Slippery Paraelectric Transition-Metal Dichalcogenide Bilayers.

Traditional ferroelectrics undergo thermally induced phase transitions whereby their structural symmetry increases. The associated higher-symmetry structure is dubbed paraelectric. Ferroelectric transition-metal dichalcogenide bilayers have been recently shown to become paraelectric, but not much has been said of the atomistic configuration of such a phase. As discovered through numerical calculations that include molecular dynamics here, their paraelectricity can only be ascribed to a time average of ferroelectric phases with opposing intrinsic polarizations, whose switching requires macroscopically large areas to slip in unison.

Topological semimetal in honeycomb lattice LnSI.

Recognized as elementary particles in the standard model, Weyl fermions in condensed matter have received growing attention. However, most of the previously reported Weyl semimetals exhibit rather complicated electronic structures that, in turn, may have raised questions regarding the underlying physics. Here, we report promising topological phases that can be realized in specific honeycomb lattices, including ideal Weyl semimetal structures, 3D strong topological insulators, and nodal-line semimetal configurations. In particular, we highlight a semimetal featuring both Weyl nodes and nodal lines. Guided by this model, we showed that GdSI, the long-perceived ideal Weyl semimetal, has two pairs of Weyl nodes residing at the Fermi level and that LuSI (YSI) is a 3D strong topological insulator with the right-handed helical surface states. Our work provides a mechanism to study topological semimetals and proposes a platform for exploring the physics of Weyl semimetals as well as related device designs.

Hierarchical Hybridization in Plasmonic Honeycomb Lattices.

This paper reports hierarchical hybridization as a mode-mixing scheme to account for the unique optical properties of non-Bravais lattices of plasmonic nanoparticles (NPs). The formation of surface lattice resonances (SLRs) mediated by localized surface plasmons (LSPs) of different multipolar orders (dipole and quadrupole) can result in asymmetric electric near-field distributions surrounding the NPs. This asymmetry is because of LSP hybridization at the individual NP level from LSPs of different multipole order and at the unit cell level (NP dimer) from LSPs of the same multipole order. Fabricated honeycomb lattices of silver NPs exhibit ultrasharp SLRs at the Γ point that can also facilitate nanolasing. Modeling of the stimulated emission process revealed that the multipolar component of the lattice plasmon mode was responsible for feedback for lasing. By leveraging multipolar LSP responses in Al NP lattices, we achieved two distinct Γ point band-edge modes from a single honeycomb lattice. This work highlights how multipolar LSP coupling in plasmonic lattices with a non-Bravais symmetry has important implications for the design of SLRs and their associated plasmonic near-field distributions. These relatively unexplored degrees of freedom can decrease both ohmic and radiative losses in nanoscale systems and enable SLRs to build unanticipated connections among photonics and nanochemistry.

Epitaxial Growth of Flat Antimonene Monolayer: A New Honeycomb Analogue of Graphene.

Group-V elemental monolayers were recently predicted to exhibit exotic physical properties such as nontrivial topological properties, or a quantum anomalous Hall effect, which would make them very suitable for applications in next-generation electronic devices. The free-standing group-V monolayer materials usually have a buckled honeycomb form, in contrast with the flat graphene monolayer. Here, we report epitaxial growth of atomically thin flat honeycomb monolayer of group-V element antimony on a Ag(111) substrate. Combined study of experiments and theoretical calculations verify the formation of a uniform and single-crystalline antimonene monolayer without atomic wrinkles, as a new honeycomb analogue of graphene monolayer. Directional bonding between adjacent Sb atoms and weak antimonene-substrate interaction are confirmed. The realization and investigation of flat antimonene honeycombs extends the scope of two-dimensional atomically-thick structures and provides a promising way to tune topological properties for future technological applications.

AgRuO3 , a Strongly Exchange-Coupled Honeycomb Compound Lacking Long-Range Magnetic Order.

Quasi two-dimensional (2D) oxide-based honeycomb lattices have attracted great attention for displaying specific electronic instabilities, which give rise to unconventional bonding patterns and unexpected magnetic exchange couplings. The synthesis of AgRuO3 , another representative exhibiting unique structural properties, is reported here. The stacking sequence of the honeycomb layers (Ru2 O6 ) differs from analogous precedents; in particular, the intercalating silver atoms are shifted from the middle of the interspaces and cap the void octahedral sites of the (□Ru2 O6 ) slabs from both sides. This way, charge neutral, giant 2D "molecules" of Ag/Ru2 O6 /Ag result; a feature that significantly enhances the overall 2D character of AgRuO3 . Measurements of magnetization have revealed extremely strong magnetic exchange coupling to be present, surviving to a temperature as high as 673 K, which is the temperature of thermal decomposition. No indication for long-range magnetic order has, however, been observed. Theoretical analyses confirm the pronounced 2D character of the electronic system, and in particular reveal the inter-honeycomb layer coupling Jc to be distinctly weak.

Hydrophobicity-Driven Self-Assembly of an Eighteen-Membered Honeycomb Lattice with Almost Classical Spins.

The design and synthesis of model compounds that do not exist naturally is one of the important targets in modern coordination chemistry. Herein, an eighteen-membered honeycomb structure with equal numbers of MnII (s=5/2) and GdIII (s=7/2) metal centers has been prepared, for the first time, by using a hydrophobic force-directed self-assembling process. Due to the weakly coupled GdIII pairs, the magnetic properties are mainly determined by eight-membered chains in the experimentally considered temperature range. These [Mn4 Gd4 ] "finite-size" chains, albeit with large Hilbert space, can be fully resolved by the high-temperature series expansion and the powerful finite-temperature Lanczos method, which reveal that the exchange-couplings between the metal centers are antiferromagnetic and consistent with the magnetization measurement. Interestingly, from the surface-engineering point of view, the [Mn4 Gd4 ] chains are "precisely" assembled into a 2D honeycomb pattern, which is potentially desirable in the design of weakly coupled qubits.

Construction of 2D atomic crystals on transition metal surfaces: graphene, silicene, and hafnene.

The synthesis and structures of graphene on Ru(0001) and Pt(111), silicene on Ag(111) and Ir(111) and the honeycomb hafnium lattice on Ir(111) are reviewed. Epitaxy on a transition metal (TM) substrate is a pro-mising method to produce a variety of two dimensional (2D) atomic crystals which potentially can be used in next generation electronic devices. This method is particularly valuable in the case of producing 2D materials that do not exist in 3D forms, for instance, silicene. Based on the intensive investigations of epitaxial graphene on TM in recent years, it is known that the quality of graphene is affected by many factors, including the interaction between the 2D material overlayer and the substrate, the lattice mismatch, the nucleation density at the early stage of growth. It is found that these factors also apply to many other epitaxial 2D crystals on TM. The knowledge from the reviewed systems will shine light on the design and synthesis of new 2D crystals with novel properties.

Designing edge states from fractional polarization insulators.

We theoretically investigated disconnected dispersive edge states in an anisotropic honeycomb lattice without chiral symmetry. When both mirror and chiral symmetries are present, this system is defined by a topological quantity known as fractional polarization (FP) term and exhibits a bulk band gap, classifying it as an FP insulator. While the FP insulator accommodates robust, flat topological edge states (TES), it also offers the potential to engineer these edge states by deliberately disrupting a critical symmetry that safeguards the underlying topology. These symmetry-breaking terms allow the edge states to become dispersive and generate differing configurations along the open boundaries. Furthermore, disconnected helical-like and chiral-like edge states analogous to TES seen in quantum spin and anomalous hall effect are achieved by the finite size effect, not possible from the symmetry-breaking terms alone. The demonstration of manipulating these edge states from a FP insulator can open up new avenues in constructing devices that utilize topological domain walls.

High-temperature magnetic anomaly via suppression of antisite disorder through synthesis route modification in a Kitaev candidate Cu2IrO3.

By incorporating inert KCl into the Na2IrO3+ 2CuCl → Cu2IrO3+ 2NaCl topochemical reaction, we significantly reduced the synthesis temperature of Cu2IrO3from the 350 °C reported in previous studies to 170 °C. This adjustment decreased the Cu/Ir antisite disorder concentration in Cu2IrO3from ∼19% to ∼5%. Furthermore, magnetic susceptibility measurements of the present Cu2IrO3sample revealed a weak ferromagnetic-like anomaly with hysteresis at a magnetic transition temperature of ∼70 K. Our research indicates that the spin-disordered ground state reported in chemically disordered Cu2IrO3is an extrinsic phenomenon, rather than an intrinsic one, underscoring the pivotal role of synthetic chemistry in understanding the application of Kitaev model to realistic materials.

Chiral Honeycomb Lattices of Nonplanar π-Conjugated Supramolecules with Protected Dirac and Flat Bands.

The honeycomb lattice is a fundamental two-dimensional (2D) network that gives rise to surprisingly rich electronic properties. While its expansion to 2D supramolecular assembly is conceptually appealing, its realization is not straightforward because of weak intermolecular coupling and the strong influence of a supporting substrate. Here, we show that the application of a triptycene derivative with phenazine moieties, Trip-Phz, solves this problem due to its strong intermolecular π-π pancake bonding and nonplanar geometry. Our scanning tunneling microscopy (STM) measurements demonstrate that Trip-Phz molecules self-assemble on a Ag(111) surface to form chiral and commensurate honeycomb lattices. Electronically, the network can be viewed as a hybrid of honeycomb and kagome lattices. The Dirac and flat bands predicted by a simple tight-binding model are reproduced by total density functional theory (DFT) calculations, highlighting the protection of the molecular bands from the Ag(111) substrate. The present work offers a rational route for creating chiral 2D supramolecules that can simultaneously accommodate pristine Dirac and flat bands.

High-field magnetization and electronic spin resonance study in the twisted honeycomb latticeα-Mn2V2O7.

We report the single-crystal growth of Mn2V2O7and the results of magnetic susceptibility, high-field magnetization up to 55 T and high-frequency electric spin resonance (ESR) measurements for its low-temperatureαphase. Two antiferromagnetic (AFM) ordering at 17.5 K and 3 K and obvious magnetic anisotropy are observed inα-Mn2V2O7upon cooling. In pulsed high magnetic fields, the compound reaches the saturation magnetic moment of ∼10.5µBfor each molecular formula at around 45 T after two undergoing AFM phase transitions atHc1≈ 16 T,Hc2≈ 34.5 T forH//[11-0] andHsf1= 2.5 T,Hsf2= 7 T forH//[001]. In these two directions, two and seven resonance modes are detected by ESR spectroscopy, respectively. Theω1andω2modes ofH//[11-0] can be well described by two-sublattice AFM resonance mode with two zero-field gaps at 94.51 GHz and 169.28 GHz, indicating a hard-axis feature. The seven modes forH//[001] are partially separated by the critical fields ofHsf1andHsf2, displaying the two signs of spin-flop transition. The fittings ofωc1andωc2modes yield zero-field gaps at 69.50 GHz and 84.73 GHz forH//[001], confirming the axis-type anisotropy. The saturated moment and gyromagnetic ratio indicate the Mn2+ion inα-Mn2V2O7is in a high spin state with orbital moment completely quenched. A quasi-one-dimensional magnetism with a zig-zag-chain spin configuration is suggested inα-Mn2V2O7, due to the special neighbor interactions caused by a distorted network structure with honeycomb layer.

Imaging of Antiferroelectric Dark Modes in an Inverted Plasmonic Lattice.

Plasmonic lattice nanostructures are of technological interest because of their capacity to manipulate light below the diffraction limit. Here, we present a detailed study of dark and bright modes in the visible and near-infrared energy regime of an inverted plasmonic honeycomb lattice by a combination of Au+ focused ion beam lithography with nanometric resolution, optical and electron spectroscopy, and finite-difference time-domain simulations. The lattice consists of slits carved in a gold thin film, exhibiting hotspots and a set of bright and dark modes. We proposed that some of the dark modes detected by electron energy-loss spectroscopy are caused by antiferroelectric arrangements of the slit polarizations with two times the size of the hexagonal unit cell. The plasmonic resonances take place within the 0.5-2 eV energy range, indicating that they could be suitable for a synergistic coupling with excitons in two-dimensional transition metal dichalcogenides materials or for designing nanoscale sensing platforms based on near-field enhancement over a metallic surface.

Successive Short- and Long-Range Magnetic Ordering in Ba2Mn3(SeO3)6 with Honeycomb Layers of Mn3+ Ions Alternating with Triangular Layers of Mn2+ Ions.

Mixed-valent Ba2Mn2+Mn23+(SeO3)6 crystallizes in a monoclinic P21/c structure and has honeycomb layers of Mn3+ ions alternating with triangular layers of Mn2+ ions. We established the key parameters governing its magnetic structure by magnetization M and specific heat Cp measurements. The title compound exhibits a close succession of a short-range correlation order at Tcorr = 10.1 ± 0.1 K and a long-range Néel order at TN = 5.7 ± 0.1 K, and exhibits a metamagnetic phase transition at T < TN with hysteresis most pronounced at low temperatures. The causes for these observations were found using the spin exchange parameters evaluated by density functional theory calculations. The title compound represents a unique case in which uniform chains of integer spin Mn3+ (S = 2) ions interact with those of half-integer spin Mn2+ (S = 5/2) ions.

A Generalized Nomenclature Scheme for Graphene Pores, Flakes, and Edges, and an Algorithm for Their Generation and Numbering.

In the present study, we generalize our recently proposed nomenclature scheme for porous graphene structures to include graphene flakes and (periodic) edges, i.e., nanographenes and graphene nanoribbons. The proposed nomenclature scheme is a complete scheme that similarly treats all these structures. Beyond this generalization, we study the geometric features of graphene flakes and edges based on ideas from the graph theory, as well as the pore-flake duality. Based on this study, we propose an algorithm for the systematic generation, identification, and numbering of graphene pores, flakes, and edges. The algorithm and the nomenclature scheme can also be used for flakes and edges of similar honeycomb systems.

Stability and mixing behavior of vanadium-iron oxide monolayers on Pt(111) and Ru(0001) substrates.

Cation mixing is a well-recognized means to obtain oxides of desired functionality with predetermined structure and stoichiometry, which yet has been only little analyzed at the nanoscale. In this context, we present a comparative analysis of the stability and mixing properties of O-poor and O-rich two-dimensional V-Fe oxides grown on Pt(111) and Ru(0001) surfaces, with the aim of gaining an insight into the role of substrate and oxygen conditions on the accessible Fe contents. We find that due to the high oxygen affinity of the Ru substrate, the mixed O-rich layers are highly stable while the stability of O-poor layers is limited to inaccessibly oxygen-poor environments. In contrast, on the Pt surface, O-poor and O-rich layers coexist with, however, a much lower Fe content in the O-rich phase. We show that cationic mixing (formation of mixed V-Fe pairs) is favored in all considered systems. It results from local cation-cation interactions, reinforced by a site effect in O-rich layers on the Ru substrate. In O-rich layers on Pt, Fe-Fe repulsion is so large that it precludes the possibility of substantial Fe content. These findings highlight the subtle interplay between structural effects, oxygen chemical potential, and substrate characteristics (work function and affinity towards oxygen), which governs the mixing of complex 2D oxide phases on metallic substrates.

Electronic Structures of Kitaev Magnet Candidates RuCl3 and RuI3.

Layered honeycomb magnets with strong atomic spin-orbit coupling at transition metal sites have been intensively studied for the search of Kitaev magnetism and the resulting non-Abelian braiding statistics. α-RuCl3 has been the most promising candidate, and there have been several reports on the realization of sibling compounds α-RuBr3 and α-RuI3 with the same crystal structure. Here, we investigate correlated electronic structures of α-RuCl3 and α-RuI3 by employing first-principles dynamical mean-field theory. Our result provides a valuable insight into the discrepancy between experimental and theoretical reports on transport properties of α-RuI3, and suggests a potential realization of correlated flat bands with strong spin-orbit coupling and a quantum spin-Hall insulating phase in α-RuI3.

Spin-glass behavior in Li3NiCuBiO6: a two-dimensional distorted honeycomb-lattice.

We report a detailed experimental study on the structural and magnetic properties of Li3NiCuBiO6by means of various characterization techniques. It crystallizes into a monoclinic crystal structure composed of a layered magnetic honeycomb lattice along thec-axis. The existence of glassy state below 4 K is indicated by dc and ac susceptibility measurements. Magnetic contribution to the total heat capacity also peaks around the freezing temperature, and its linear temperature dependence backs our claim of a glassy state in the compound. The calculated magnetic entropy unveils that only ∼26% of the total entropy is released for the system (S=3/2), and a tremendous amount of spin entropy is still retained in the system. Further, analysis of the frequency-dependent freezing temperature with the help of power law confirms the presence of a spin glass state. Moreover, the appearance of magnetic memory and relaxation effect below freezing temperature manifest the development of the system via a large number of intermediate metastable states. All these measurements confirm the spin-glass behavior of the compound. We consider the presence of different magnetic atoms in honeycomb lattice as the main driving factor for the spin-glass ground state.

Honeycomb lattice iridate on the verge of Mott-collapse.

A new honeycomb lattice iridate (La,Na)IrO3(≈LaNaIr2O6) is successfully synthesized from the spin-orbit coupled Mott insulator Na2IrO3by replacing the interlayer Na+ions with La3+ions. (La,Na)IrO3shows a finite Sommerfeld term in heat capacity and a -lnTdependence of resistivity, indicating a realization of a metallic state driven by a Mott collapse. Furthermore, crystal structure analysis reveals the formation of Ir zig-zag chains with metal-metal bonding, increasing kinetic energy resulting in the Mott collapse. This observation would be due to a Mott collapse induced in aJeff= 1/2 spin-orbit coupling Mott insulator with an Ir honeycomb lattice by topochemical control of the ionic configuration.

Magnetic Properties of A2Ni2TeO6 (A = K, Li): Zigzag Order in the Honeycomb Layers of Ni2+ Ions Induced by First and Third Nearest-Neighbor Spin Exchanges.

The static and dynamic magnetic properties and the specific heat of K2Ni2TeO6 and Li2Ni2TeO6 were examined and it was found that they undergo a long-range ordering at TN = 22.8 and 24.4 K, respectively, but exhibit a strong short-range order. At high temperature, the magnetic susceptibilities of K2Ni2TeO6 and Li2Ni2TeO6 are described by a Curie-Weiss law, with Curie-Weiss temperatures Θ of approximately -13 and -20 K, respectively, leading to the effective magnetic moment of about 4.46 ± 0.01 µB per formula unit, as expected for Ni2+ (S = 1) ions. In the paramagnetic region, the ESR spectra of K2Ni2TeO6 and Li2Ni2TeO6 show a single Lorentzian-shaped line characterized by the isotropic effective g-factor, g = 2.19 ± 0.01. The energy-mapping analysis shows that the honeycomb layers of A2Ni2TeO6 (A = K, Li) and Li3Ni2SbO6 adopt a zigzag order, in which zigzag ferromagnetic chains are antiferromagnetically coupled, because the third nearest-neighbor spin exchanges are strongly antiferromagnetic while the first nearest-neighbor spin exchanges are strongly ferromagnetic, and that adjacent zigzag-ordered honeycomb layers prefer to be ferromagnetically coupled. The short-range order of the zigzag-ordered honeycomb lattices of K2Ni2TeO6 and Li2Ni2TeO6 is equivalent to that of an antiferromagnetic uniform chain, and is related to the short-range order of the ferromagnetic chains along the direction perpendicular to the chains.

Effects of Non-Stoichiometry on the Ground State of the Frustrated System Li0.8Ni0.6Sb0.4O2.

The non-stoichiometric system Li0.8Ni0.6Sb0.4O2 is a Li-deficient derivative of the zigzag honeycomb antiferromagnet Li3Ni2SbO6. Structural and magnetic properties of Li0.8Ni0.6Sb0.4O2 were studied by means of X-ray diffraction, magnetic susceptibility, specific heat, and nuclear magnetic resonance measurements. Powder X-ray diffraction data shows the formation of a new phase, which is Sb-enriched and Li-deficient with respect to the structurally honeycomb-ordered Li3Ni2SbO6. This structural modification manifests in a drastic change of the magnetic properties in comparison to the stoichiometric partner. Bulk static (dc) magnetic susceptibility measurements show an overall antiferromagnetic interaction (Θ = -4 K) between Ni2+ spins (S = 1), while dynamic (ac) susceptibility reveals a transition into a spin glass state at a freezing temperature TSG ~ 8 K. These results were supported by the absence of the λ-anomaly in the specific heat Cp(T) down to 2 K. Moreover, combination of the bulk static susceptibility, heat capacity and 7Li NMR studies indicates a complicated temperature transformation of the magnetic system. We observe a development of a cluster spin glass, where the Ising-like Ni2+ magnetic moments demonstrate a 2D correlated slow short-range dynamics already at 12 K, whereas the formation of 3D short range static ordered clusters occurs far below the spin-glass freezing temperature at T ~ 4 K as it can be seen from the 7Li NMR spectrum.