The advent of nanotechnology has hurtled the discovery and development of nanostructured materials with stellar chemical and physical functionalities in a bid to address issues in energy, environment, telecommunications and healthcare. In this quest, a class of two-dimensional layered materials consisting of alkali or coinage metal atoms sandwiched between slabs exclusively made of transition metal and chalcogen (or pnictogen) atoms arranged in a honeycomb fashion have emerged as materials exhibiting fascinatingly rich crystal chemistry, high-voltage electrochemistry, fast cation diffusion besides playing host to varied exotic electromagnetic and topological phenomena. Currently, with a niche application in energy storage as high-voltage materials, this class of honeycomb layered oxides serves as ideal pedagogical exemplars of the innumerable capabilities of nanomaterials drawing immense interest in multiple fields ranging from materials science, solid-state chemistry, electrochemistry and condensed matter physics. In this review, we delineate the relevant chemistry and physics of honeycomb layered oxides, and discuss their functionalities for tunable electrochemistry, superfast ionic conduction, electromagnetism and topology. Moreover, we elucidate the unexplored albeit vastly promising crystal chemistry space whilst outlining effective ways to identify regions within this compositional space, particularly where interesting electromagnetic and topological properties could be lurking within the aforementioned alkali and coinage-metal honeycomb layered oxide structures. We conclude by pointing towards possible future research directions, particularly the prospective realisation of Kitaev-Heisenberg-Dzyaloshinskii-Moriya interactions with single crystals and Floquet theory in closely-related honeycomb layered oxide materials.
Two-dimensional electron dispersions with peculiar band crossings provide a platform for realizing topological phases of matter. Here we theoretically show that the $e_g$-orbital manifold of honeycomb-layered transition metal compounds accommodates a plethora of peculiar band crossings, such as multiple Dirac point nodes, quadratic band crossings, and line nodes. From the tight-binding analysis, we find that the band topology is systematically changed by the orbital dependent transfer integrals on the honeycomb network of edge-sharing octahedra, which can be modulated by distortions of the oct…
Natural abundance, impressive chemical characteristics and economic feasibility have rekindled the appeal for rechargeable sodium (Na) batteries as a practical solution for the growing energy demand, environmental sustainability and energy independence. However, the scarcity of viable positive electrode materials remains a huge impediment to the actualization of this technology. In this paper, we explore honeycomb layered oxides adopting the composition Na$_2$Ni$_{2-x}$Co$_x$TeO$_6$ ($x = 0, 0.25$ and $0.50$) as feasible positive electrode (cathode) materials for rechargeable sodium batteries …
Perovskite bilayers with (111)-orientation combine a honeycomb lattice as a key feature with the strongly correlated, multiorbital nature of electrons in transition metal oxides. In a systematic DFT+$U$ study of (111)-oriented (La$X$O$_3$)$_2$/(LaAlO$_3$)$_4$ superlattices, we establish trends in the evolution of ground states versus band filling in (111)-oriented (La$X$O$_3$)$_2$/(LaAlO$_3$)$_4$ superlattices, with $X$ spanning the entire $3d$ transition metal series. The competition between local quasi-cubic and global triangular symmetry triggers unanticipated broken symmetry phases, with m…
Advances in honeycomb layered oxides: Part II -- Theoretical advances in the characterisation of honeycomb layered oxides with optimised lattices of cations
Honeycomb layered oxides have garnered tremendous research interest in a wide swath of disciplines owing not only to the myriad physicochemical properties they exhibit, but also their rich crystal structural versatility. Herein, a comprehensive crystallographic study of a sodium-based $\rm Na_2Ni_2TeO_6$ honeycomb layered oxide has been performed using atomic-resolution transmission electron microscopy, elucidating a plethora of atomic arrangement (stacking) disorders in the pristine material. Stacking disorders in the arrangement of honeycomb metal slab layers (stacking faults) occur predomin…
We report the structures and physical properties of two new iridates, NaIrO$_3$ and Sr$_3$CaIr$_2$O$_9$, both of which contain continuous two-dimensional honeycomb connectivity. NaIrO3 is produced by room temperature oxidative deintercalation of sodium from Na$_2$IrO$_3$, and contains edge-sharing IrO6 octahedra that form a planar honeycomb lattice. Sr$_3$CaIr$_2$O$_9$, produced via conventional solid-state synthesis, hosts a buckled honeycomb lattice with novel corner-sharing connectivity between IrO6 octahedra. Both of these new compounds are comprised of Ir$^{5+}$ (5$d^4$) and exhibit negli…
We present a first-principles study of the atomic, electronic, and magnetic properties of two-dimensional (2D), single and bilayer ZnO in honeycomb structure and its armchair and zigzag nanoribbons. In order to reveal the dimensionality effects, our study includes also bulk ZnO in wurtzite, zincblende, and hexagonal structures. The stability of 2D ZnO, its nanoribbons and flakes are analyzed by phonon frequency, as well as by finite temperature ab initio molecular-dynamics calculations. 2D ZnO in honeycomb structure and its armchair nanoribbons are nonmagnetic semiconductors but acquire net ma…
Rational design of novel two-dimensional (2D) electrode materials with high capacity is crucial for the further development of Li-ion and Na-ion batteries. Herein, based on first-principles calculations, we systemically investigate Li and Na storage behaviors in the recently discovered 2D topological nodal-loop metal - the honeycomb borophene oxide (h-B2O). We show that h-B2O is an almost ideal anode material. It has good conductivity before and after Li/Na adsorption, fast ion diffusion with diffusion barrier less than 0.5 eV, low open-circuit voltage (less than 1 V), and small lattice change…
Defects and their interactions in crystalline solids often underpin material properties and functionality as they are decisive for stability, result in enhanced diffusion, and act as a reservoir of vacancies. Recently, lithium-rich layered oxides have emerged among the leading candidates for the next-generation energy storage cathode material, delivering 50 % excess capacity over commercially used compounds. Oxygen-redox reactions are believed to be responsible for the excess capacity, however, voltage fading has prevented commercialization of these new materials. Despite extensive research th…
Honeycomb layered oxides are a novel class of nanostructured materials comprising alkali or alkaline earth metals intercalated into transition metal slabs. The intricate honeycomb architecture and layered framework endows this family of oxides with a tessellation of features such as exquisite electrochemistry, unique topology and fascinating electromagnetic phenomena. Despite having innumerable functionalities, these materials remain highly underutilized as their underlying atomistic mechanisms are vastly unexplored. Therefore, in a bid to provide a more in-depth perspective, we propose an ide…
Endowed with a multitude of exquisite properties such as rich electrochemistry, superb topology and eccentric electromagnetic phenomena, honeycomb layered oxides have risen to the top echelons of science with applications in diverse fields ranging from condensed matter physics, solid-state chemistry, materials science, solid-state ionics to electrochemistry. However, these oxides are vastly underutilised as their underlying atomistic mechanisms remain unexplored. Therefore, in this study, atomic-resolution imaging on pristine $\rm K_2Ni_2TeO_6$ along multiple zone axes was conducted using sphe…
Li3Co2SbO6 is prepared by molten salt ion exchange and its structure refined by the Rietveld method confirming the honeycomb-type Co/Sb ordering of its Na precursor. Monoclinic rather than trigonal symmetry of Na3Co2SbO6 is directly demonstrated for the first time by peak splitting in the high-resolution synchrotron XRD pattern. The long-range antiferromagnetic order is established at TN about 6.7 K and 9.9 K in Na3Co2SbO6 and Li3Co2SbO6, respectively, confirmed by both the magnetic susceptibility and specific heat. Spin-wave analysis of specific heat data indicates the presence of 3D AFM magn…
Computational searching and screening of new functional materials exploiting earth abundant elements can accelerate developments of their energy applications. Based on a state-of-the-art materials search algorithm and ab initio calculations, we demonstrate a recently suggested stable silicon oxide with a layered structure (Si$_{3}$O) as an ideal photovoltaic material. With many-body first-principles approaches, the monolayer and layered bulk of Si$_{3}$O show direct quasiparticle gaps of 1.85 eV and 1.25 eV, respectively, while an optical gap of about 1.2 eV is nearly independent of the number…
In the quest of finding novel and efficient batteries, a great interest has raised in K-based honeycomb layer oxide materials both for their fundamental properties and potential applications. A key issue in the realization of efficient batteries based on such compounds, is to understand the K-ion diffusion mechanism. However, investigation of potassium-ion (K$^+$) dynamics in materials using magneto-spin properties has so far been challenging, due to its inherently weak nuclear magnetic moment, in contrast to other alkali ions such as lithium and sodium. Spin-polarised muons, having a high gyr…
Honeycomb layered tellurates represent a burgeoning class of multi-functional materials with fascinating crystal-structural versatility and a rich composition space. Despite their multifold capabilities, their compositional diversity remains underexplored due to complexities in experimental design and syntheses. Thus, in a bid to expand this frontier and derive relevant insights into allowed metastable compositions, we employ a density functional theory ($\rm DFT$) approach to predict $in$ $silico$ the crystal structures of new honeycomb layered tellurates embodied by the composition, $A\rm_2 …
A polymorph of RuI$_3$ synthesized under high pressure was found to have a two-layered honeycomb structure. The resistivity of RuI$_3$ exhibits a semimetallic behavior, in contrast to insulating properties in $α$-RuCl$_3$. In addition, Pauli paramagnetic behavior was observed in the temperature dependence of a magnetic susceptibility and a nuclear spin-lattice relaxation rate 1/$T_1$. The band structure calculations indicate that contribution of the I 5$p$ components to the low-energy $t_\mathrm{2g}$ bands effectively decreases Coulomb repulsion, leading to semimetallic properties. The physica…
Layered d-metal pnictide oxides are a unique class of compounds which consists of characteristic d-metal pnictide layers and metal oxide layers. More than 100 of these layered compounds, including the recently discovered Fe-based superconducting pnictide oxides, can be classified into 9 structure types. These structure types and the chemical and physical properties of the characteristic d-metal pnictide layers and metal oxide layers of the layered d-metal pnictide oxides are reviewed and discussed. Furthermore, possible approaches to design new superconductors based on these layered d-metal pn…
The marriage between a two-dimensional layered material (2DLM) and a complex transition metal oxide (TMO) results in a variety of physical and chemical phenomena that would not have been achieved in either material alone. Interesting recent discoveries in systems such as graphene/SrTiO3, graphene/LaAlO3/SrTiO3, graphene/ferroelectric oxide, MoS2/SrTiO3, and FeSe/SrTiO3 heterostructures include voltage scaling in field-effect transistors, charge state coupling across an interface, quantum conductance probing of the electrochemical activity, novel memory functions based on charge traps, and grea…
The structural, electronic, and optical properties of twelve multicomponent oxides with layered structure, RAMO$_4$, where R$^{3+}$=In or Sc; A$^{3+}$=Al or Ga; and M$^{2+}$=Ca, Cd, Mg, or Zn, are investigated using first-principles density functional approach. The compositional complexity of RAMO$_4$ leads to a wide range of band gap values varying from 2.45 eV for InGaCdO$_4$ to 6.29 eV for ScAlMgO$_4$. Strikingly, despite the different band gaps in the oxide constituents, namely, 2-4 eV in CdO, In$_2$O$_3$, or ZnO; 5-6 for Ga$_2$O$_3$ or Sc$_2$O$_3$; and 7-9 eV in CaO, MgO, or Al$_2$O$_3$, …
The Kitaev model predicts that quantum spin liquids (QSLs) will form at low temperatures under certain special conditions, and materials hosting the QSL state are frequently sought. The layered honeycomb lattice material α-RuCl3 has emerged as a prime candidate for displaying the Kitaev QSL state. Here we describe a new polymorph of RuI3 with a layered honeycomb lattice structure, synthesized at moderately high pressures and stable under ambient conditions. Preliminary characterization reveals metallic, paramagnetic behavior, the absence of long-range magnetic order down to 0.35 K and an unusu…
Microstructured honeycomb materials may exhibit exotic, extreme and tailorable mechanical properties, suited for innovative technological applications in a variety of modern engineering fields. The paper is focused on analysing the directional auxeticity of tetrachiral materials, through analytical, numerical and experimental methods. Theoretical predictions about the global elastic properties have been successfully validated by performing tensile laboratory tests on tetrachiral samples, realized with high precision 3D printing technologies. Inspired by the kinematic behaviour of the tetrachir…
We predict high thermoelectric efficiency in the layered perovskite La$_2$Ti$_2$O$_7$, based on calculations (mostly ab-initio) of the electronic structure, transport coefficients, and thermal conductivity in a wide temperature range. The figure of merit $ZT$ computed with a temperature-dependent relaxation time increases monotonically from just above 1 at room temperature to over 2.5 at 1200 K, at an optimal carrier density of around 10$^{20}$ cm$^{-3}$. The Seebeck thermopower coefficient is between 200 and 300 $μ$V/K at optimal doping, but can reach nearly 1 mV/K at low doping. Much of the …
Correlated electron systems on a honeycomb lattice have emerged as a fertile playground to explore exotic electronic phenomena. Theoretical and experimental work has appeared to realize novel behavior, including quantum Hall effects and valleytronics, mainly focusing on van der Waals compounds, such as graphene, chalcogenides, and halides. In this article, we review our theoretical study on perovskite transition-metal oxides (TMOs) as an alternative system to realize such exotic phenomena. We demonstrate that novel quantum Hall effects and related phenomena associated with the honeycomb struct…
We develop a self-consistently renormalized spin-wave theory, within a mean-field approximation, for the two-dimensional Heisenberg ferromagnet with perpendicular easy-axis anisotropy on the honeycomb lattice, as well as its few-layer and bulk extensions. In this method, the magnetization dependence on temperature is found as the solution of the self-consistency equation. Furthermore, we account for the physical difference of surface and bulk layers by treating the layers as separate sublattices. Thus, the method can be readily generalized to study various magnetic phenomena in a broad range o…
Manipulation of octahedral distortion at atomic length scale is an effective means to tune the physical ground states of functional oxides. Previous work demonstrates that epitaxial strain and film thickness are variable parameters to modify the octahedral rotation and tilt. However, selective control of bonding geometry by structural propagation from adjacent layers is rarely studied. Here we propose a new route to tune the ferromagnetic response in SrRuO3 (SRO) ultrathin layers by oxygen coordination of adjacent SrCuO2 (SCO) layers. The infinite-layered CuO2 in SCO exhibits a structural tran…
Honeycomb layered oxides with monovalent or divalent, monolayered cationic lattices generally exhibit myriad crystalline features encompassing rich electrochemistry, geometries and disorders, which particularly places them as attractive material candidates for next-generation energy storage applications. Herein, we report global honeycomb layered oxide compositions, ${\rm Ag_2}M_2{\rm TeO_6}$ ($M = \rm Ni, Mg, \textit{etc}.$) exhibiting $\rm Ag$ atom bilayers with sub-valent states within Ag-rich crystalline domains of ${\rm Ag_6}M_2{\rm TeO_6}$ and $\rm Ag$-deficient domains of ${\rm Ag}_{2 -…
Doping lithium-ion battery electrode materials LiMO$_2$ (M = Co, Ni, Mn) with impurities has been shown to be an effective way to optimize their electrochemical properties. Here, we report a detailed first-principles study of layered oxides LiCoO$_2$, LiNiO$_2$, and LiMnO$_2$ lightly doped with transition-metal (Fe, Co, Ni, Mn) and non-transition-metal (Mg, Al) impurities using hybrid-density-functional defect calculations. We find that the lattice site preference is dependent on both the dopant's charge and spin states, which are coupled strongly to the local lattice environment and can be af…
Layered materials tend to exhibit intriguing crystalline symmetries and topological characteristics based on their two dimensional (2D) geometries and defects. We consider the diffusion dynamics of positively charged ions (cations) localized in honeycomb lattices within layered materials when an external electric field, non-trivial topologies, curvatures and cationic vacancies are present. The unit (primitive) cell of the honeycomb lattice is characterized by two generators, $J_1, J_2 \in \rm SL_2(\mathbb{Z})$ of modular symmetries in the special linear group with integer entries, correspondin…
We report a comprehensive first-principles study of the thermodynamics and transport of intrinsic point defects in layered oxide cathode materials LiMO$_2$ (M=Co, Ni), using density-functional theory and the Heyd-Scuseria-Ernzerhof screened hybrid functional. We find that LiCoO$_2$ has a complex defect chemistry; different electronic and ionic defects can exist under different synthesis conditions, and LiCoO$_2$ samples free of cobalt antisite defects can be made under Li-excess (Co-deficient) environments. A defect model for lithium over-stoichiometric LiCoO$_2$ is also proposed, which involv…
Honeycomb layered oxides constitute an emerging class of materials that show interesting physicochemical and electrochemical properties. However, the development of these materials is still limited. Here, we report the combined use of alkali atoms ($\rm Na$ and $\rm K$) to produce a mixed alkali honeycomb layered oxide material, namely, $\rm NaKNi_2TeO_6$. Via transmission electron microscopy measurements, we reveal the local atomic structural disorders characterised by aperiodic stacking and incoherency in the alternating arrangement of $\rm Na$ and $\rm K$ atoms. We also investigate the poss…
The search for materials with novel and unusual electronic properties is at the heart of condensed matter physics as well as the basis to develop conceptual new technologies. In this context, the correlated honeycomb transition metal oxides attract large attention for both, being a possible experimental realization of the theoretically predicted magnetic Kitaev exchange and the theoretical prospect of topological nontriviality. The Mott insulating sodium iridate is prototypical among these materials with the promising prospect to bridge the field of strongly correlated systems with topology, f…
In the quest for quantum spin liquids, thin films are expected to open the way for the control of intricate magnetic interactions in actual materials by exploiting epitaxial strain and two-dimensionality. However, materials compatible with conventional thin-film growth methods have largely remained undeveloped. As a promising candidate towards the materialization of quantum spin liquids in thin films, we here present a robust ilmenite-type oxide with a honeycomb lattice of edge-sharing IrO$_6$ octahedra artificially stabilized by superlattice formation with an ilmenite-type antiferromagnetic o…
The search for topological semimetals is mainly focused on heavy-element compounds as following the footsteps of previous research on topological insulators, with less attention on light-element materials. However, the negligible spin orbit coupling with light elements may turn out to be beneficial for realizing topological band features.Here, using first-principles calculations, we propose a new two-dimensional light-element material-the honeycomb borophene oxide (h-B2O), which has nontrivial topological properties.The proposed structure is based on the recently synthesized honeycomb borophen…
This paper is concerned with the analysis of effective thermomechanical properties of multi- layered materials of interest for solid oxide fuel cells (SOFC) and lithium ions batteries fabrication. The recently developed asymptotic homogenization procedure is applied in order to express the overall thermoelastic constants of the first order equivalent continuum in terms of microfluctuations functions, and these functions are obtained by the solution of the corresponding recursive cell problems. The effects of thermal stresses on periodic multi-layered thermoelastic composite reproducing the cha…
We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit-cell as a prerequisite for forming weak topological insulators. Here, the single-layered KHgSb is the most suitable candidate for its large bulk energy gap of 0.24 eV. Its side surface hosts metallic surface states, forming two anisotropic Dirac cones. Though the stacking of even-layered structures leads to trivial insulators, the structures can host a quantum spin Hall layer with a large bulk gap, if an additional si…
Graphene-based membranes have been investigated as promising candidates for water filtration and gas separation applications. Experimental evidences have shown that graphene oxide can be impermeable to liquids, vapors and gases, while allowing a fast permeation of water molecules. This phenomenon has been attributed to the formation of a network of nano capillaries that allow nearly frictionless water flow while blocking other molecules by steric hindrance effects. It is supposed that water molecules are transported through the percolated two-dimensional channels formed between graphene-based …
The synthesis of IrI$_3$ at high pressure in its layered honeycomb polymorph is reported. Its crystal structure is refined by single crystal X-ray diffraction. Faults in the honeycomb layer stacking are observed by single crystal diffraction, synchrotron powder diffraction, and transmission electron microscopy. A previously unreported hyperhoneycomb polymorph of IrI$_3$ ($β$-IrI$_3$), is also described. Its structure in space group Fddd is determined by single crystal XRD. Both materials are highly-resistive diamagnetic semiconductors, consistent with a low spin d$^6$ configuration for Ir(III)…
Using density functional theory calculations including an on-site Coulomb term, we explore electronic and possibly topologically nontrivial phases in $3d$ transition metal oxide honeycomb layers confined in the corundum structure ($α$-Al$_2$O$_3$) along the [0001] direction. In most cases the ground state is a trivial antiferromagnetic Mott insulator, often with distinct orbital or spin states compared to the bulk phases. With imposed symmetry of the two sublattices the ferromagnetic phases of Ti, Mn, Co and Ni exhibit a characteristic set of four bands, two relatively flat and two with a Dira…
