Bilayer Phosphorene Research Articles

A DFT study for improving the thermoelectric efficiency in AB bilayer phosphorene using uniaxial strain

Phosphorene is a two-dimensional (2D) semiconductor material that has attracted a lot of interest in several fields of applications. The anisotropic character of this new category of materials allows the tunability of electrical, optical, thermal, and other properties by the application of fields or forces. In the present work, using density functional theory (DFT) with the hybrid functional and Boltzmann transport equation, electronic properties, phonon dispersion and thermoelectric properties were calculated for AB bilayer phosphorene. To study the effect of the layer deformation on the thermoelectric properties of phosphorene, uniaxial tensile and compressive strain along the armchair and the zigzag direction was applied. The results revealed that AB bilayer phosphorene under a uniaxial tensile strain of 3 % along the armchair direction improve the thermoelectric properties, giving rise to a significant increase of the figure of merit to ZT = 1.24 at n-type doping. The increase of ZT upon uniaxial deformation corresponds to an increase of 110 % with respect to ZT of the unstrained AB bilayer phosphorene structure (ZT = 0.59 at 300 K).

The effect of vacancy induced localized states on the thermoelectric properties of armchair bilayer phosphorene nanoribbons

We examine an armchair bilayer phosphorene connected to two leads, one hot and one cold, on both sides, investigating the thermoelectric properties of this system with periodic vacancies along the armchair direction and at the center of the nanoribbon. Initially, we analytically demonstrate that the creation of a vacancy results in the generation of a localized state around it. Subsequently, we illustrate that the presence of periodic vacancies leads to the formation of a new energy band in the energy bandstructure. Our calculations reveal that by varying the distance between vacancies, one can tune the width of the corresponding transmission channel, the generated electric power, and the thermoelectric efficiency.

Electrostatic Gating of Phosphorene Polymorphs.

The ability to directly monitor the states of electrons in modern field-effect transistors (FETs) could transform our understanding of the physics and improve the function of related devices. In particular, phosphorene allotropes present a fertile landscape for the development of high-performance FETs. Using density functional theory-based methods, we have systematically investigated the influence of electrostatic gating on the structures, stabilities, and fundamental electronic properties of pristine and carbon-doped monolayer (bilayer) phosphorene allotropes. The remarkable flexibility of phosphorene allotropes, arising from intra- and interlayer van der Waals interactions, causes a good resilience up to equivalent gate potential of two electrons per unit cell. The resilience depends on the stacking details in such a way that rotated bilayers show considerably higher thermodynamical stability than the unrotated ones, even at a high gate potential. In addition, a semiconductor to metal phase transition is observed in some of the rotated and carbon-doped structures with increased electronic transport relative to graphene in the context of real space Green's function formalism.

Insight into the stacking effect on shifted patterns of bilayer phosphorene: a comprehensive first-principles study

It is crucial to deeply understand how the interlayer interaction acts on controlling the structural and electronic properties of shifted patterns of bilayer phosphorene. A comprehensive first-principles study on the bilayer phosphorene through relative translation along different directions has revealed that there is a direct correlation between the potential energy surface and the interlayer equilibrium distance. The shorter the interlayer distance, the lower the potential energy surface. The shifted patterns with the most stable state, the metastable state, and the transition state (with energy barrier of ∼1.3 meV/atom) were found associated with the AB, the Aδ, and the TS stacking configurations, respectively. The high energy barriers, on the other hand, are ∼9.3 meV/atom at the AA stacking configuration along the zigzag pathway, ∼5.3 meV/atom at the AB′ stacking configuration along the armchair pathway, and ∼11.2 meV/atom at the AA′ stacking configuration along the diagonal pathway, respectively. The character of electronic bandgap with respect to the shifting shows an anisotropic behavior (with the value of 0.69–1.22 eV). A transition from the indirect to the direct bandgap occurs under the shifting, implying a tunable bandgap by stacking engineering. Furthermore, the orbital hybridization at the interfacial region induces a redistribution of the net charge (∼0.002–0.011 e) associated with the relative shifting between layers, leading to a strong polarization with stripe-like electron depletion near the lone pairs and accumulation in the middle of the interfacial region. It is expected that such interesting findings will provide a fundamental reference to deeply understand and analyze the complex local structural and electronic properties of twisted bilayer phosphorene and will make the shifted patterns of bilayer phosphorene promising for nanoelectronics as versatile shiftronics materials.

Photonic spin Hall effect in twisted bilayer phosphorene

We investigate the photonic spin Hall effect of a linearly polarized Gaussian beam reflected on the surface of twisted bilayer phosphorene. The photonic spin shift depends strongly on optical resonance behavior, which is determined by the twist angle. The magnified spin shift near the Brewster angle is sensitive to the twist angle and can be fitted by numerical models. In particular, the spin shifts in the terahertz region of frequency are well within the current experimental detection precision. Our findings suggest that the photonic spin Hall effect is promising for precise characterization of the optical property and the structure of twisted bilayer phosphorene.

Investigation of localized wave function in bilayer phosphorene nanoribbon

Investigation of localized wave function in bilayer phosphorene nanoribbon

Fermi velocity and effective mass of quasiparticles in bilayer phosphorene nanoribbons

Based on the Green’s function approach in combination with the tight-binding approximation, we have investigated the electronic properties of zigzag bilayer phosphorene nanoribbons (ZBLPNRs). A complete and fully reversible metal-to-semiconductor or insulator phase transition has been observed via tuning a perpendicular electric field. We explain the effect of the interlayer hopping parameter on the electronic characterizations, namely, the energy band-gap, Fermi velocity, and effective mass of carriers in biased ZBLPNRs. In the presence of the interlayer hopping term, the band structure of a ZBLPNR in the vicinity of the Fermi level has the form of two tilted Dirac cones, while, in the absence of it, the created cones are not tilted. Besides, the bands above and below the Fermi level are not symmetric, i.e., there is no electron–hole symmetry for both limits of the interlayer coupling. A remarkable tuning of both the Fermi velocity and the reciprocal effective mass can be observed by adjusting the external bias voltage. At certain critical bias voltages, the band edge reciprocal masses and carrier velocities become zero, i.e., the electrons exhibit localization behaviour. This phenomenon is indeed a transition from massive to massless Dirac fermions and vice versa. The possibility of simultaneous control of the thermal and magnetic properties using an electric agent, which can be realized experimentally by using a perpendicular potential difference, opens up possibilities for low-power-consuming thermomagnetic devices based on ZBLPNRs.

Prediction of superconductivity in Li, K, Ca, and Sr-intercalated blue phosphorene bilayer using first-principle calculations

Blue phosphorene is an interesting two-dimensional (2D) material, which has attracted the attention of researchers, due to its affluent physical and chemical properties. In recent years, it was discovered that the intercalation of alkali metals and alkaline earth metals in 2D materials may lead to conventional Bardeen–Cooper–Schrieffer (BCS) superconductivity. In this work, the electronic structure, phonon dispersion, Eliashberg spectral function, electron–phonon coupling (EPC), and the critical temperature of blue phosphorene bilayer intercalated by alkali metals (Li, and K) and alkaline earth metals (Ca, and Sr) for both AB and AC stacking orders are studied using the density functional theory and the density functional perturbation theory, within the generalized gradient approximation with van der Waals correction. The present work shows that the blue phosphorene bilayer is dynamically stable in AB stacking for Li and AC stacking for K, Ca, and Sr, and after intercalation, it transforms from a semiconductor to a metal owing to charge transfer between intercalated atoms and phosphorene. Furthermore, the EPC constant and the critical temperature are higher than those of 2D BCS-type superconductors. They are about 3 and 24.61 K respectively for K-intercalated blue phosphorene bilayer. Thus, our results suggest that blue phosphorene is a good candidate for a superconductor.

Quantum manifestations in electronic properties of bilayer phosphorene nanoribbons.

Recently, a new edge structure named ZZ(U) has been evidenced as the lowest-energy structure for bilayer phosphorene nanoribbons (PNRs). Owing to strong quantum confinement effects and edge states, width and edge are the two most important factors that influence the properties of PNRs in nanosized microelectronics. In this study, we systematically investigated the evolution of the electronic properties of bilayer PNRs with different edge configurations as the widths vary. The four types of edges explored include ZZ(Pristine), ZZ(Klein), ZZ(Tube), and newly found ZZ(U). As the widths change from 14 to 40 Å, the ZZ(Pristine) are always metallic with edge states penetrating the Fermi level, while the others are semiconductors. The edge states in ZZ(Klein) are located in the two lowest conduction bands. However, in ZZ(U), the edge states are nearly hidden in the bulk band structure, and its carrier transportation exhibits almost perfect 2D layers, nearly eliminating the U-edge influence. Our results pave the way for phosphorene's utilization in electronics and optoelectronics.

Multidirectional strain-induced thermoelectric figure of merit enhancement of zigzag bilayer phosphorene nanoribbons

We have theoretically investigated strain-induced thermoelectric power generation properties of zigzag bilayer phosphorene nanoribbon. Since energy bandgap size and edge state dispersion play a significant role in the thermoelectric properties of such a structure, we have investigated the effect of strain in different directions on these two quantities. We have shown that by applying both tensile and compressive strains in different directions, it is possible to properly tune the energy bandgap size and adjust the edge state dispersion. We have also selected strain combinations in different directions that simultaneously increase the size of the energy bandgap and decrease the dispersion of the edge state. It has shown that with such combinations of strains, the maximal figure of merit has been improved by about two times compared to the pristine case.

First-principles investigation of aluminum intercalation in bilayer blue phosphorene for Al-ion battery

Here, we investigate the possibility of bilayer phosphorene as an anode material for aluminum-ion batteries using first-principles calculations. The characteristics of negative electrode materials are desirable with small volume expansion, large capacity and high mobility. We calculated the adsorption energies, optimal adsorption sites, diffusion barriers, theoretical capacities, open circuit voltages (OCVs), and structural stability of aluminum (Al) on the surface and interlayers of bilayer phosphorene. The intercalation of Al did not significantly change the volume of the bilayer phosphorene. The diffusion barrier of Al on the surface along the zigzag direction is 0.13 eV, while the diffusion barrier along the armchair direction is 0.49 eV. When Al is intercalated into the phosphorene interlayer, the diffusion barriers along the armchair and zigzag directions are 0.77 eV and 0.47 eV, respectively. It can be seen that the diffusion of Al between layers is also relatively easy. And with the increase of Al intercalation concentration, the theoretical capacity of bilayer phosphorene can reach 1047 mAhg−1. These results demonstrate that bilayer phosphorene is a potential candidate as anode material for aluminum-ion batteries.

Unveiling the moiré pattern evolution and superlubricity in twisted bilayer 2D phosphorene at atomistic scale

Moiré patterns are commonly evidenced on two-dimensional (2D) van der Waals (vdW) bilayers stacked with rotational misalignment or slight lattice mismatch, which can dramatically influence the interface mechanical properties. Understanding the basic characteristics of moiré patterns are essential to tune the interfacial mechanical properties. Herein, molecular dynamics (MD) simulations are performed to capture the atomic evolution in the interface of the bilayer phosphorene during rotation and sliding. The hexagonal moiré patterns are observed in bilayer blue phosphorene, while the transition from quadrate to one dimensional stripe-like moiré pattern is evidenced in bilayer black phosphorene as the twist angle increases. However, the unique one-dimensional stripe-like moiré pattern always exists in black phosphorene/blue phosphorene heterogeneous interface during rotation. The reconstruction and deformation of Moiré pattern are determined by the competition between intralayer strain and interlayer coupling. The energy barrier for the rotation of heterogeneous bilayers is almost an order of magnitude smaller than that in homogeneous bilayers. As a result, the friction forces of heterogeneous bilayer during sliding can fall in the scope of superlubricity more possibly. However, the surface roughness, contact size and twist angle also alter the friction force. The results provide a comprehensive understanding on the Moiré superlattices.

Atomically Sharp, Closed Bilayer Phosphorene Edges by Self-Passivation.

Two-dimensional 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 surface contamination and reduce e-beam damage, allowing us to observe intrinsic edge configurations. The bilayer zigzag (ZZ) edge was found to be the most stable edge configuration under e-beam irradiation. Through first-principles calculations and TEM image analysis under various tilting and defocus conditions, we find that bilayer ZZ edges undergo edge reconstruction and so acquire closed, self-passivated edge configurations. The extremely low formation energy of the closed bilayer ZZ edge and its high stability against e-beam irradiation are confirmed by first-principles calculations. Moreover, we fabricate bilayer phosphorene nanoribbons with atomically sharp closed ZZ edges. The identified bilayer ZZ edges will aid in the fundamental understanding of the synthesis, degradation, reconstruction, and applications of phosphorene and related structures.

Direct mapping of edge states in bilayer zigzag phosphorene nanoribbons into a SSH ladder model and optimizing their thermoelectric performance via edge state engineering

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 applying periodic point potentials at the boundaries.

Magneto-thermoelectric transport of bilayer phosphorene: A generalized tight-binding model study

In this study, we investigate the thermoelectric transport properties of bilayer phosphorene under a composite magnetic and electric field (Ez and Bz). The complete Landau level spectrum and the real-space Landau wavefunctions are obtained using the generalized tight-binding model, which simultaneously considers the effects of geometrical structures, atomic interactions, and external fields. To our knowledge, this is the first study that uses spatially distributed subenvelope functions based on real sublattices to calculate the transition rate of Landau states in a truly two-dimensional system. The results show the nonmonotonic dependences of conductivity on the Fermi level, Ez strength, and direction, which enrich the thermopower and Nernst signal behaviors.

Thermal conductivity of two stable bilayer phosphorene stackings: A computation study

We report the thermal conductivity of two dynamically stable bilayer phosphorene stackings, i.e., a twisted phase with a twist angle of ∼70.5° (or 2O-tαP phase) and a shifting phase with half of the lattice constants (or AB phase). This was achieved by using the first-principles-driven lattice dynamics calculations and a fully iterative solver of the Boltzmann transport equation, the latter including an anharmonic phonon–phonon scattering effect. At room temperature, the thermal conductivity of the 2O-tαP phase is 146 and 108 W/mK along its two orthogonal lattice basis vectors, respectively, larger than that along the armchair direction (69 W/mK) of the AB phase, while smaller than that along the AB zigzag direction (164 W/mK); with an increasing temperature, the conductivity decreases along the basis vectors of the 2O-tαP and AB stackings, and the anisotropy lessens for both stackings. The thermal transport anisotropies for the two kinds of bilayer stacking can be attributed to the different proportions of their acoustic branches along different directions. In particular, the phonon mean free path showed that the in-plane transverse acoustic branch is the main contribution of the thermal conductivity along the short lattice constant direction of the 2O-tαP phase due to the twist angle extending the propagation path of transverse acoustic waves in the direction. Finally, the thermal conductivity accumulation was revealed to increase in the form of a hyperbolic tangent with mean free path of the phonons, which can be used to evaluate the size effect of the stacking materials in practice.

Modulation of the electronic properties of blue phosphorene/stanene heterostructures by electric field and interlayer distance

Two-dimensional (2D) materials of perpendicular integration have recently emerged, which can be used to design novel electronic and optoelectronic devices. The heterostructures composed of stanene and blue phosphorene are investigated, the band structures and electronic properties of stanene/blue phosphorene are explored by using the First-principle calculation. It can be found that tuning the interlayer distance between stanene and blue phosphorene can effectively modulate the electronic structure of stanene/blue phosphorene heterostructures. The results show that the intrinsic electronic properties of stanene and blue phosphorene are well preserved in the unconstrained bilayers. Vertical positive and negative electric fields are applied in the heterostructure with electric fields between −0.6 and 0.7 V/Å, and the band gap increases with electric fields increasing. When in-plane biaxial tensile strain is applied, the band gap value increases with strain value increasing. The maximum band gap value is obtained at about strain 4%. When compressive strain is applied, the band gap decreases with the increase of the electric field and transforms to metallic at about strain −3%. The present work provides an effective way to tune the electronic structure and band gap of the stanene/blue phosphorene bilayer.

Eliminating Edge Electronic and Phonon States of Phosphorene Nanoribbon by Unique Edge Reconstruction (Small 2/2022)

Edge Reconstruction An unprecedented U-edge reconstruction with the lowest energy is revealed to occur easily in the bilayer phosphorene. Such U-edge reconstruction exhibits unexpectedly ultrafast electronic and thermal transport, nearly without edgeless scattering. More information can be found in article number 2105130 by Junfeng Gao, Gang Zhang, and co-workers.

Twist-angle two-dimensional superlattices and their application in (opto)electronics

Twist-angle two-dimensional systems, such as twisted bilayer graphene, twisted bilayer transition metal dichalcogenides, twisted bilayer phosphorene and their multilayer van der Waals heterostructures, exhibit novel and tunable properties due to the formation of Moiré superlattice and modulated Moiré bands. The review presents a brief venation on the development of “twistronics” and subsequent applications based on band engineering by twisting. Theoretical predictions followed by experimental realization of magic-angle bilayer graphene ignited the flame of investigation on the new freedom degree, twist-angle, to adjust (opto)electrical behaviors. Then, the merging of Dirac cones and the presence of flat bands gave rise to enhanced light-matter interaction and gate-dependent electrical phases, respectively, leading to applications in photodetectors and superconductor electronic devices. At the same time, the increasing amount of theoretical simulation on extended twisted 2D materials like TMDs and BPs called for further experimental verification. Finally, recently discovered properties in twisted bilayer h-BN evidenced h-BN could be an ideal candidate for dielectric and ferroelectric devices. Hence, both the predictions and confirmed properties imply twist-angle two-dimensional superlattice is a group of promising candidates for next-generation (opto)electronics.

Spin-gapless semiconducting Cl-intercalated phosphorene bilayer: a perfect candidate material to identify its ferroelectric states by spin-Seebeck currents

Two-dimensional multiferroic materials, combining the ferroelectric (FE) state with the ferromagnetic (FM) state, have long been regarded as one of the core topics in materials science.