Hexagonal Bilayer Research Articles

Quantum Valley Hall Effect without Berry Curvature.

The quantum valley Hall effect (QVHE) is characterized by the valley Chern number (VCN) in a way that one-dimensional (1D) chiral metallic states are guaranteed to appear at the domain walls (DW) between two domains with opposite VCN for a given valley. Although in the case of QVHE, the total Berry curvature (BC) of the system is zero, the BC distributed locally around each valley makes the VCN well defined as long as intervalley scattering is negligible. Here, we propose a new type of valley-dependent topological phenomenon that occurs when the BC is strictly zero at each momentum. Such zero Berry curvature (ZBC) QVHE is characterized by the valley Euler number (VEN) which is computed by integrating the Euler curvature around a given valley in two-dimensional (2D) systems with space-time inversion symmetry. 1D helical metallic states can be topologically protected at the DW between two domains with the opposite VENs when the DW configuration preserves either the mirror symmetry with respect to the DW or the combination of the DW space-time inversion and chiral symmetries. We establish the fundamental origin of ZBC QVHE. Also, by combining tight-binding model study and first-principles calculations, we propose stacked hexagonal bilayer lattices including h-BX (X=As, P) and large-angle twisted bilayer graphenes as candidate systems with robust helical DW states protected by VEN.

Two-dimensional bilayer blue phosphorus Dirac-like material: a multi-orbital tight-binding investigation.

This study presents a theoretical examination of the electronic band structure of AA (AB) stacked bilayer blue phosphorus system within the fifth intralayer (5NN) and second interlayer nearest-neighbor (2NN) multi-orbital tight-binding (MOTB) approach. The variation of energy levels has been investigated through the symmetrical tensile strain of the low-buckled honeycomb lattice. Here, the primary objective is to examine the existence of Dirac electronic features in hexagonal stacked bilayer geometry. Our theoretical calculations predict that the AA bilayer is a new hexagonal two-dimensional material with px,y-orbital Dirac-like states at the high-symmetry K point. Consequently, these systems can host massless (massive) Dirac fermions. In particular, the AA bilayer exhibits zero-gap Dirac-like properties and manifests distinguishable Dirac-like cones in the presence of weak spin-orbit coupling when a modest stretch of 2.30% is achieved with a remarkably high Fermi velocity of approximately vf ≈ 0.12 × 105 m s-1. The behavior of the dispersion bands aligns reasonably well with recent experimental observations. Moreover, a stretch of 7.17% breaks some of the sublattice equivalence and enhances the spin-orbit interaction, resulting in the emergence of an electronic band gap of approximately ≈ 0.27 eV in the proximity of the high-symmetry K point. Furthermore, the tiny gap induced by the spin-orbit interaction implies topological nontriviality in the electronic state (quantum anomalous Hall state) of the honeycomb lattice. These findings categorize the AA bilayer as a rare two-dimensional Dirac-like material. This work provides, to the extent of our knowledge, a pioneering investigation into the existence of Dirac electronic properties in bilayer blue phosphorus. In addition, we present the first derivation of the MOTB model. However, the identified electronic characteristics designate this two-dimensional system as an ideal candidate for high-performance nanoelectronic devices.

Comparison of lattice thermal conductivity using ab-initio DFT, machine learning interatomic potentials, and temperature dependent effective potential: a case study of hexagonal BN and BP bilayer

Discovering high thermal conductivity materials is essential for various practical applications, particularly in electronic cooling. The significance of two-dimensional (2D) materials lies in their unique properties that emerge due to their reduced dimensionality, making them highly promising for a wide range of applications. Hexagonal boron nitride (BN), both monolayer and bilayer forms, has garnered attention for its fascinating properties. In this work, we focus on bilayer boron phosphide (BP), which is isostructural to its BN analogue. The lattice thermal conductivity of both bilayer BN and BP have been calculated using ab-initio density functional theory, machine learning with the moment tensor potential method, and the temperature-dependent effective-potential method (TDEP). The TDEP approach gives more accurate results for both BN and BP materials. The lattice thermal conductivity of bilayer BP is lower than that of bilayer BN at room temperature, attributed to increased phonon anharmonicity. This study highlights the importance of understanding phonon scattering mechanisms in determining the thermal conductivity of 2D materials, contributing to the broader understanding and potential applications of these materials in future technologies.

2D bilayer chromium pnictogens as a metallic material under DFT investigation through their structural, vibrational, electronic, and elastic properties

A comprehensive investigation of the structural, vibrational, electronic, and elastic characteristics of four hexagonal bilayer chromium pnictogens (CrX; X = N, P, As, Sb) materials has been conducted using first-principles calculations based on density functional theory (DFT). The phonon dispersion investigations demonstrate the dynamic stability of the examined hexagonal bilayers belonging to pnictogens group, in their planar structure. According to our phonon dispersion analysis, only two materials, CrN/CrN and CrP/CrP, are found to be dynamically stable, while the other two, CrAs/CrAs and CrSb/CrSb are reveal to be dynamically unstable. The band structure calculations carried out utilizing HSE06 hybrid functionals reveals the metallic nature of bilayer chromium pnictogens. In all CrX materials, the highest work function we observed for CrN/CrN material as 5.17 eV. Along the armchair direction in CrN/CrN compounds, highest elastic constants (C2D) is obtained among all CrX compounds, measured as 192.47 Nm−1 for electron carriers. In addition to examining the phonon dispersion, we also assessed their mechanical stability by the computation of elastic characteristics. Our calculated elastic parameters and polar diagrams of Young's modulus and Poisson's ratio indicate the mechanical stability of all the systems under consideration. To further our understanding of CrX compounds, we also acquired data on their deformation potential for electron carriers in both armchair and zigzag orientations. This work unequivocally demonstrates the advantages of CrX bilayers as potential materials for upcoming robust conducting devices and also possible applications for a 2D metallic material.

First-principles study of bilayer hexagonal structure CrN2 nanosheets: A ferromagnetic semiconductor with high Curie temperature and tunable electronic properties

Two-dimensional magnetic materials have been increasingly studied and discussed in the field of spintronics due to their unique electronic properties, high spin polarizability, and a variety of magnetic properties. In this paper, we report a new two-dimensional bilayer hexagonal monolayer material bilayer hexagonal structure (BHS)-CrN2 by first-principles calculations. The BHS-CrN2 nanosheet is an intrinsic ferromagnetic semiconductor material, and the Curie temperature obtained by Monte Carlo simulation is 343 K. The absence of a significant imaginary frequency in the phonon spectrum indicates the dynamic stability of BHS-CrN2. After ab initio molecular dynamics simulation, the supercell of BHS-CrN2 remains a complete structure, indicating its thermal stability. The calculated elastic moduli satisfy the Born–Huang criterion, indicating that the BHS-CrN2 system has good mechanical stability. Interestingly, the compressive strain and O atom doping can transform the electronic structure of BHS-CrN2 from a semiconductor to a half-metal, and the Curie temperature of BHS-CrN2 can be further increased to 1059 K when a 5% tensile strain is applied. Furthermore, the BHS-CrN2 in the ferromagnetic state shows a significant in-plane magnetic anisotropy energy of 0.01 meV per Cr, and the CrP2 and CrAs2 show a large out-of-plane magnetic anisotropy energy of 0.207 and 0.988 meV per Cr, respectively. The results show that the intrinsic ferromagnetic semiconductor BHS-CrN2 has good stability, high Curie temperature, and tunable magnetic properties, which is a promising material for room-temperature spintronic devices.

In-Plane Flexoelectricity in Two-Dimensional D_{3d} Crystals.

We predict a large in-plane polarization response to bending in a broad class of trigonal two-dimensional crystals. We define and compute the relevant flexoelectric coefficients from first principles as linear-response properties of the undistorted layer by using the primitive crystal cell. The ensuing response (evaluated for SnS_{2}, silicene, phosphorene, and RhI_{3} monolayers and for a hexagonal BN bilayer) is up to 1 order of magnitude larger than the out-of-plane components in the same material. We illustrate the topological implications of our findings by calculating the polarization textures that are associated with a variety of rippled and bent structures. We also determine the longitudinal electric fields induced by a flexural phonon at leading order in amplitude and momentum.

Enumeration of Moiré patterns of a hexagonal twisted bilayer: Applications to intercalated transition metals

A real-space method using generating integers is used to determine possible commensurate lattice Moiré patterns for a bilayer of two equal hexagonal lattices, which can in principle be extended to lattice mismatched bilayers. These Moiré patterns can be classified by a pair of relatively prime integers (n,m), wherein a rotation θ(n,m) of the top hexagonal lattice maps its lattice vector (n,m) to (m,n) of the bottom lattice. Within this formulation, the area of the commensurate supercell is proportional to (n2+m2+nm) and the number of coincident lattice sites per supercell is given by (n−m)2. Taking bilayer boron nitride (BN) as an example, we present how to systematically generate Moiré patterns and explore the differences in local chemistry in the interstitial region by impurity intercalation. Systematic calculations of the properties of intercalated 3d transition metals were performed in an h-BN (4,3) bilayer, corresponding to a rotation of 9.43 degrees. These calculations reveal that local symmetry in the intercalated region significantly affect the energetics and magnetization of the intercalated species. These results highlight that Moiré pattern physics is not limited to optoelectronic/electronic phenomena, such as interfacial exciton formation or magic angle superconductivity, but it also produces chemical and magnetic atomic site selectivity, which may play important roles in adsorption, catalysis, or quantum information.

Realization of a full hierarchical topology in hexagonal bilayer acoustic crystals

Realization of a full hierarchical topology in hexagonal bilayer acoustic crystals

Structural classification of boron nitride twisted bilayers and ab initio investigation of their stacking-dependent electronic structure

Since the discovery of superconductive twisted bilayer graphene which initiated the field of twistronics, moiré systems have not ceased to exhibit fascinating properties. We demonstrate that in boron nitride twisted bilayers, for a given moiré periodicity, there are five different stackings which preserve the monolayer hexagonal symmetry (i.e. the invariance upon rotations of 120°) and not only two as always discussed in literature. We introduce some definitions and a nomenclature that identify unambiguously the twist angle and the stacking sequence of any hexagonal bilayer with order-3 rotation symmetry. Moreover, we employ density functional theory to study the evolution of the band structure as a function of the twist angle for each of the five stacking sequences of boron nitride bilayers. We show that the gap is indirect at any angle and in any stacking, and identify features that are conserved within the same stacking sequence irrespective of the angle of twist.

Perturbation Theory Treatment of Spin–Orbit Coupling. III: Coupled Perturbed Method for Solids

A previously proposed noncanonical coupled-perturbed Kohn-Sham density functional theory (KS-DFT)/Hartree-Fock (HF) treatment for spin-orbit coupling is here generalized to infinite periodic systems. The scalar-relativistic periodic KS-DFT/HF solution, obtained with a relativistic effective core potential, is taken as the zeroth-order approximation. Explicit expressions are given for the total energy through third-order, which satisfy the 2N + 1 rule (i.e., requiring only the first-order perturbed wave function for determining the energy through third-order). Expressions for additional second-order corrections to the perturbed wave function (as well as related one-electron properties) are worked out at the uncoupled-perturbed level of theory. The approach is implemented in the Crystal program and validated with calculations of the total energy, electronic band structure, and density variables of spin-current DFT on the tungsten dichalcogenide hexagonal bilayer series (i.e., WSe2, WTe2, WPo2, WLv2), including 6p and 7p elements as a stress test. The computed properties through second- or third-order match well with those from reference two-component self-consistent field (2c-SCF) calculations. For total energies, E(3) was found to consistently improve the agreement against the 2c-SCF reference values. For electronic band structures, visible differences w.r.t. 2c-SCF remained through second-order in only the single-most difficult case of WLv2. As for density variables of spin-current DFT, the perturbed electron density, being vanishing in first-order, is the most challenging for the perturbation theory approach. The visible differences in the electron densities are, however, largest close to the core region of atoms and smaller in the valence region. Perturbed spin-current densities, on the other hand, are well reproduced in all tested cases.

BN Diamane-like Quasicrystal Based on 30° Twisted H-BN Bilayers and Its Approximants: Features of the Atomic Structure and Electronic Properties

The dodecagonal graphene quasicrystal (GQC) based on a 30° twisted bigraphene has been well investigated. Recently, the sp3-hybridizated carbon analog, the diamane quasicrystal as a H(F) functionalized GQC was proposed. Here we present a study of a similar sp3-hybridizated boron nitride 3-fold symmetry piezoelectric quasicrystal (BNnQC) based on a 30° twisted hexagonal BN bilayer (BNQC). The analysis of the atomic and electronic structures of its approximants based on 29.4° and 27.8° twisted h-BN bilayers has been carried by using of the density functional theory (DFT). The calculated values of the energy gaps ∼5 eV classify this predicted boron nitride material as a new wide-gap 2D quasicrystal.

Graphene Formation through Spontaneous Exfoliation of Graphite by Chlorosulfonic Acid: A DFT Study

Using exfoliating agents is one of the most promising ways for large-scale production of liquid dispersed graphenic materials from graphite. Therefore, it is crucial to know the reason why some molecules have a larger exfoliating power than others. The highest reported experimental yield for the liquid phase single-surfactant spontaneous exfoliation of graphite, i.e., without sonication, has been obtained using chlorosulfonic acid. The ability of this acid to disperse graphite is studied within the framework of Density Functional Theory (DFT). Equilibrium configurations, electron transfers, binding energies, and densities of states are presented for two acid concentrations and for two situations: adsorption (on monolayer and bilayer graphene) and intercalation (in between simple hexagonal and Bernal-stacked bilayer graphene). Experimental exfoliation power and dispersion stability are explained in terms of charge transfer—the largest found among several studied exfoliating and surfactant agents—facilitated by the good geometrical matching of chlorosulfonic acid molecules to constituent carbon rings of graphene. This matching is in the origin of the tendency toward adsorption of chlorosulfonic acid molecules on graphene monolayers when they separate, originating the charging of the monolayers that precludes their reaggregation.

A discrete-to-continuum model of weakly interacting incommensurate two-dimensional lattices: The hexagonal case

In this paper, we extend the discrete-to-continuum procedure we developed in Español et al. (2018) to derive a continuum variational model for a hexagonal twisted bilayer material in which one layer is fixed. We use a discrete energy containing elastic terms and a weak interaction term that could utilize either a Lennard-Jones potential or a Kolmogorov–Crespi potential. To validate our modeling, we perform numerical simulations to compare the predictions of the original discrete model and the proposed continuum model, which also show an agreement with experimental findings for, e.g., twisted bilayer graphene.

Computational study on the impact of Nb doping on electronic structure, magnetic and optical properties of hexagonal bilayer BN

We investigate the impact of Niobium (Nb) doping on the electronic structure, and magnetic and optical properties of the bilayer hexagonal boron nitride (BL hBN) using spin-polarized density functional theory (DFT). The calculated values of formation energy reveal the structural stability of Nb-doped BL hBN. The structural parameter analysis indicates the bond length and lattices constant of BL hBN increase due to Nb doping. In addition, it is found that the energy band gap of BL hBN is reduced from 5.1 eV to 3.9 eV due to 5.5% of Nb doping. Moreover, the obtained magnetic moment of 2 μ B and 4 μ B for Nb concentrations of 5.55% and 11.11% respectively, indicate the turning of the paramagnetic behavior of pure BL hBN to ferromagnetic. Besides, we have also found that the first and second nearest neighboring (NN) magnetic interaction between two dopants (Nb atoms) is ferromagnetic. Whereas, the third nearest neighbor interaction is antiferromagnetic. More interestingly, using mean field theory together with spin-polarized DFT ferromagnetic transition temperature (T c ) of 367 K is obtained for 11.11% of Nb-doped BL hBN. Furthermore, a significant enhancement of the absorption coefficient due to Nb doping in both the visible and mid-to-far-infrared regions was observed. Based on those results, we suggest that Nb-doped BL hBN is a good candidate material for nanoelectronics, spintronics, and optoelectronics applications.

The encapsulation of atomically-thin MgB2-based superconductors in two-dimensional material bilayers

Two-dimensional (2D) superconductors are a class of materials with unique properties that can potentially exhibit novel superconductivity at a reduced dimensionality, as well as pave the way for miniaturizing superconducting devices at the atomic limit. However, such materials are highly sensitive to interaction with their substrates and the environment, and therefore it is necessary to find potential methods for chemically isolating them. We address this problem by examining the possibility of isolating the medium-temperature 2D MgB2-based superconductors. We examine two possible structures: the monolayer stoichiometric MgB2 and the B-caged Mg3B8 structure. By solving the anisotropic Eliashberg equations, we predict that the latter possesses K upon application of a small lateral (3% tensile) strain, with an electron–phonon coupling of 0.88. To investigate protecting the superconductivity of these two layers, we apply density functional theory calculations to examine their encapsulation in a graphene bilayer or a hexagonal boron nitride bilayer. We find that both have high potential as encapsulation systems to protect the superconductivity of the 2D MgB2-based superconductors, in particular B-caged (B–Mg) n systems.

Effects of Electric Field and External Magnetic Field on the Electronic and Thermoelectric Properties of the h-BAs Monolayer and Bilayer: Tight-Binding Approach

Newly, two-dimensional (2D) materials atoms of groups IV and III-V have obtained extensive attention due to their novel properties. In this work, we apply the tight-binding model and Green’s function approach to the hexagonal boron arsenide (h-BAs) monolayer and bilayer to investigate their electronic and thermoelectric properties. We find that the h-BAs monolayer behaves as a p-type semiconductor and it can be changed to the n-type by applying the external magnetic field. Also, the h-BAs bilayer with (A-A) stacked has a semi-metallic property but (A-B) stacked is a semiconductor. The results show that the band gap can be controlled by applying an electric field and an external magnetic field. We obtain that the thermal and electrical conductivity of the h-BAs monolayer and bilayer increase in the presence of an electric field and an external magnetic field. More, controlling the Seebeck coefficient of the material is a unique phenomenon that provides advanced applications for these materials in thermoelectric coolers and waste heat harvesting. Here, we have been able to regulate the Seebeck coefficient of the h-BAs monolayer and bilayer by using the electric and external magnetic fields.

Density functional theory: The structural, electronic, optical, mechanical, and vibrational properties of bulk and Te-doped SnSe2

This work performs a computational prediction on SnSe2 and Te-doped bilayer material. Doping the Te element onto SnSe2 can lead to a decrease in bandgap [Formula: see text] energy (from 1.95 eV to 0.94 eV) and cause a drop in both conduction band (CB) and valence band (VB), apart from the valence band maximum (VBM). This may lead to an increase in electrical conductivity. The decrease in [Formula: see text] parameter may result in an impact on electronic effective mass and transport properties when the SnSe2 bilayer is doped with Te. A redshift observed on both the optical absorption and the dielectric constant plots may suggest that a tensile force could be possibly induced when we dope the SnSe2 compound. The identical elastic constants of C[Formula: see text] and C[Formula: see text] evaluated could describe the nature of the close-packed hexagonal bilayer. Finally, the ductility slightly increases when we mix the Te element onto the SnSe2 alloy. It is also worth noting that both SnSe2 and Te-doped are dynamically stable, according to the phonon dispersion.

Effect of External Electric Field Applied to Bilayer Graphene Bandgap: Density Functional Theory Study

Graphene is a prominent material in a wide range of applications, however, the gapless nature of graphene limits its great performance in certain applications, such as in optoelectronic and photocatalytic applications field. Opening the bandgap has become one of the focused studies on graphene material today. Here, we used density functional theory (DFT) calculation to investigate the bandgap opening of bilayer graphene by external electric field applying. The calculation was performed on hexagonal stacked bilayer graphene structure using three different approximations and functional DFT; that is generalized gradient approximation (GGA) PBE and PW-91, as well as Local-density approximations (LDA) -CAPZ. The external electric field varied from 0.0 to 0.5 eV/Å/e in various electric field directions. The calculations results shows that the external E-F applied in perpendicular direction open the bandgap almost 4-times than non-determined the electric field direction. The bandgap opening by LDA functional calculation perform smaller bandgap opening compared to GGA calculation results, while the PBE and PW-91 of GGA produced similar values at low electric field applied. The larger bandgap of 0.80 eV obtained at 0.3 eV/Å/e electric field applied calculated with both GGA functional At 0.5 eV/Å/e electric field applied, bandgap with GGA-PBE almost zero, and the crystal structure changed from cubic to triclinic with layer position become apart.

Scanning probe analysis of twisted graphene grown on a graphene/silicon carbide template

Overlayer growth of graphene on an epitaxial graphene/silicon carbide (SiC) as a solid template by ethanol chemical vapor deposition is performed over a wide growth temperature range from 900 °C to 1450 °C. Structural analysis using atomic force and scanning tunneling microscopies reveal that graphene islands grown at 1300 °C form hexagonal twisted bilayer graphene as a single crystal. When the growth temperature exceeds 1400 °C, the grown graphene islands show a circular shape. Moreover, moiré patterns with different periods are observed in a single graphene island. This means that the graphene islands grown at high temperature are composed of several graphene domains with different twist angles. From these results, we conclude that graphene overlayer growth on the epitaxial graphene/SiC solid at 1300 °C effectively synthesizes the twisted few-layer graphene with a high crystallinity.

On the Formation of Honeycomb Superlattices from PbSe Quantum Dots: The Role of Solvent-Mediated Repulsion and Facet-to-Facet Attraction in NC Self-Assembly and Alignment.

Semiconductor superstructures made from assembled and epitaxially connected colloidal nanocrystals (NCs) hold promise for crystalline solids with atomic and nanoscale periodicity, whereby the band structure can be tuned by the geometry. The formation of especially the honeycomb superstructure on a liquid substrate is far from understood and suffers from weak replicability. Here, we introduce 1,4-butanediol as an unreactive substrate component, which is mixed with reactive ethylene glycol to tune for optimal reactivity. It shows us that the honeycomb superlattice has a NC precursor state before oriented attachment occurs, in the form of a self-assembled hexagonal bilayer. We propose that the difference between the formation of the square or honeycomb superstructure occurs during the self-assembly phase. To form a honeycomb superstructure, it is crucial to stabilize the hexagonal bilayer in the presence of solvent-mediated repulsion. In contrast, a square superstructure benefits from the contraction of a hexagonal monolayer due to the absence of a solvent. A second experiment shows the very last stage of the process, where the increasing alignment of NCs is quantified using selected-area electron diffraction (SAED). The combination of transmission electron microscopy (TEM), SAED, and tomography used in these experiments shows that the (100)/(100) facet-to-facet attraction is the main driving force for NC alignment and attachment. These findings are validated by coarse-grained molecular dynamic simulations, where we show that an optimal NC repulsion is crucial to create the honeycomb superstructure.