Topological materials are fertile ground for investigating topological phases of matter and topological phase transitions. In particular, the quest for novel topological phases in 2D materials is attracting fast growing attention. Here, using Floquet-Bloch theory, we propose to realize chiral topological phases in 2D hexagonal FeX2 (X=Cl, Br, I) monolayers under irradiation of circularly polarized light. Such 2D FeX2 monolayers are predicted to be dynamical stable, and exhibit both ferromagnetic and semiconducting properties. To capture the full topological physics of the magnetic semiconductor under periodic driving, we adopt ab initio Wannier-based tight-binding methods for the Floquet-Bloch bands, with the light-induced band gap closings and openings being obtained as the light field strength increases. The calculations of slab with open boundaries show the existence of chiral edge states. Interestingly, the topological transitions with branches of chiral edge states changing from zero to one and from one to two by tuning the light amplitude are obtained, showing that the topological floquet phase of high Chern number can be induced in the present Floquet-Bloch systems.
We demonstrate single crystal growth of wafer-scale hexagonal boron nitride (hBN), an insulating atomic thin monolayer, on high-symmetry index surface plane Cu(111). The unidirectional epitaxial growth is guaranteed by large binding energy difference, ~0.23 eV, between A- and B-steps edges on Cu(111) docking with B6N7 clusters, confirmed by density functional theory calculations.
In monolayer hexagonal lattices, two inequivalent valleys appear in the Brillouin zone. With inversion symmetry breaking, we find chiral phonons with valley contrasting circular polarization and ionic magnetic moment. At valley centers, there is a three-fold rotational symmetry endowing phonons with a quantized pseudo angular momentum, which includes spin and orbital parts. From conservation of the pseudo angular momentum, crystal momentum and energy, selection rules in intervalley scattering of electrons by phonons are obtained. The chiral valley phonons are verified and the selection rules a…
Elemental phosphorous is believed to have several stable allotropes that are energetically nearly degenerate, but chemically reactive. To prevent chemical degradation under ambient conditions, these structures may be capped by monolayers of hexagonal boron nitride ({\em h}-BN) or graphene. We perform {\em ab initio} density functional calculations to simulate scanning tunneling microscopy (STM) images of different layered allotropes of phosphorus and study the effect of capping layers on these images. We find that protective monolayers of insulating {\em h}-BN allow to distinguish between the …
We design a hybrid graphene/hexagonal boron nitride superlattice monolayer and investigate its thermoelectric properties using density functional theory and Boltzmann transport equations with the relaxation time accurately treated by electron-phonon coupling calculations. Compared with that of pristine graphene, the lattice thermal conductivity of the superlattice structure is more than two orders of magnitude lower due to the enhanced three-phonon scattering process originated from the mixed-bond characteristics. Besides, the coexistence of light and heavy bands around the Fermi level leads t…
We demonstrate electrical spin injection from a ferromagnet to a bilayer graphene (BLG) through a monolayer (ML) of single-crystal hexagonal boron nitride (h-BN). A Ni81Fe19/ML h-BN/BLG/h-BN structure is fabricated using a micromechanical cleavage and dry transfer technique. The transport properties across the ML h-BN layer exhibit tunnel barrier characteristics. Spin injection into BLG has been detected through non local magnetoresistance measurements.
Group IV and V monolayers are very crucial 2D materials for their high carrier mobilities, tunable band gaps, and optical linear dichroism. Very recently, a novel group IV-V binary compound, Sn2Bi, has been synthesized on silicon substrate, and has shown very interesting electronic properties. Further investigations have revealed that the monolayer would be stable in freestanding form by hydrogenation. Inspired by this, by means of first-principles calculations, we systematically predict and investigate eight counterparts of Sn2Bi, namely Si2P, Si2As, Si2Sb, Si2Bi, Ge2P, Ge2As, Ge2Sb, and Ge2B…
Novel materials with tunable magnetic states play a significant role in the development of next-generation spintronic devices. In this paper, we examine the role of biaxial strain on the electronic properties of vacancy-decorated hexagonal boron nitride (h-BN) monolayers using density functional theory calculations. We found that the strain can lead to switching of the magnetic state for h-BN monolayers with boron vacancy or divacancy. Our findings promise a new route for the operation of low-dimensional spintronic devices.
The strong light-matter interaction in transition Metal dichalcogenides (TMDs) monolayers (MLs) is governed by robust excitons. Important progress has been made to control the dielectric environment surrounding the MLs, especially through hexagonal boron nitride (hBN) encapsulation, which drastically reduces the inhomogeneous contribution to the exciton linewidth. Most studies use exfoliated hBN from high quality flakes grown under high pressure. In this work, we show that hBN grown by molecular beam epitaxy (MBE) over a large surface area substrate has a similarly positive impact on the optic…
We investigate the adsorption of a flexible polymer at a hexagonally patterned monolayer. All conformational polymer phases are identified, which enables the construction of a hyperphase diagram, parameterized by temperature and monolayer adsorption strength. The energy scale associated with the adsorption strength is a material parameter of the hybrid system that generically accommodates the behavior of entire classes of polymers interacting with hexagonal substrates. We also discuss a bridge-building mechanism for the formation of unique layered polymer structures with potential for applicat…
The electronic structure of monolayer hexagonal boron nitride grown on Ni by the diffusion and precipitation method was studied by x-ray absorption spectroscopy, emission spectroscopy, x-ray photoelectron spectroscopy and micro-ultraviolet photoemission spectroscopy. No indication of hybridization between h-BN pi and Ni 3d orbitals was observed. That is, the monolayer h-BN was found to be in the quasi-free-standing state. These results are in striking contrast to those of previous studies in which h-BN was strongly bound to the Ni surface by the orbital hybridization. The absence of hybridizat…
We model optical absorption of monolayer and bilayer graphene on hexagonal boron nitride for the case of closely-aligned crystal lattices. We show that perturbations with different spatial symmetry can lead to similar absorption spectra. We suggest that a study of the absorption spectra as a function of the doping for almost completely full first miniband is necessary to extract meaningful information about the moire characteristics from optical absorption measurements and to distinguish between various theoretical proposals for the physically realistic interaction. Also, for bilayer graphene,…
Using scanning tunneling microscopy, we show that Si deposition on Pt(111) at 300K leads to a network of one-dimensional Si chains. On the bare Pt(111) surface, the chains, embedded into the Pt surface, are orientated along the <112>-direction. They disappear within a few hours in ultrahigh vacuum due to the presence of residual gas. Exposing the chains to different gases deliberately reveals that CO is largely responsible for the disappearance of the chains. The chains can be stabilized by a monolayer of hexagonal boron nitride, which is deposited prior to the Si deposition. The resulting Si …
Embedding a WS$_2$ monolayer in flakes of hexagonal boron nitride allowed us to resolve and study the photoluminescence response due to both singlet and triplet states of negatively charged excitons (trions) in this atomically thin semiconductor. The energy separation between the singlet and triplet states has been found to be relatively small reflecting rather weak effects of the electron-electron exchange interaction for the trion triplet in a WS$_2$ monolayer, which involves two electrons with the same spin but from different valleys. Polarization-resolved experiments demonstrate that the h…
Puckered honeycomb Sb monolayer, the structural analog of black phosphorene, has been recently successfully grown by means of molecular beam epitaxy. However, little is known to date about the growth mechanism for such puckered honeycomb monolayer. In this study, by using scanning tunneling microscopy in combination with first-principles density functional theory calculations, we unveil that the puckered honeycomb Sb monolayer takes a kinetics-limited two-step growth mode. As the coverage of Sb increases, the Sb atoms firstly form the distorted hexagonal lattice as the half layer, and then the…
Folded regions are commonly encountered in a number of hexagonal boron nitride (h-BN) based bulk and nanostructured materials. Two types of structural modifications occur in folded h-BN layers: local curvature at the folded edges and interlayer shear of the layers which changes the stacking of the overlapping flat regions. In this work we discuss, via density functional theory simulations, the impact of these structural modifications on the ground state electronic structure of the pristine monolayer. We show that, depending on the fold orientation, the overlapping region might present differen…
Stepwise deposition of Li atoms onto hexagonal boron nitride (hBN) monolayer on Ir(111) is investigated by means of angle-resolved photoemission spectroscopy and low-energy electron diffraction. Sequential Li deposition progressively shifts the band structure of hBN to higher binding energies due to the induction of a variable electric potential originating from electronic charge donation by alkali atoms. At small coverages, Li atoms preferably intercalate under the hBN layer, where they are highly charged and give rise to a large initial shift of the band structure. Additionally, intercalated…
Diffusion currents are theoretically examined in two-dimensional Dirac materials, such as those of the transition metal dichalcogenides (TMD) family. The transversal effects are analogues of the valley Hall (VHE) and photogalvanic (PGE) transport phenomena in case when the electron driving force is not an electric field but a gradient of electron density distribution in the sample. The latter can be created by a finite-sized laser spot or by the injection of electrons from other materials. We develop the theory of diffusive VHE effect assuming the anisotropic electron-short-range-impurity skew…
Monolayer of hexagonal boron nitride (h-BN), commonly known as "white graphene" is a promising wide bandgap semiconducting material for deep-ultaviolet optoelectronic devices. In this report, the light absorption of a single layer hexagonal boron nitride is calculated using a tight-binding Hamiltonian. The absorption is found to be monotonically decreasing function of photon energy compared to graphene where absorption coefficient is independent of photon energy and characterized by the effective fine-structure constant.
We study silicene on hexagonal boron nitride, using first principles calculations. Since hexagonal boron nitride is semiconducting, the interaction with silicene is weaker than for metallic substrates. It therefore is possible to open a 50 meV band gap in the silicene. We further address the effect of Mn decoration by determining the onsite Hubbard interaction parameter, which turns out to differ significantly for decoration at the top and hollow sites. The induced magnetism in the system is analyzed in detail.
We theoretically study physical properties of the most promising color center candidates for the recently observed single-photon emissions in hexagonal boron nitride (h-BN) monolayers. Through our group theory analysis combined with density functional theory (DFT) calculations we provide several pieces of evidence that the electronic properties of the color centers match the characters of the experimentally observed emitters. We calculate the symmetry-adapted multi-electron wavefunctions of the defects using group theory methods and analyze the spin-orbit and spin-spin interactions in detail. …
We propose monolayer epitaxial graphene and hexagonal boron nitride (h-BN) as ultimate thickness covalent spacers for magnetoresistive junctions. Using a first-principles approach, we investigate the structural, magnetic and spin transport properties of such junctions based on structurally well defined interfaces with (111) fcc or (0001) hcp ferromagnetic transition metals. We find low resistance area products, strong exchange couplings across the interface, and magnetoresistance ratios exceeding 100% for certain chemical compositions. These properties can be fine tuned, making the proposed ju…
It is highly desirable to search for promising two-dimensional (2D) monolayer materials for deep insight of 2D materials and applications. We use first-principles method to investigate tetragonal perovskite oxide monolayers as 2D materials. We find four stable 2D monolayer materials from SrTiO$_3$, LaAlO$_3$, KTaO$_3$, and BaFeO$_3$, denoting them as STO-ML, LAO-ML, KTO-ML, and BFO-ML. Our further study shows that through overcoming dangling bonds the first three monolayers are 2D wide-gap semiconducotors, and BFO-ML is a 2D isotropic Heisenberg ferromagnetic metal. There is a large electrosta…
Group theory and density functional theory methods are combined to obtain compact and accurate $k\cdot p$ Hamiltonians that describe the bandstructures around the $K$ and $Γ$ points for the 2D material hexagonal boron arsenide (h-BAs) predicted to be an important low-bandgap material for electric, thermoelectric, and piezoelectric properties that supplements the well-studied 2D material hexagonal boron nitride. Hexagonal boron arsenide is a direct bandgap material with band extrema at the $K$ point. The bandgap becomes indirect with a conduction-band minimum at the $Γ$ point subject to a stron…
Recently a stable monolayer of antimony in buckled honeycomb structure called antimonene was successfully grown on 3D topological insulator Bi$_2$Te$_3$ and Sb$_2$Te$_3$, which displays semiconducting properties. By first principle calculations, we systematically investigate the phononic, electronic and optical properties of $α-$ and $β-$ allotropes of monolayer arsenene/antimonene. We investigate the dynamical stabilities of these four materials by considering the phonon dispersions. The obtained electronic structures reveal the direct band gap of monolayer $α-$As/Sb and indirect band gap of …
Unlike the electrical conductance that can be widely modulated within the same material even in deep nanoscale devices, tuning the thermal conductance within a single material system or nanostructure is extremely challenging and requires a large-scale device. This prohibits the realization of robust ON/OFF states in switching the flow of thermal currents. Here, we present the theory of a thermal switch based on resonant coupling of three photonic resonators, in analogy to the field-effect electronic transistor composed of a source, gate, and drain. As a material platform, we capitalize on the …
We study the carbon dimer defect in a hexagonal boron-nitride monolayer using the GW and Bethe-Salpeter many-body perturbation theories within a finite size cluster approach. While quasiparticle energies converge very slowly with system size due to missing long-range polarization effects, optical excitations converge much faster, with a $1/R^3$ scaling law with respect to cluster average radius. We obtain a luminescence zero-phonon energy of 4.36 eV, including significant 0.13 eV zero-point vibrational energy and 0.15 eV reorganization energy contributions. Inter-layer screening decreases furt…
The chemical activity of ionized hydrogen describes the potency of protons in solution and is used to define the pH with wide-ranging applications in biological and materials sciences. Measuring pH with graphene field-effect transistors (FETs) has been described in the past but has yet to be characterized with a monolayer hexagonal boron nitride (hBN) capping layer. hBN capping is hypothesized to lower the chemical affinity of protons to oxidized defects in the graphene crystal and lower the standard deviation of pH measurement via screening charge density. First, the electronic properties of …
Bottom-up Synthesis of Metastable 2D Hexagonal Copper(I) Iodide on Monolayer and within Bilayer Graphene
Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；Leibniz Institute of Photonic Technology (Leibniz-IPHT)（莱布尼茨光子技术研究所）；Ulm University（乌尔姆大学）；University of Nottingham（诺丁汉大学）；Freie Universität Berlin（柏林自由大学）；Leibniz Institute of Surface Engineering (IOM)（莱布尼茨表面工程研究所）
The recently synthesized two-dimensional electride Gd$_2$C was proposed to be a ferromagnetic metal that possesses multiple pairs of Weyl points and may display a large anomalous Hall conductivity [Liu \textit{et al.}, Phys. Rev. Lett. \textbf{125}, 187203 (2020)]. In view of its layered structure, here we carry out first-principles studies on the magnetic and electronic properties of Gd$_2$C in the ultrathin monolayer limit. We find that monolayer Gd$_2$C remains ferromagnetic like the bulk form and the hydrogenation can effectively tune its magnetism and electronic structure. With one-sided …
The extraordinary properties and the novel applications of black phosphorene induce the research interest on the monolayer group-IV monochalcogenides. Here using the first-principles calculations, we systematically investigate the electronic, transport and optical properties of monolayer $α-$ and $β-$GeSe, the latter of which was recently experimentally realized. We found that, monolayer $α-$GeSe is a semiconductor with direct band gap of 1.6 eV, and $β-$GeSe displays indirect semiconductor with the gap of 2.47 eV, respectively. For monolayer $β-$GeSe, the electronic/hole transport is anisotro…
We derive electronic tight-binding Hamiltonians for strained graphene, hexagonal boron nitride and transition metal dichalcogenides based on Wannier transformation of {\it ab initio} density functional theory calculations. Our microscopic models include strain effects to leading order that respect the hexagonal crystal symmetry and local crystal configuration, and are beyond the central force approximation which assumes only pair-wise distance dependence. Based on these models, we also derive and analyze the effective low-energy Hamiltonians. Our {\it ab initio} approaches complement the symme…
We show that carbon-doped hexagonal boron nitride (h-BN) has extraordinary properties with many possible applications. We demonstrate that the substitution-induced impurity states, associated with carbon atoms, and their interactions dictate the electronic structure and properties of C-doped h-BN. Furthermore, we show that stacking of localized impurity states in small C clusters embedded in h-BN forms a set of discrete energy levels in the wide gap of h-BN. The electronic structures of these C clusters have a plethora of applications in optics, magneto-optics, and opto-electronics.
We show that thermally evaporated lead (Pb) preserves the electronic properties of organic monolayers on Si and the surface passivation of the Si surface itself. The obtained current-voltage characteristics are in accordance with results from the well-established hanging mercury drop method and preserve both the molecule-induced dipolar effect and length-attenuation of current. We rationalize our findings by the lack of interaction between the Pb and the Si substrate. Our method is fast, scalable, compatible to standard semiconductor processing, and can help to spur the large-scale utilization…
We propose an effective lattice Hamiltonian for monolayer MoS$_2$ in order to describe the low-energy band structure and investigate the effect of perpendicular electric and magnetic fields on its electronic structure. We derive a tight-binding model based on the hybridization of the $d$ orbitals of molybdenum and $p$ orbitals of sulfur atoms and then introduce a modified two-band continuum model of monolayer MoS$_2$ by exploiting the quasi-degenerate partitioning method. Our theory proves that the low-energy excitations of the system are no longer massive Dirac fermions. It reveals a differen…
Moiré superlattices of van der Waals heterostructures provide a powerful new way to engineer the electronic structures of two-dimensional (2D) materials. Many novel quantum phenomena have emerged in different moiré heterostructures, such as correlated insulators, superconductors, and Chern insulators in graphene systems and moiré excitons in transition metal dichalcogenide (TMDC) systems. Twisted phosphorene offers another attractive system to explore moiré physics because phosphorene features an anisotropic rectangular lattice, different from the isotropic hexagonal lattice in graphene and TM…
The monolayer WSe2 is interesting and important for future application in nanoelectronics, spintronics and valleytronics devices, because it has the largest spin splitting and longest valley coherence time among all the known monolayer transition-metal dichalcogenides (TMDs). To obtain the large-area monolayer TMDs' crystal is the first step to manufacture scalable and high-performance electronic devices. In this letter, we have successfully fabricated millimeter-sized monolayer WSe2 single crystals with very high quality, based on our improved mechanical exfoliation method. With such superior…
The two-dimensional boron monolayers were reported to be metallic both in previous theoretical predictions and experimental observations, however, we have firstly found a family of boron monolayers with the novel semiconducting property as confirmed by the first-principles calculations with the quasi-particle G0W0 approach. We demonstrate that the vanished metallicity characterized by the pz-derived bands cross the Fermi level is attributed to the motif of a triple-hexagonal-vacancy, with which various semiconducting boron monolayers are designed to realize the band-gap engineering for the pot…
Optical reflectivity contrast provides a simple, fast and noninvasive method for characterization of few monolayer samples of two-dimensional materials. Here we apply this technique to measure the thickness of thin flakes of hexagonal Boron Nitride (hBN), which is a material of increasing interest in nanodevice fabrication. The optical contrast shows a strong negative peak at short wavelengths and zero contrast at a thickness dependent wavelength. The optical contrast varies linearly for 1-80 layers of hBN, which permits easy calibration of thickness. We demonstrate the applicability of this q…
In a pristine monolayer graphene subjected to a constant electric field along the layer, the Bloch oscillation of an electron is studied in a simple and efficient way. By using the electronic dispersion relation, the formula of a semi-classical velocity is derived analytically, and then many aspects of Bloch oscillation, such as its frequency, amplitude, as well as the direction of the oscillation, are investigated. It is interesting to find that the electric field affects the component of motion, which is non-collinear with electric field, and leads the particle to be accelerated or oscillate…
The two-dimensional atomically thin insulator hexagonal boron nitride (h-BN) constitutes a new paradigm in tunnel based devices. A large band gap along with its atomically flat nature without dangling bonds or interface trap states makes it an ideal candidate for tunnel spin transport in spintronic devices. Here, we demonstrate the tunneling of spin-polarized electrons through large area monolayer h-BN prepared by chemical vapor deposition in magnetic tunnel junctions. In ferromagnet/h-BN/ferromagnet heterostructures fabricated over a chip scale, we show tunnel magneto resistance at room tempe…
Monolayer WSe$_2$ hosts bright single-photon emitters. Because of its compliance, monolayer WSe$_2$ conforms to patterned substrates without breaking, thus creating the potential for large local strain, which is one activation mechanism of its intrinsic quantum emitters. Here, we report an approach to creating spatially and spectrally isolated quantum emitters from WSe$_2$ monolayers with few or no detrimental sources of emission. We show that a bilayer of hexagonal boron nitride (hBN) and WSe$_2$ placed on a nanostructured substrate can be used to create and shape wrinkles that communicate lo…
2H phase (trigonal prismatic D3h) of layered two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted a lot of interests due to the superior electronic and optoelectronic properties. However, flexible electronic devices and thermoelectric performances based on 2H phase have been potentially limited by the strain sensitive electronic band gap and high lattice thermal conductivity (kappa_L). Here, we predict and calculate two 1T (octahedral Oh) phase monolayer telluride materials SnTe2 and SiTe2 with soft mechanics, ultralow kappa_L and electronic properties. The calculated in…
Using two pairs of lattice equations deduced from a microscopic dipole lattice model taking into account electronic polarization (EP) of ions and local field effects (LFEs) self-consistently, in-plane and out-of-plane optical vibrations in two-dimensional (2D) hexagonal BN are studied theoretically. The three mutually independent coefficients of either pair of lattice equations are determined by a set of three generally known quantities such as the 2D electronic and static susceptibilities and phonon frequency, making the lattice equations very useful for calculating the lattice dynamical prop…
We theoretically investigate the electronic structures of moiré superlattices arising in monolayer / bilayer graphene stacked on hexagonal boron nitride (hBN) in presence and absence of magnetic field. We develop an effective continuum model from a microscopic tight-binding lattice Hamiltonian, and calculate the electronic structures of graphene-hBN systems with different rotation angles. Using the effective model, we explain the characteristic band properties such as the gap opening at the corners of the superlattice Brillouin zone (mini-Dirac point). We also investigate the energy spectrum a…
We performed calculations of electronic, optical and transport properties of graphene on hBN with realistic moiré patterns. The latter are produced by structural relaxation using a fully atomistic model. This relaxation turns out to be crucially important for electronic properties. We describe experimentally observed features such as additional Dirac points and the "Hofstadter butterfly" structure of energy levels in a magnetic field. We find that the electronic structure is sensitive to many-body renormalization of the local energy gap.
The recent discovery of two-dimensional (2D) magnetic materials which are compound of transition metal (TM) with other elements, has opened new avenues for basic research on low-dimensional magnetism and potential applications in spintronics. To further explore new 2D magnets of pure TM is thus of an interesting topic. Based on the first-principles calculations, here we propose a strategy of obtaining monolayer TM magnets, i.e., depositing TM atoms on graphyne (Gy) which has proper hexagonal hollow geometry. We find that TM monolayer with perfect hexagonal geometry can be formed on Gy. The TM …
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and connectivity group theory show that Weyl points are generated by band crossings in accordion-like and hourglass-like dispersion relations. These Weyl points are stable against weak perturbations and are protected by the screw rotation symmetry. Based on first-principles calculations we found a complete agreement between the topological predicted energy dispersion rela…
Using first-principles calculations, we systematically investigate the electronic structures and band topologies of four kinds of group-V elemental (P, As, Sb and Bi) monolayers with buckled honeycomb structure. It is found that all these monolayers can change from semiconducting to semimetallic under compressive strain. If a tensile strain is however applied, the P, As and Sb monolayers undergo phase transition from topologically trivial to non-trivial regime, whereas the topological insulating nature of Bi monolayer remains unchanged. With tunability of the band gaps and band topologies, it …
Hexagonal boron nitride is an ideal dielectric to form two-dimensional heterostructures due to the fact that it can be exfoliated to be just few atoms thick and its a very low density of defects. By placing graphene nanoribbons on high quality hexagonal boron nitride it is possible to create ideal quasi one dimensional (1D) systems with very high mobility. The availability of high quality one-dimensional electronic systems is of great interest also given that when in proximity to a superconductor they can be effectively engineered to realize Majorana bound states. In this work we study how a b…
Using an ab initio density functional theory (DFT) based electronic structure method, we study the effects of adatoms on the electronic properties of monolayer transition metal dichalcogenide (TMD) Molybdenum-disulfide (MoS2). We consider the 1st (Li, Na, K) and 7th (F, Cl, Br) column atoms and metals (Sc, Ti, Ta, Mo, Pd, Pt, Ag, Au). Three high symmetry sites for the adatom on the surface of monolayer MoS2 are examined as starting points to search for the most energetically stable configuration for each adatom-monolayer MoS2 system, as well as the type of associated bonding. For the most stab…
