functional theory calculations. Similar to black phosphorous, the EELS of undoped monolayer phosphorene is characterized by anisotropic excitonic peaks for energies in vicinity of the bandgap, and by interband plasmon peaks for higher energies. On doping, an additional intraband plasmon peak also appears for energies within the bandgap. Similar to other two dimensional systems, the intraband plasmon peak disperses as $ω_{\rm pl} \propto \sqrt{q}$ i…
The possibility of an inhomogeneous charge density wave phase is investigated in a system of two coupled electron and hole monolayers separated by a hexagonal boron nitride insulating layer. The charge density wave state is induced through the assumption of negative compressibility of electron/hole gases in a Coulomb drag configuration between the electron and hole sheets. Under equilibrium conditions, we derive analytical expressions for the density oscillation along the zigzag and armchair directions. We find that the density modulation not only depends on the sign of the compressibility but…
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…
Electric and thermoelectric properties of silicene nanoribbons doped with Al and P impurity atoms are investigated theoretically for both antiparallel and parallel orientations of the edge magnetic moments. In the former case, appropriately arranged impurities can lead to a net magnetic moment and thus also to spin thermoelectric effects. In the latter case, in turn, spin thermoelectric effects also occur in the absence of impurities. Numerical results based on ab-initio calculations show that the spin thermopower can be considerably enhanced by the impurities.
We present electronic and transport properties of a zigzag nanoribbon made of alpha-$\mathcal{T}_3$ lattice. Our particular focus is on the effects of the continous evolution of the edge modes ( from flat to dispersive) on the thermoelectric transport properties. Unlike the case of graphene nanoribbon, the zigzag nanoribbon of $α-\mathcal{T}_3$ lattice can host a pair of dispersive (chiral) edge modes at the two valleys for specific width of the ribbon. Moreover, gap opening can also occur at the two valleys depending on the width. The slope of the chiral edge modes and the energy gap strongly…
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…
