Buckled Honeycomb Lattice Research Articles

Entanglement harvesting in buckled honeycomb lattices by vacuum fluctuations in a microcavity

We study the entanglement harvesting between two identical buckled honeycomb lattices placed inside a planar microcavity. By applying time dependent perturbation theory, we obtain quantum correlations between both layers induced by the cavity field. Considering the vacuum state as the initial state of the cavity field and tracing out the time-evolved degrees of freedom, we analyze the entanglement formation using the concurrence measure. We show that the concurrence depends on the virtual photon exchanged and the positions of the layer through the interlayer photon propagator. Furthermore, we find that the formation of entanglement between equal energy electrons tends to be enhanced when they move in perpendicular directions. Our results indicate that a buckled honeycomb structure and a large spin-orbit interaction favor the entanglement harvesting.

Elemental topological ferroelectrics and polar metals of few-layer materials

Ferroelectricity can exist in elemental phases as a result of charge transfers between atoms occupying inequivalent Wyckoff positions. We investigate the emergence of ferroelectricity in two-dimensional elemental materials with buckled honeycomb lattices. Various multibilayer structures hosting ferroelectricity are designed by stacking engineering. Ferroelectric materials candidates formed by group IV and V elements are predicted theoretically. Ultrathin Bi films show layer-stacking-dependent physical properties of ferroelectricity, topology, and metallicity. The two-bilayer Bi film with a polar stacking sequence is found to be an elemental topological ferroelectric material. Three and four bilayers Bi films with polar structures are ferroelectriclike elemental polar metals with topological nontrivial edge states. For Ge and Sn, trivial elemental polar metals are predicted. Our work reveals the possibility of designing two-dimensional elemental topological ferroelectrics and polar metals by stacking engineering. Published by the American Physical Society 2024

Faraday rotation and transmittance as markers of topological phase transitions in 2D materials

We analyze the magneto-optical conductivity (and related magnitudes like transmittance and Faraday rotation of the irradiated polarized light) of some elemental two-dimensional Dirac materials of group IV (graphene analogues, buckled honeycomb lattices, like silicene, germanene, stannane, etc.), group V (phosphorene), and zincblende heterostructures (like HgTe/CdTe quantum wells) near the Dirac and gamma points, under out-of-plane magnetic and electric fields, to characterize topological-band insulator phase transitions and their critical points. We provide plots of the Faraday angle and transmittance as a function of the polarized light frequency, for different external electric and magnetic fields, chemical potential, HgTe layer thickness and temperature, to tune the material magneto-optical properties. We have shown that absortance/transmittance acquires extremal values at the critical point, where the Faraday angle changes sign, thus providing fine markers of the topological phase transition. In the case of non-topological materials as phosphorene, a minimum of the transmittance is also observed due to the energy gap closing by an external electric field.

Boundary-obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field

In this work, we show that a buckled honeycomb lattice can host a boundary-obstructed topological superconductor (BOTS) in the presence of f-wave spin-triplet pairing (fSTP). The underlying buckled structure allows for the manipulation of both chemical potential and sublattice potential using a double gate setup. Although a finite sublattice potential can stabilize the fSTP with a possible higher-order band topology, because it also breaks the relevant symmetry, the stability of the corner modes is not guaranteed. Here we show that the fSTP on the honeycomb lattice gives BOTS under nonzero sublattice potential, thus the corner modes can survive as long as the boundary is gapped. Also, by examining the large sublattice potential limit where the honeycomb lattice can be decomposed into two triangular lattices, we show that the boundary modes in the normal state are the quintessential ingredient leading to the BOTS. Thus the effective boundary Hamiltonian becomes nothing but the Hamiltonian for Kitaev chains, which eventually gives the corner modes of the BOTS.

Electronic structure and elasticity of two-dimensional metals of group 10: A DFT study

The discovery of two-dimensional (2D) iron monolayer in graphene pores stimulated experimental and computational material scientists to investigate low-dimensional elemental metals. There have been many advances in their synthesis, stability, and properties in the last few years. Inspired by these advancements, we investigated the electronic structure and elasticity of free-standing monolayers of group 10 elemental metals, viz. Ni, Pd, and Pt. Using density-functional theory (DFT), we explored the energetic, geometric, electronic, and elastic properties of hexagonal, honeycomb, and square lattice structures of each element, in both planar and buckled forms. Among planar configurations, the order of increasing stability is honeycomb, square, and hexagonal. In buckled form, this ordering remains the same for Pt but is reversed for Ni and Pd. Upon geometrical optimization, the extent of buckling for Pt was found to be small compared to Ni and Pd. The effect of buckling on the electronic structure was further scrutinized through the projected density of states, and it was found that highly buckled configurations derive their of states from 3D bulk, which highlights the correlation between buckled configurations and 3D bulk. For Pt in buckled square and honeycomb lattices, the density of states correlates more closely to their 2D monolayers. Regarding elasticity, the in-plane elastic constants indicate that all planar and buckled square lattices are unstable.

Topological phonon analysis of the two-dimensional buckled honeycomb lattice: An application to real materials

By means of group theory, topological quantum chemistry, first-principles, and Monte Carlo calculations, we analyze the topology of the 2D buckled honeycomb lattice phonon spectra. Taking the pure crystal structure as an input, we show that eleven distinct phases are possible, five of which necessarily have nontrivial topology according to topological quantum chemistry. Another four of them are also identified as topological using Wilson loops in an analytical model that includes all the symmetry allowed force constants up to third-nearest neighbors, making a total of nine topological phases. We then compute the ab initio phonon spectra for the two-dimensional crystals of Si, Ge, P, As, and Sb in this structure and construct its phase diagram. Despite the large proportion of topological phases found in the analytical model, all of the crystals lie in a trivial phase. By analyzing the force constants space using Monte Carlo calculations, we elucidate why topological phonon phases are physically difficult to realize in real materials with this crystal structure.

Electrically switchable giant Berry curvature dipole in silicene, germanene and stanene

The anomalous Hall effect in time-reversal symmetry broken systems is underpinned by the concept of Berry curvature in band theory. However, recent experiments reveal that the nonlinear Hall effect (NHE) can be observed in non-magnetic systems without applying an external magnetic field. The emergence of NHE under time-reversal symmetric conditions can be explained in terms of non-vanishing Berry curvature dipole (BCD) arising from inversion symmetry breaking. In this work, we availed realistic tight-binding models, first-principles calculations, and symmetry analyses to explore the combined effect of transverse electric field and strain, which leads to a giant BCD in the elemental buckled honeycomb lattices—silicene, germanene, and stanene. The external electric field breaks the inversion symmetry of these systems, while strain helps to attain an asymmetrical distribution of Berry curvature of a single valley. Furthermore, the topology of the electronic wavefunction switches from the band inverted quantum spin Hall state to normal insulating one at the gapless point. This band gap closing at the critical electric field strength is accompanied by an enhanced Berry curvature and concomitantly a giant BCD at the Fermi level. Our results predict the occurrence of an electrically switchable nonlinear electrical and thermal Hall effect in a new class of elemental systems that can be experimentally verified.

Buckled Honeycomb Lattice Compound Sr3CaOs2O9 Exhibiting Antiferromagnetism above Room Temperature

Synthesis, crystal structure and magnetic properties of a new 2:1 ordered triple perovskite Sr3CaOs2O9 are reported. The compound crystallizes in P21/c space group and features a unique buckled honeycomb lattice of osmium. It exhibits long-range antiferromagnetic ordering with a high Neel temperature of 385 K as confirmed by susceptibility, heat capacity and neutron diffraction measurements and is electrically insulating. This compound is also the first example of a 2:1 ordered osmate perovskite. Theoretical investigations indicate that Sr3CaOs2O9 features a sizeable antiferromagnetic exchange between the puckered planes resulting in a high TN. The magnetic properties of the known compound Sr3CaRu2O9 are elucidated in comparison. It shows antiferromagnetic order below TN = 200 K.

Antiferromagnetic spin ordering in two-dimensional honeycomb lattice of SiP3.

Magnetism in low-dimensional materials has been of sustained interest due to its intriguing quantum mechanical origin and promising device applications. Here, we propose a buckled honeycomb lattice of stoichiometry SiP3, a two-dimensional binary group-IV and V material that exhibits an antiferromagnetic ground state with itinerant electrons. Here we perform elemental Si substitution in pristine blue phosphorene to downshift the Fermi energy and induce the Fermi instability that results in a spin polarized ground state. Within first-principles calculations, we observe antiferromagnetic spin alignment between adjacent ferromagnetic triangular domains where each Si atom is coupled with three neighboring P atoms with a ferromagnetic interaction. Such unique spin structure and resulting magnetic ground state are unprecedented in defect-free two-dimensional materials made of only p-block elements. This metal-free magnetism can be exploited for advanced spintronic and memory storage applications.

Tailoring and probing the quantum states of matter of 2D Dirac materials with a buckled honeycomb structure

The quantum state of matter of a two-dimensional Dirac material with a buckled honeycomb structure can be tuned by an electric field. In the absence of an external electric field the material is a topological insulator owing to the spin-orbit coupling, which opens a band gap at the K and K ’ points of the Brillouin zone. The size of this band gap decreases with increasing electric field until eventually the band gap completely closes at a critical electric field E c and the material becomes a semi-metal. For electric fields exceeding E c the band gaps reopens again and the material undergoes a topological phase transition from a semi-metal to a normal band insulator. The electric field in a tunnel junction depends on the applied voltage bias across the junction as well as the difference in work function of the two electrodes. Here we show how scanning tunneling microscopy can be employed to simultaneously apply an electric field and study the electronic structure of a two-dimensional Dirac material with a buckled honeycomb structure. The electric field applied by the scanning tunneling microscope offers the possibility to locally alter the quantum state of matter of two-dimensional topological insulator to a semi-metal or normal band insulator. This results in the development of topologically protected spin polarized edge states within the material. We present a spectroscopic method to probe these topologically protected edge states. • Electric field induces topological phase transitions in 2D materials. •A method to probe topologically protected edge modes in a 2D Dirac material is proposed. • The band gap in a 2D Dirac material with a buckled honeycomb lattice can be tuned by an electric field.

Chern and Z2 topological insulating phases in perovskite-derived 4d and 5d oxide buckled honeycomb lattices

Based on density functional theory calculations including a Coulomb repulsion parameter U, we explore the topological properties of (LaXO3)2/(LaAlO3)4 (111) with X = 4d and 5d cations. The metastable ferromagnetic phases of LaTcO3 and LaPtO3 with preserved P321 symmetry emerge as Chern insulators (CI) with C = 2 and 1 and band gaps of 41 and 38 meV at the lateral lattice constant of LaAlO3, respectively. Berry curvatures, spin textures as well as edge states provide additional insight into the nature of the CI states. While for X = Tc the CI phase is further stabilized under tensile strain, for X = Pd and Pt a site disproportionation takes place when increasing the lateral lattice constant from aLAO to aLNO. The CI phase of X = Pt shows a strong dependence on the Hubbard U parameter with sign reversal for higher values associated with the change of band gap opening mechanism. Parallels to the previously studied (X2O3)1/(Al2O3)5 (0001) honeycomb corundum layers are discussed. Additionally, non-magnetic systems with X = Mo and W are identified as potential candidates for Z2 topological insulators at aLAO with band gaps of 26 and 60 meV, respectively. The computed edge states and Z2 invariants underpin the non-trivial topological properties.

Spin-orbit torques from intrinsic spin-orbit couplings in a periodically buckled honeycomb lattice

In this paper, we study the spin-orbit torques (SOTs) originated from the spin-orbit coupling (SOC) of intrinsic type in a periodically buckled honeycomb nanoribbon such as silicene. Using the Green function formalism with density matrix expressions, we analyze the SOT contributions from the Fermi-level and -sea electrons. We find that the intrinsic-SOC-induced inverse spin galvanic effect generates spin accumulations perpendicular to the honeycomb plane. The anti-damping torque results purely from the Fermi-level contribution, while the field-like torque from both the Fermi-level and -sea contributions. At zero bias voltage, the SOT is symmetric with respect to the Fermi energy (i.e., an even function of the Fermi energy), whereas the presence of bias further introduces the anti-symmetric torque components. When the ferromagnet magnetization lies in the honeycomb plane, all Fermi-sea contributions disappear. The maximum SOT among different Fermi energies is also inspected. For large enough in-plane magnetization compared to the staggered potential, the field-like torque has a maximum at zero Fermi energy. When the magnetization is smaller than some value characterized by the intrinsic SOC, the maximum of the anti-damping torque occurs at the cross point of the two Dirac linear bands in the leads. More importantly, we find that the anti-damping torques responsible for magnetic switching as well as the torkance require staggered potential from an applied out-of-plane electric field, i.e., lattice buckling is essential to the switching. When the electric field is reversed, the anti-damping torque and the torkance are also reversed. Accordingly, full electric control of the SOTs can be realized in this buckled system.

Strain effects on the mechanical properties of Group-V monolayers with buckled honeycomb structures

Based on first-principles calculations, we study systematically the ideal tensile stress-strain relations of three monoatomic group-V monolayer two dimensional (2D) materials with buckled honeycomb lattices: blue phosphorene, β-arsenene, and β-antimonene. The ideal strengths and critical strains for these 2D materials are investigated under uniaxial and equibiaxial strains. It is found that the ideal strengths decrease significantly as the atomic number increases, while the critical strains change not so much. In particular, the ideal strength of antimonene along armchair direction is found to exceed Griffith strength limit. The distributions of charge density, buckling heights, bond lengths and bond angles are also studied under different types of strains. It can be concluded that the critical strain is determined by the stretch and rotation of bonds simultaneously. Furthermore, the phonon dispersions, phonon instabilities, and failure mechanism of these materials under three types of strains are also calculated and explored.

Van der Waals integration of silicene and hexagonal boron nitride

Silicene, the silicon analogue of graphene, consists of an atomically buckled honeycomb lattice of silicon atoms. Theory predicts exceptional electronic properties, including Dirac fermions and a topological spin Hall insulator phase. An important obstacle impeding exploration of such properties in electronic devices is the chemical sensitivity of silicene, hampering its incorporation in layer stacks. Here we show experimentally that epitaxial silicene and hexagonal boron nitride (h-BN) can be stacked without perturbing the electronic properties of silicene. Intercalated silicene underneath epitaxial h-BN on ZrB2(0 0 0 1) substrate films is obtained by depositing Si atoms at room temperature. Using (angle resolved) photoelectron spectroscopy (ARPES, PES) and scanning tunneling microscopy (STM) we find that the intercalated silicene exhibits the same electronic properties as epitaxial silicene on ZrB2, while it resists oxidation in air up to several hours. This is an essential step towards the development of layer stacks that allow for fabrication of devices.

Self-Encapsulation of Silicene in Cubic Diamond Si: Topological Semimetal in Covalent Bonding Networks

Silicene has a two-dimensional buckled honeycomb lattice and is chemically reactive because of its mixed sp2–sp3 bonding character unlike graphene. Despite recent advances in epitaxial growth, it r...

Highly stable phosphorene isomers based on a buckled honeycomb lattice.

Due to their high stabilities and tuneable electronic structures, two dimensional isomers of black phosphorene (BP) have drawn great attention recently. By carefully considering the bonding characteristics of phosphorus atoms, we propose a buckled honeycomb lattice strategy to search for possible highly stable phosphorene isomers. As an example, phosphorene isomers with a unit cell size no larger than 8 atoms are fully explored and 14 isomers, including the well-known α-, β-, γ-, δ-, and ε-phosphorene, are discovered and named from P-I to P-XIV in the order of their relative stabilities. Among these isomers, P-II and P-III are two newly found isomers with superior stability comparable to BP, whose formation energies are just 0.01 and 0.03 eV per atom higher than that of BP (α-phosphorene), respectively, and both are more stable than the well-known blue phosphorene (β-phosphorene). These new phosphorene isomers exhibit a wide range of medium energy band gaps from 0.30 to 2.66 eV, various HOMO/LUMO energy levels and, therefore, can be used for various optoelectronic and device applications.

Temperature- and frequency-dependent optical and transport conductivities in doped buckled honeycomb lattices

Temperature- and frequency-dependent optical and transport conductivities in doped buckled honeycomb lattices

First-principles studies electronic structures and opticalproperties of four new phosphorene polymorphs

Black phosphorus (α-P), a new member of two-dimensional (2D) materials, which has the common advantages of graphene and transition metal dichalcogenides (TMDs), is of great concern. Based on the studies of black phosphorus, three new monolayer phosphorene polymorphs (e-P, ζ-P, and θ-P) have been predicted recently, which greatly enrich the phosphorene structures. Three new monolayer phosphorene polymorphs, composed of P4 square units (e-P, ζ-P) or P5 pentagon units (θ-P), all exhibit buckled honeycomb lattices akin to black phosphorus. Remarkably, the θ-P is equally stable as the black phosphorus, and more stable than the other two new phosphorene polymorphs. In this paper, electronic structures and optical properties of monolayer black phosphorus (α-P) and three new monolayer phosphorene polymorphs (e-P, ζ-P and θ-P) have been investigated based on the first-principles density functional theory (DFT). In comparison with Perdew-Burke-Ernzerh of generalized gradient approximation (GGA-PBE) with ultra-soft pseudopotential, hybrid density functional (HSE06) with norm-conserving pseudopotential is selected for subsequent calculation, because it is closer to experimental data. The calculation results show that, α-P and e-P are direct semiconductors with band gaps of 1.542 and 0.973 eV, respectively. ζ-P and θ-P are indirect semiconductors with band gaps of 1.874 and 1.772 eV, respectively. Based on the electronic properties, the optical properties are discussed in detail. It is found that α-P and three new monolayer phosphorene polymorphs have good permeability in the whole infrared and visible region, which means that they can be used as optical transparent materials. Moreover, the peaks of reflectance and absorption spectra are in the ultraviolet region, indicating that they can be used as ultraviolet protection materials or ultraviolet detection equipment. This research is aimed at enhancing the understanding of the photoelectric properties of α-P and three new monolayer phosphorene polymorphs, and providing an useful theoretical basis for the practical application as photoelectric materials.

In-plane magnetization-induced quantum anomalous Hall effect in atomic crystals of group-V elements

We theoretically demonstrate that the in-plane magnetization induced quantum anomalous Hall effect (QAHE) can be realized in atomic crystal layers of group-V elements with buckled honeycomb lattice. We first construct a general tight-binding Hamiltonian with $sp^3$ orbitals via Slater-Koster two-center approximation, and then numerically show that for weak and strong spin-orbit couplings the systems harbor QAHEs with Chern numbers of $\mathcal{C}=\pm1$ and $\pm2$ , respectively. For the $\mathcal{C}=\pm1$ phases, we find the critical phase-transition magnetization from a trivial insulator to QAHE can become extremely small by tuning the spin-orbit coupling strength. Although the resulting band gap is small, it can be remarkably enhanced by orders via tilting the magnetization slightly away from the in-plane orientation. For the $\mathcal{C}=\pm2$ phases, we find that the band gap is large enough for the room-temperature observation. Although the critical magnetization is relatively large, it can be effectively decreased by applying a strain. All these suggest that it is experimentally feasible to realize high-temperature QAHE from in-plane magnetization in atomic crystal layers of group-V elements.

Temperature-dependent collective effects for silicene and germanene

We have numerically calculated electron exchange and correlation energies and dynamical polarization functions for recently discovered silicene, germanene and other buckled honeycomb lattices at various temperatures. We have compared the dependence of these energies on the chemical potential, field-induced gap and temperature and we have concluded that in many cases they behave qualitatively in a similar way, i.e. increasing with the doping, decreasing significantly at elevated temperatures, and displaying different dependences on the asymmetry gap at various temperatures. Furthermore, we have used the dynamical polarizability to study the ‘split’ plasmon branches in the buckled lattices and predicted a unique splitting, different from that in gapped graphene, for various energy gaps. Our results are crucial for stimulating electronic, transport and collective studies of silicene and germanene, as well as for enhancing silicene-based fabrication and technologies for photovoltaics and transistor devices.