Two-dimensional Honeycomb Lattice Research Articles

Realization of Honeycomb Tellurene with Topological Edge States.

The two-dimensional (2D) honeycomb lattice has attracted intensive research interest due to the appearance of Dirac-type band structures as the consequence of two sublattices in the honeycomb structure. Introducing strong spin-orbit coupling (SOC) leads to a gap opening at the Dirac point, transforming the honeycomb lattice into a 2D topological insulator as a platform for the quantum spin Hall effect (QSHE). In this work, we realize a 2D honeycomb-structured film with tellurium, the heaviest nonradioactive element in Group VI, namely, tellurene, via molecular beam epitaxy. We revealed the gap opening of 160 meV at the Dirac point due to the strong SOC in the honeycomb-structured tellurene by angle-resolved photoemission spectroscopy. The topological edge states of tellurene are detected via scanning tunneling microscopy/spectroscopy. These results demonstrate that tellurene is a novel 2D honeycomb lattice with strong SOC, and they unambiguously prove that tellurene is a promising candidate for a room-temperature QSHE system.

Solitons in binary compounds with stacked two-dimensional honeycomb lattices

Solitons in binary compounds with stacked two-dimensional honeycomb lattices

Geometry-dependent acoustic higher-order topological phases on a two-dimensional honeycomb lattice

Higher-order topological states, as emergent topological phases of matter, originating from condensed matter physics, have sparked a vibrant exploration of topological insulators. Their topologically protected multidimensional localized states are typically associated with nontrivial bulk band topology, and the significant impact of lattice geometry is unconsciously overlooked. Here, we construct coupled acoustic cavities on a two-dimensional honeycomb lattice to investigate the sensitivity of higher-order topological modes to the variations of edge contour. Fractional charge is utilized to accurately predict topological modes with distinct topological orders, in spite of the minimal bulk bandgaps inherent in the honeycomb lattice and bound states in the continuum. It is found that the presence and absence of the first-order and higher-order topological modes in the same topological phase are tightly linked to the sample boundaries, which can be demonstrated by both theoretical analysis and numerical calculation. Our study also discusses potential physical realization of geometry-dependent topological states across different platforms, providing inspiration for the prospective application of topological devices in acoustics.

Growing sp2 materials on transition metals: calculated atomic adsorption energies of hydrogen, boron, carbon, nitrogen, and oxygen atoms, C2 and BN dimers, C6 and (BN)3 hexamers, graphene and h-BN with and without atomic vacancies.

The growth of graphene and hexagonal boron nitride on hot transition metal surfaces involves the adsorption of precursor molecules, and their dissociation and assembly into two-dimensional honeycomb lattices. In a recent account it was found that h-BN may be distilled on a rhodium metal surface, which yields higher quality h-BN [Cun et al., ACS Nano, 2020, 15, 1351]. In this context, we calculated in a systematic approach the adsorption energies and sites of hydrogen, boron, carbon, nitrogen, and oxygen atoms and from the site dependence the activation energy for diffusion. Existing computed values of the solvation energy into the bulk were compared to the present ones with our calculation scheme and found to be in good agreement. For the distinction of different systems we introduce the concepts of epiphilicity and epiphobicity. The adsorption energies and stabilities of the C2 and BN dimers, the C6 and (BN)3 ring-hexamers and the graphene and h-BN monolayers allow the prediction of the performance of different substrates in chemical vapor deposition (CVD) processes for the growth of graphene and h-BN. Finally, vacancy creation energies were calculated as a criterion for the stability of graphene and h-BN on metallic substrates.

Many Body Aspects on the Lattice Vibrational Properties of Germanene and Silicene along Highly Symmetry Directions

The investigation of lattice vibrational properties in monolayer two-dimensional honeycomb lattices comprising 2D group-IV semiconductor materials such as Germanene and Silicene (Low Buckled structure) holds immense significance in the realm of research, owing to their potential integration into the forthcoming electronic sector for information technology. The ductile nature of 2D group-IV semiconductor materials enables seamless integration with existing semiconductor technology on substrates, setting them apart from Graphene. Our primary objective revolves around comprehending the lattice vibrational properties of Germanene and Silicene (LB) through the examination of their honeycomb and buckled lattice structures. We use the Adiabatic Bond Charge Model with a Python program to derive vibrational frequencies at the Г points along highly symmetrical directions. Moreover, we extensively analyze the acoustical and optical contributions to the lattice vibrational frequencies. We anticipate that the phonon frequencies along the Г‒M direction for 2D atomically thin Germanene and Silicene will yield reasonably similar outcomes to those other research groups achieve.

Anomalous Nernst effect in honeycomb and kagome magnet LaCo5 at room temperature

Magnetic order-induced time reversal symmetry breaking in the kagome lattice is predicted to generate Weyl semimetal and Chern insulating phases. The two-dimensional (2D) honeycomb lattices with spin orbit coupling (SOC) and ferromagnetism are also known to host the Chern insulating phase. Here, we study the transport properties of the ferromagnetic topological material LaCo5 crystals with TC = 840 K, which is the highest among the reported magnetic topological materials up to now. It is composed of 2D Co2 kagome layers that are separated by La–Co1 layers, in which the Co1 atoms exhibit a honeycomb structure. Both the 2D kagome and honeycomb layers exhibit out-of-plane magnetization. The large intrinsic anomalous Hall effect and anomalous Nernst effect of about 4.6 μVK−1 are observed in the ab plane with the B//c configuration at room temperature, which can be attributed to non-zero Berry curvature according to the first-principles calculations. Our results enrich the magnetic topological materials with honeycomb and kagome lattices, providing a good platform for the further study of the QAHE. The excellent thermoelectric performance, high TC, nontoxicity, and low cost also make LaCo5 a promising candidate for the applications of thermoelectric generators and heat flow sensors at high temperatures.

Field and temperature tuning of magnetic diode in permalloy honeycomb lattice

The observation of magnetic diode behavior with ultra-low forward voltage renders new venue for energetically efficient spintronic device research in the unconventional system of two-dimensional permalloy honeycomb lattice. However, detailed understanding of temperature and magnetic field tuning of diode behaviors are imperative to any practical application. In this report, our study unveils many important properties of magnetic diode that not only pave the way for practical applications, but also underlines the role of emergent phenomena of magnetic charge correlation on honeycomb vertices. We find that magnetic diode behavior persists across a broad temperature range. In a surprising observation, magnetic field application tends to induce a peculiar reentrant characteristic where diode behavior is suppressed in remnant field but reappears after warming to room temperature. Analysis of $I-V$ data suggests a modest energy gap, $∖sim$ 0.03 - 0.1 eV, which is comparable to magnetic Coulomb’s interaction energy between emergent magnetic charges on honeycomb vertices in the reverse biased state. It affirms the role of magnetic charge correlation in unidirectional conduction in 2D honeycomb lattice. The experimental results are expected to spur the utilization of magnetic diode in next generation spintronic device applications.

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.

Photonic topological Anderson insulator in a two-dimensional atomic lattice

Disorder in atomic positions can induce a topologically nontrivial phase - topological Anderson insulator (TAI) - for transverse electric optical quasimodes of a two-dimensional honeycomb lattice of immobile atoms. TAI requires both time-reversal and inversion symmetries to be broken to similar extents. It is characterized by a nonzero topological invariant, a reduced density of states and spatially localized quasimodes in the bulk, as well as propagating edge states. A transition from TAI to the topological insulator (TI) phase can take place at a constant value of the topological invariant, showing that TAI and TI represent the same topological phase.

Quantum spin liquids of Rydberg excitations in a honeycomb lattice induced by density-dependent Peierls phases

We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit-coupled Rydberg atoms gives rise to disordered quantum phases which are topological and may be candidates for quantum spin liquids. As recently demonstrated by Lienhard et al. [Phys. Rev. X 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of spin excitations which behave as hard-core bosons. Using exact diagonalization (ED), we numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms as well as density-density interactions. In mean-field approximation there is a phase transition from a condensate to a ${120}^{\ensuremath{\circ}}$ phase when the amplitude of the complex hopping exceeds that of the direct one. In the full model a new phase emerges close to the mean-field critical point as a result of quantum correlations induced by the density dependence of the complex hopping. We show that without density-density interactions this phase is a genuine disordered one, has large spin chirality, and is characterized by a nontrivial many-body Chern number. The Chern number is found to be robust to disorder. ED simulations of small lattices with up to 30 lattice sites give indications for a nondegenerate ground state with finite spin and collective gaps and thus for a bosonic integer quantum Hall phase, protected by $\mathrm{U}(1)$ symmetry. On the other hand, while staying finite, the many-body gap varies substantially when different twisted boundary conditions are applied, which points to a gapless phase. For very strong negative nonlinear hopping amplitudes we find another disordered regime with vanishing spin gap. This phase also has a large spin chirality and could be a gapless spin liquid but lies outside the parameter regime experimentally accessible in the Rydberg system.

Engineering topological states in a two-dimensional honeycomb lattice.

In this work, we use first-principles calculations to determine the interplay between spin-orbit coupling (SOC) and magnetism which can not only generate a quantum anomalous Hall state but can also result in topologically trivial states although some honeycomb systems host large band gaps. By employing tight-binding model analysis, we have summarized two types of topologically trivial states: one is due to the coexistence of quadratic non-Dirac and linear Dirac bands in the same spin channel that act together destructively in magnetic materials (such as, CrBr3, CrCl3, and VBr3 monolayers); the other one is caused by the destructive coupling effect between two different spin channels due to small magnetic spin splitting in heavy-metal-based materials, such as, BaTe(111)-supported plumbene. Further investigations reveal that topologically nontrivial states can be realized by removing the Dirac band dispersion of the magnetic monolayers for the former case (such as in alkali metal doped CrBr3), while separating the two different spin channels from each other by enhancing the magnetic spin splitting for the latter case (such as in half-iodinated silicene). Thus, our work provides a theoretical guideline to manipulate the topological states in a two-dimensional honeycomb lattice.

2차원 코발트 벌집격자 화합물에서의 키타에프 자성

2차원 벌집격자 위에서의 키타에프 자성 및 이를 통한 마요라나 페르미온의 구현은 현재 응집물질물리 및 양자 자성 연구에서 가장 주목받는 연구 중의 하나이며, 본 논문에서는 이러한 키타에프 자성을 코발트를 기반으로 한 3d-전이금속 화합물에서 구현하고자 하는 최근에 이론적 및 실험적 시도들에 대한 간략한 소개를 제공하고자 한다. Study on realization of Kitaev magnetism in two-dimensional honeycomb lattices is one of the cutting-edge research topics in condensed matter physics and quantum magnetism researches. In this paper I will briefly review recent theoretical and experimental ongoing progresses to engineer Kitaev magnetism in cobalt-based transition metal compounds.

Topological lattices realized in superconducting circuit optomechanics.

Cavity optomechanics enables the control of mechanical motion through the radiation-pressure interaction1, and has contributed to the quantum control of engineered mechanical systems ranging from kilogramme-scale Laser Interferometer Gravitational-wave Observatory (LIGO)mirrors to nanomechanical systems, enabling ground-state preparation2,3, entanglement4,5, squeezing of mechanical objects6, position measurements at the standard quantum limit7 and quantum transduction8. Yet nearly all previous schemes have used single- or few-mode optomechanical systems. By contrast, new dynamics and applications are expected when using optomechanical lattices9, which enable the synthesis of non-trivial band structures, and these lattices have been actively studied in the field of circuit quantum electrodynamics10. Superconducting microwave optomechanical circuits2 are a promising platform to implement such lattices, but have been compounded by strict scaling limitations. Here we overcome this challenge and demonstrate topological microwave modes in one-dimensional circuit optomechanical chains realizing the Su-Schrieffer-Heeger model11,12. Furthermore, we realize the strained graphene model13,14 in a two-dimensional optomechanical honeycomb lattice. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode functions of the hybridized modes without using any local probe15,16. This enables us to reconstruct the full underlying lattice Hamiltonian and directly measure the existing residual disorder. Such optomechanical lattices, accompanied by the measurement techniques introduced, offer an avenue to explore collective17,18, quantum many-body19 and quench20 dynamics, topological properties9,21 and, more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedom22-24.

Evidence for a Phase Transition in the Quantum Spin Liquid State of a Kitaev Candidate α-RuCl3

The Kitaev quantum spin liquid (QSL) on the two-dimensional honeycomb lattice epitomizes an entangled topological state, where the spins fractionalize into Majorana fermions. This state has aroused tremendous interest because it harbors non-Abelian anyon excitations. The half-integer quantized thermal Hall (HIQTH) conductance observed in $\alpha$-RuCl$_3$ is a key signature of these excitations. However, the fate of this topologically nontrivial state at intense fields remains largely elusive. Here, we report the thermal conductivity $\kappa$ and specific heat $C$ of $\alpha$-RuCl$_3$ with in-plane magnetic fields $H$. For the field direction perpendicular to the Ru-Ru bond, where the HIQTH effect is observed, we find a discontinuous jump in $\kappa(H)$ and a peak anomaly in $C(H)$ at $\mu_0H^*\approx11$\,T, evidencing a weak first-order phase transition. Remarkably, the HIQTH effect vanishes close to $H^*$. Furthermore, we find that the spin-fractionalization feature is retained well above $H^\ast$. These imply the emergence of the phase transition that separates two QSL phases with distinct topological properties.

Theory of triangulene two-dimensional crystals

Abstract Equilateral triangle-shaped graphene nanoislands with a lateral dimension of n benzene rings are known as [n] triangulenes. Individual [n] triangulenes are open-shell molecules, with single-particle electronic spectra that host n − 1 half-filled zero modes and a many-body ground state with spin S = ( n − 1 ) / 2 . The on-surface synthesis of triangulenes has been demonstrated for n = 3 , 4 , 5 , 7 and the observation of a Haldane symmetry-protected topological phase has been reported in chains of [3]triangulenes. Here, we provide a unified theory for the electronic properties of a family of two-dimensional honeycomb lattices whose unit cell contains a pair of triangulenes with dimensions n a , n b . Combining density functional theory and tight-binding calculations, we find a wealth of half-filled narrow bands, including a graphene-like spectrum (for n a = n b = 2 ), spin-1 Dirac electrons (for n a = 2 , n b = 3 ), p x , y -orbital physics (for n a = n b = 3 ), as well as a gapped system with flat valence and conduction bands (for n a = n b = 4 ). All these results are rationalized with a class of effective Hamiltonians acting on the subspace of the zero-energy states that generalize the graphene honeycomb model to the case of fermions with an internal pseudospin degree of freedom with C 3 symmetry.

Graphene Incorporated Electrospun Nanofiber for Electrochemical Sensing and Biomedical Applications: A Critical Review.

The extraordinary material graphene arrived in the fields of engineering and science to instigate a material revolution in 2004. Graphene has promptly risen as the super star due to its outstanding properties. Graphene is an allotrope of carbon and is made up of sp2-bonded carbon atoms placed in a two-dimensional honeycomb lattice. Graphite consists of stacked layers of graphene. Due to the distinctive structural features as well as excellent physico-chemical and electrical conductivity, graphene allows remarkable improvement in the performance of electrospun nanofibers (NFs), which results in the enhancement of promising applications in NF-based sensor and biomedical technologies. Electrospinning is an easy, economical, and versatile technology depending on electrostatic repulsion between the surface charges to generate fibers from the extensive list of polymeric and ceramic materials with diameters down to a few nanometers. NFs have emerged as important and attractive platform with outstanding properties for biosensing and biomedical applications, because of their excellent functional features, that include high porosity, high surface area to volume ratio, high catalytic and charge transfer, much better electrical conductivity, controllable nanofiber mat configuration, biocompatibility, and bioresorbability. The inclusion of graphene nanomaterials (GNMs) into NFs is highly desirable. Pre-processing techniques and post-processing techniques to incorporate GNMs into electrospun polymer NFs are precisely discussed. The accomplishment and the utilization of NFs containing GNMs in the electrochemical biosensing pathway for the detection of a broad range biological analytes are discussed. Graphene oxide (GO) has great importance and potential in the biomedical field and can imitate the composition of the extracellular matrix. The oxygen-rich GO is hydrophilic in nature and easily disperses in water, and assists in cell growth, drug delivery, and antimicrobial properties of electrospun nanofiber matrices. NFs containing GO for tissue engineering, drug and gene delivery, wound healing applications, and medical equipment are discussed. NFs containing GO have importance in biomedical applications, which include engineered cardiac patches, instrument coatings, and triboelectric nanogenerators (TENGs) for motion sensing applications. This review deals with graphene-based nanomaterials (GNMs) such as GO incorporated electrospun polymeric NFs for biosensing and biomedical applications, that can bridge the gap between the laboratory facility and industry.

Fabrication of honeycomb AuTe monolayer with Dirac nodal line fermions

Two-dimensional honeycomb lattices show great potential in the realization of Dirac nodal line fermions (DNLFs). Here, we successfully synthesized a gold telluride (AuTe) monolayer by direct tellurizing an Au(111) substrate. Low energy electron diffraction measurements reveal that it is (2×2) AuTe layer stacked onto (3×3) Au(111) substrate. Moreover, scanning tunneling microscopy images show that the AuTe layer has a honeycomb structure. Scanning transmission electron microscopy reveals that it is a single-atom layer. In addition, first-principles calculations demonstrate that the honeycomb AuTe monolayer exhibits Dirac nodal line features protected by mirror symmetry, which is validated by angle-resolved photoemission spectra. Our results establish that monolayer AuTe can be a good candidate to investigate 2D DNLFs and provides opportunities to realize high-speed low-dissipation devices.

Dipole-exchange spin waves in two-dimensional van der Waals ferromagnetic films and stripes

A spin-wave (SW) theory that includes the long-range dipole–dipole interactions is presented for monolayers of van der Waals (vdW) ferromagnets for which the magnetic ions lie on a two-dimensional honeycomb lattice. The dipolar interactions provide an additional anisotropy in these materials, along with the Ising exchange interaction and/or single-ion anisotropies that typically stabilize the two-dimensional magnetic ordering. Analytical results for the linearized SW energies are obtained for the ferromagnets in two geometries: complete films and finite-width stripes (or ribbons). In both cases it is found that the inclusion of the dipole–dipole interactions leads to a shift and sometimes a splitting of the magnetic modes in the vdW structure. Also, in the latter case, where the edges are assumed to be along the zigzag lattice directions, the dipole–dipole interactions are found to play a role, as well as the exchange interactions, in modifying the localized edge SWs. Numerical examples are given, including applications to the ferromagnet CrI3.

Multiple topological transitions and topological edge states of triple-site honeycomb lattice photonic crystals

We propose a two-dimensional (2D) triple-site honeycomb lattice (TSHL) photonic crystal (PC) by rotating the three dielectric rods six times, forming unit cell, and then arraying the unit cells in the triangular lattice. The TSHL PC structure can achieve topological phase transitions in three ways, which are changing the position or size of the rods, and rotating the rods. By calculating the band structure under different parameters, the law of topological phase transition for TSHL PC is analyzed. The topological edge state can be adjusted by changing the rotation angle of the dielectric rods. Based on this, a frequency-selective beam splitter is designed. Compared with previous studies, this flexible topological system shows more abundant physical phenomena, enriches the implementation of topological photonics , and promotes the research of topological edge states and the development of topological insulators in practical applications. • We propose a two-dimensional triple-site honeycomb lattice photonic crystal, which has the high degrees of freedom. • The triple-site honeycomb lattice unit cell can achieve topological phase transitions in three ways, which are changing the position or size of the cylinders, and rotating the cylinders. • We design a frequency-selective beam splitter, by changing the rotation angle of the dielectric rods.

Gapless Dirac magnons in CrCl3

Bosonic Dirac materials are testbeds for dissipationless spin-based electronics. In the quasi two-dimensional honeycomb lattice of CrX3 (X = Cl, Br, I), Dirac magnons have been predicted at the crossing of acoustical and optical spin waves, analogous to Dirac fermions in graphene. Here we show that, distinct from CrBr3 and CrI3, gapless Dirac magnons are present in bulk CrCl3, with inelastic neutron scattering intensity at low temperatures approaching zero at the Dirac K point. Upon warming, magnon-magnon interactions induce strong renormalization and decreased lifetimes, with a ~25% softening of the upper magnon branch intensity from 5 to 50 K, though magnon features persist well above TN. Moreover, on cooling below ~50 K, an anomalous increase in the a-axis lattice constant and a hardening of a ~26 meV phonon feature are observed, indicating magnetoelastic and spin-phonon coupling arising from an increase in the in-plane spin correlations that begins tens of Kelvin above TN.