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Honeycomb layered oxides are a novel class of nanostructured materials comprising alkali or coinage metal atoms 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 underutilised as their underlying atomistic mechanisms are vastly unexplored. Therefore, in a bid to provide a more in-depth perspective, we propose an idealised diffusion model of the charged alkali cations (such as lithium, sodium or potassium) in the two-dimensional (2D) honeycomb layers within the multi-layered crystal of honeycomb layered oxide frameworks. This model not only explains the correlation between the excitation of cationic vacancies (by applied electromagnetic fields) and the Gaussian curvature deformation of the 2D surface, but also takes into consideration, the quantum properties of the cations and their inter-layer mixing through quantum tunnelling. Through this work, we offer a novel theoretical framework for the study of multi-layered materials with 2D cationic diffusion currents, as well as providing pedagogical insights into the role of topological phase transitions in these materials in relation to Brownian motion and quantum geometry.

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 ∈ SL 2 ( Z ) of modular symmetries in the special linear group with integer entries, corresponding to discrete re-scaling and rotations respectively. Moreover, applying a 2D conformal metric in an idealized model, we can consistently treat cationic vacancies as topological defects in an emergent manifold. The framework can be utilized to elucidate the molecular dynamics of the cations in exemplar honeycomb layered frameworks and the role of quantum geometry and topological defects not only in the diffusion process such as prediction of conductance peaks during cationic (de-)intercalation process, but also pseudo-spin and pseudo-magnetic field degrees of freedom on the cationic honeycomb lattice responsible for bilayers.

Rechargeable potassium-ion batteries have been gaining traction as not only promising low-cost alternatives to lithium-ion technology, but also as high-voltage energy storage systems. However, their development and sustainability are plagued by the lack of suitable electrode materials capable of allowing the reversible insertion of the large potassium ions. Here, exploration of the database for potassium-based materials has led us to discover potassium ion conducting layered honeycomb frameworks. They show the capability of reversible insertion of potassium ions at high voltages (~4 V for K 2 Ni 2 TeO 6 ) in stable ionic liquids based on potassium bis(trifluorosulfonyl) imide, and exhibit remarkable ionic conductivities e.g. ~0.01 mS cm −1 at 298 K and ~40 mS cm –1 at 573 K for K 2 Mg 2 TeO 6 . In addition to enlisting fast potassium ion conductors that can be utilised as solid electrolytes, these layered honeycomb frameworks deliver the highest voltages amongst layered cathodes, becoming prime candidates for the advancement of high-energy density potassium-ion batteries. The development of potassium-ion batteries requires cathode materials that can maintain the structural stability during cycling. Here the authors have developed honeycomb-layered tellurates K 2 M 2 TeO 6 that afford high ionic conductivity and reversible intercalation of large K ions at high voltages.

Potassium‐ion batteries (KIBs) are increasingly attractive owing to their high voltage and projected low cost. However, the advancement of KIBs has been constrained by challenges related to electrolyte stability and interface compatibility. Traditional liquid electrolytes pose significant risks, including leakage and flammability, prompting a shift towards solid‐state electrolytes, which offer improved energy density, safety and thermal stability. This Perspective explores the current state of inorganic solid‐state electrolytes entailing oxides, chalcogenides, halides and hydrides. We delve into their recent advancements, identifying key challenges and future research opportunities, with the aim of advancing the development of high‐performance all‐solid‐state potassium batteries. Potassium‐ion batteries (KIBs) offer high voltage and low cost, yet face challenges related to electrolyte stability and flammability. Inorganic solid‐state electrolytes – spanning oxides, chalcogenides, halides, and borohydrides – offer promising solutions by enhancing safety and thermal stability. This Perspective delves into the latest advancements, identifies persistent challenges, and explores future opportunities to accelerate the development of high‐performance all‐solid‐state KIBs.

The central equations in classical general relativity are the Einstein Field equations, which accurately describe not only the generation of pseudo-Riemannian curvature by matter and radiation manifesting as gravitational effects, but more importantly mass-energy dynamics, evolution and distribution on the space-time manifold. Herein, we introduce a geometric phase in general relativity corresponding to Schwarzschild black hole information content. This quantity appropriately satisfies a local conservation law subject to minimal coupling, with other desirable properties such as the quantization of the black hole horizon in units of Planck area. The local conservation law is imposed by field equations, which not only contain the trace of Einstein Field equations, but also a complex-valued function with properties analogous to the quantum-mechanical wave function. Such success attests to the utility of the proposed field equations in capturing key aspects of quantum gravity theories.

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 (Na and K) to produce a mixed-alkali honeycomb layered oxide material, namely, NaKNi 2 TeO 6 . Via transmission electron microscopy measurements, we reveal the local atomic structural disorders characterised by aperiodic stacking and incoherency in the alternating arrangement of Na and K atoms. We also investigate the possibility of mixed electrochemical transport and storage of Na + and K + ions in NaKNi 2 TeO 6 . In particular, we report an average discharge cell voltage of about 4 V and a specific capacity of around 80 mAh g –1 at low specific currents (i.e., < 10 mA g –1 ) when a NaKNi 2 TeO 6 -based positive electrode is combined with a room-temperature NaK liquid alloy negative electrode using an ionic liquid-based electrolyte solution. These results represent a step towards the use of tailored cathode active materials for “dendrite-free” electrochemical energy storage systems exploiting room-temperature liquid alkali metal alloy materials. Honeycomb layered oxides are an emerging class of materials with peculiar physicochemical properties. Here, the authors report the synthesis and electrochemical energy storage characterisations of a mixed-alkali honeycomb layered oxide material capable of storing Na and K ions simultaneously.

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, global honeycomb‐layered oxide compositions, Ag2M2TeO6 (M=Ni,Mg,etc $M = \\rm Ni, Mg, etc$ .) exhibiting Ag $\\rm Ag$atom bilayers with sub‐valent states within Ag‐rich crystalline domains of Ag6M2TeO6 and Ag $\\rm Ag$ ‐deficient domains of Ag2−xNi2TeO6 ${\\rm Ag}_{2 - x}\\rm Ni_2TeO_6$(0

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