Triangular Lattice Research Articles

(Invited) Collective Radial Breathing Modes in Homogeneous Nanotube Bundles

Carbon nanotubes (CNTs) exist in many atomic structures typically grow as mixtures of of many chiralities with a vast variety of properties. Identical CNTs that are arranged into two-dimensional hexagonal lattices, their vibrational properties have been predicted to change with additional low-frequency modes appearing in the Raman spectrum. [1] Up to now, the experimental study of collective vibrations has been limited by a lack of pure homogeneous chirality bundles. We overcome this challenge by employing a self-coil mechanism of a very long CNT that loop into itself during the growth process resulting in a tightly packed hexagonal stack [2]. This lattice is perfectly homogeneous in terms of diameter, chiral twist, and even handedness of the tube. By characterizing and comparing the physical properties of the coil with respect to its tails, the bundling effects are clearly visible. We report on two breathing-like modes for quasi-infinite bundles, compared to the single radial breathing mode characteristic for isolated tubes. The exciton-phonon coupling in these modes is probed with resonant Raman spectroscopy, revealing the same resonance energy for both breathing-like peaks. Additionally, we study the dependence of vibrational coupling on the tube diameter by analysing different tube’s diameter coils and other bundling geometries. Our experimental findings align well with previously reported theoretical studies, demonstrating a 1/d scaling for all modes, as well as confirming the relative shift of the modes dependent on intertube interaction. These vibrations provide insight into the role of intertube lattice dynamics in two-dimensional THz-range phononic crystals.[1] Popov, V. N.; Henrard, L. Evidence for the existence of two breathinglike phonon modes in infinite bundles of single-walled carbon nanotubes. Phys. Rev. B 2001, 63, 233407[2] Nakar, D.; Gordeev, G.; Machado, L. D.; Popovitz-Biro, R.; Rechav, K.; Oliveira, E. F.; Kusch, P.; Jorio, A.; Galvao, D. S.; Reich, S.; others Few-wall Carbon Nanotube Coils. Nano Letters 2019, 20, 953–962.

Covalent Patterning of Graphene: from Sophistication to Simplicity

Patterning of graphene (functionalizing some areas while leaving others intact) is challenging, as all the C atoms in the basal plane are identical, but it is also desirable for a variety of applications, like opening a bandgap in the electronic structure of graphene. Several methods have been reported to pattern graphene, but most of them are very technologically intensive. For example, some groups have explored electron beam lithography,[1] or laser writing.[2] Here, we will present the two approaches that we have studied. First, we describe a method to functionalize graphene covalently under ultra-high vacuum conditions and characterized with scanning tunnelling microscopy.[3] We achieve exquisite (>97%) atomic selectivity and yield (92%). The periodic landscape is provided by a single monolayer of graphene grown on Ru(0001) that presents a moiré pattern due to the mismatch between the carbon and ruthenium hexagonal lattices. The moiré contains periodically arranged areas where the graphene–ruthenium interaction is enhanced and shows higher chemical reactivity. Furthermore, we will show how this type of functionalized graphene acts as a catalyst for an unusual and reversible C-C bond forming reaction.[4] Secondly, we will describe easy and scalable protocol for the covalent patterning of graphene based on using microemulsions as templates.[5] This method is technologically trivial and can achieve resolution in the µm range.[1] M. C. Rodríguez González, A. Leonhardt, H. Stadler, S. Eyley, W. Thielemans, S. De Gendt, K. S. Mali, S. De Feyter, ACS Nano 2021, 15, 10618-10627.[2] K. F. Edelthalhammer, D. Dasler, L. Jurkiewicz, T. Nagel, S. Al-Fogra, F. Hauke, A. Hirsch, Angew. Chem., Int. Ed. 2020, 59, 23329-23334; T. Wei, S. Al-Fogra, F. Hauke, A. Hirsch, J. Am. Chem. Soc. 2020, 142, 21926-21931.[3] J. J. Navarro, S. Leret, F. Calleja, D. Stradi, A. Black, R. Bernardo-Gavito, M. Garnica, D. Granados, A. L. Vazquez de Parga, E. M. Perez, R. Miranda, Nano Lett. 2016, 16, 355-361; J. J. Navarro, F. Calleja, R. Miranda, E. M. Pérez, A. L. V. d. Parga, Chem. Commun. 2017, 53, 10418--10421.[4] J. J. Navarro, M. Pisarra, B. Nieto-Ortega, J. Villalva, C. G. Ayani, C. Díaz, F. Calleja, R. Miranda, F. Martín, E. M. Pérez, A. L. Vázquez de Parga, Science Advances 2018, 4, eaau9366.[5] A. Naranjo, N. Martín Sabanés, M. Vázquez Sulleiro, E. M. Pérez, Chemical Communications 2022, 58, 7813-7816.

Cr-Cr distance and magnetism in the phase diagram of triangular lattice antiferromagnets: A systematic comparative study

In this study, we investigate the influence of Cr-Cr distances on the magnetic properties of triangular lattice antiferromagnets through the lens of the recently synthesized Cr compounds LiCrSe2, LiCrTe2, and NaCrTe2. Our comprehensive analysis integrates existing magnetic structure data and new insights from muon spin rotation measurements, revealing a striking mutual influence between strongly correlated electrons and structural degrees of freedom in systems possessing very different magnetic properties despite having the same crystal symmetry. In particular, we delineate how Cr-Cr distances specifically dictate the magnetic behaviors of the triangular lattice antiferromagnets LiCrSe2, LiCrTe2, and NaCrTe2. By crafting phase diagrams based on these distances, we establish a clear correlation between the structural parameters and the magnetic ground states of these materials together with a wide variety of trivalent Cr triangular lattice layered magnets. Our analysis uncovers a transition range for in-plane and out-of-plane Cr-Cr distances that demarcates distinct magnetic behaviors, highlighting the nuanced role of lattice geometry in the spin-lattice interaction and electron correlation dynamics. Published by the American Physical Society 2024

Grid Cells in Cognition: Mechanisms and Function.

The activity patterns of grid cells form distinctively regular triangular lattices over the explored spatial environment and are largely invariant to visual stimuli, animal movement, and environment geometry. These neurons present numerous fascinating challenges to the curious (neuro)scientist: What are the circuit mechanisms responsible for creating spatially periodic activity patterns from the monotonic input-output responses of single neurons? How and why does the brain encode a local, nonperiodic variable-the allocentric position of the animal-with a periodic, nonlocal code? And, are grid cells truly specialized for spatial computations? Otherwise, what is their role in general cognition more broadly? We review efforts in uncovering the mechanisms and functional properties of grid cells, highlighting recent progress in the experimental validation of mechanistic grid cell models, and discuss the coding properties and functional advantages of the grid code as suggested by continuous attractor network models of grid cells.

Orbital Hall effect and topology on a two-dimensional triangular lattice: From bulk to edge

Orbital Hall effect and topology on a two-dimensional triangular lattice: From bulk to edge

Discovery of Living Optical Networks in Orchid Leaves as Inspiration for Light Harvesting and Redistribution in Soft, Curvilinear Material Formats

AbstractPlants and animals produce highly evolved, hierarchical systems that combine physicochemical material parameters with functional micro‐ and nanostructures to manage energy, motion, and species survival. These systems, besides providing cues on bottom‐up manufacturing of technological structures, can give insight on strategies for efficient energy management. Here is reported the observation of an optically interconnected network formed by the cells of the leaves of the Macodes petola jewel orchid that provides light harvesting and redistribution across its surface. The planar redistribution of light incident on the leaf is enabled by the distinctively rounded shape of the outer epidermal cells and by their arrangement in a short‐range ordered hexagonal lattice. Successful replication of a live leaf in a free‐standing biopolymer film validates the observation and opens avenues for the exploration of non‐traditional energy harvesting interfaces that are soft, conformal, and curvilinear.

Analysis of point and linear defects inside photonic crystals with square and hexagonal lattices for communication applications

Analysis of point and linear defects inside photonic crystals with square and hexagonal lattices for communication applications

Bridging the small and large in twisted transition metal dichalcogenide homobilayers: A tight binding model capturing orbital interference and topology across a wide range of twist angles

Many of the important phases observed in twisted transition metal dichalcogenide homobilayers are driven by short-range interactions, which should be captured by a local tight binding description since no Wannier obstruction exists for these systems. Yet, published theoretical descriptions have been mutually inconsistent, with honeycomb lattice tight binding models adopted for some twist angles, triangular lattice models adopted for others, and with tight binding models forsaken in favor of band projected continuum models in many numerical simulations. Here, we derive and study a minimal model containing both honeycomb orbitals and a triangular site that represents the band physics across a wide range of twist angles. The model provides a natural basis to study the interplay of interaction and topology in these heterostructures. It elucidates from generic features of the bilayer the sequence of Chern numbers occurring as twist angle is varied, and the microscopic origin of the magic angle at which flat-band physics occurs. At integer filling, the model successfully captures the Chern ferromagnetic and van Hove-driven antiferromagnetic insulators experimentally observed for small and large angles, respectively, and allows a straightforward calculation of the magnetoelectric properties of the system. Published by the American Physical Society 2024

Hubbard Model on a Triangular Lattice at Finite Temperatures

Hubbard Model on a Triangular Lattice at Finite Temperatures

Dispersion Analysis of Plane Wave Propagation in Lattice-Based Mechanical Metamaterial for Vibration Suppression

Phononic crystals based on lattice structures provide important wave dispersion characteristics as band structures, showing excellent compatibility with additive manufacturing. Although the lattice structures have shown the potential for vibration suppression, a design guideline to control the frequency range of the bandgap has not been well established. This paper studies the dispersion characteristics of plane wave propagation in lattice-based mechanical metamaterials to realize effective vibration suppression for potential aerospace applications. Triangular and hexagonal periodic lattice structures are mainly studied in this paper. The influence of different geometric parameters on the bandgap characteristics is investigated. A finite element approach with Floquet–Bloch’s principles is implemented to effectively evaluate the dispersion characteristics of waves in lattice structures, which is validated numerically and experimentally with a 3D-printed lattice plate. Based on numerical studies with the developed analysis framework, the influences of the geometric parameters of lattice plate structures on dispersion characteristics can mainly be categorized into three patterns: change in specific branches related to in-plane or out-of-plane vibrations, upward/downward shift in frequency range, and drastic change in dispersion characteristics. The results obtained from the study provide insight into the design of band structures to realize vibration suppression at specific frequencies for engineering applications.

Carbon nanotuballs: Can they drive the future of nanofibers?

Nanofibers are extremely thin fibers produced from materials such as carbon, polymers, ceramics, and metals with diameters in the nanometer range that gained significant interest due to their unique properties. Carbon nanotubes, which could be considered the most popular fibers in the nanoscale, have gained widespread recognition primarily due to their remarkable strength derived from their cylindrical hexagonal lattice formed by carbon covalent bonds. Here, a new family of carbon nanofibers is proposed, arising from the combination of the tubular hexagonal configuration of carbon nanotubes and the spherical nanostructure of carbon fullerenes. These novel nanofibers, hereafter named carbon nanotuballs, are expected to demonstrate new advantaged characteristics such as better cross-section properties, enhanced interfacial interactions, and other unique physical attributes when used as fillers within other phases. Some preliminary theoretical investigations based on molecular dynamics are provided here to test the structural stability and mechanical behaviour of some single-walled carbon nanotuballs.

Mechanical characterization and puncture resistance of 3D‐printed PLA lattice structures

AbstractThe increasing application of additively manufactured (AM) materials in engineering and biomedical fields highlights the necessity of understanding their mechanical behavior, particularly with complex lattice structures. Polylactic acid (PLA), a popular biopolymer in additive manufacturing, exhibits mechanical characteristics highly dependent on its structural design. This research investigates the quasi‐static puncture failure analysis and mechanical characteristics of additively manufactured (AM) polylactic acid (PLA) materials with various lattice structures. The mechanical behavior, including tensile strength, flexural properties, interlaminar shear strength (ILSS), Izod impact resistance, and quasi‐static punch shear strength (QS‐PSS), was investigated following the respective ASTM protocols. Results indicate a 6% increase in tensile strength, to ca. 28 MPa, for the triangular PLA lattice structure compared with plain lattice structures. In the flexural test, the hexagonal structure showed a 13% increase in bending strength, to ca. 45 MPa, compared with the plain structure. Additionally, the hexagonal PLA lattice structure exhibited a 24% increase in shear strength, to approximately 8 MPa, over the plain lattice structure in the interlaminar shear strength analysis. In the Izod impact analysis, the plain lattice structure demonstrated a 17% increase in impact strength, to ca. 278 J/m, compared with the circular structure. A stainless‐steel hemispherical indenter was employed to investigate the quasi‐static punch shear behavior (QS‐PSS) of different lattice structures. The triangular structure displayed increased total energy absorption capacity and specific energy absorption of ca. 19 J and 0.529 J/g, respectively, compared with other lattice structures. These results are important for the creation of additively manufactured PLA lattice structures, improving the puncture resistance of advanced composites.Highlights Polylactic acid (PLA) lattice structures were fabricated. Plain, circular, triangular, and hexagonal lattice structures were investigated. Lattice structures were used as reinforcements. The triangular structure demonstrated improved strength. The triangular structure reduced crack formation and propagation.

Flux phases in the extended Hubbard model on the triangular lattice

Flux phases in the extended Hubbard model on the triangular lattice

Simulation of the Five-Component Potts Model on Triangular Lattice by the Monte Carlo Method in Pure and Diluted Modes

Simulation of the Five-Component Potts Model on Triangular Lattice by the Monte Carlo Method in Pure and Diluted Modes

Design of hexagonal shaped spectroscopy based biosensor for the detection of tuberculosis

A proposal has been made to identify tuberculosis cells using a novel compact sensor based on photonic crystal fiber: PCF in accordance with hexagonal spectroscopy. This proposed structure, which consists of a closely packed hexagonal air hole in the cladding region and a hollow-core area, possesses a very low loss of 6.30 × 10−8 dB/m and an exceptionally high sensitivity of up to 91.75 % (tuberculosis cell for 1.345). Numerous optical parameters have been identified and assessed, comprised of the numerical aperture, the V-parameter, or normalized frequency (Veff), and the effective area (Aeff). The operational wavelength range is defined as 0.80–3.0 THz. The numerical investigation of the properties of the proposed TB sensors is performed within the environment of COMSOL Multiphysics (Version 5.3) using FV-FEM stands for the full vector finite element method. PCF sensors composed of hexagonal lattice in a circular form with ZEONEX as the backdrop material is intended to boost the sensitivity response in comparison to the earlier works. Additionally, the sensor that is being displayed achieves a single modality throughout its whole operational wavelength range. This proposed sensor may play a significant role in identifying tuberculosis thanks to its superior sensitivity response and extremely minimal confinement loss. So, it is clearly seen that this sensor could be used to bio-medical sectors with process of terahertz (THz) wave pulse.

Structural, electronic, thermoelectric and optical properties of 2D hexagonal beryllium telluride under DFT investigation

In this study we have investigated structural, electronic, thermoelectric and optical properties of monolayer beryllium telluride compound in the hexagonal lattice phase (h-BeTe) using first principle calculations under density functional theory (DFT) approach. Using the frequency dependent phonon dispersion curves, we have analyzed the stability of the h-BeTe compound. The investigation of structural properties, including density of states (DOS) and band structure, demonstrates that h-BeTe is a direct bandgap semiconductor material with bandgap value of 3.054 eV. The h-BeTe compound exhibits exceptional thermoelectric behavior for a temperature range of 50–800 K, as confirmed by the calculated thermoelectric parameters, including thermal conductivity, electrical conductivity, Seebeck coefficient and figure of merit (ZT). It is vital that h-BeTe exhibits exceptional thermoelectric properties specifically, the figure of merit (ZT > 0.9) provides the efficiency of h-BeTe compound in temperature range of 300–800 K. The optical properties of h-BeTe are investigated for the first time with its interaction in applied external electric field based on various optical parameters such as real and imaginary dielectric constant, refractive index n(ω), extinction coefficient k(ω), absorption coefficient α(ω) and reflectivity R(ω). The optical properties analysis reveals the monolayer hexagonal beryllium telluride to be mostly active in the visible-UV spectrum. These findings have the potential to foster researchers to explore h-BeTe compound experimentally for possible optoelectronic applications.

Valley-Dependent Electronic Properties of Metal Monochalcogenides GaX and Janus Ga2XY (X, Y = S, Se, and Te).

Two-dimensional (2D) materials have shown outstanding potential for new devices based on their interesting electrical properties beyond conventional 3D materials. In recent years, new concepts such as the valley degree of freedom have been studied to develop valleytronics in hexagonal lattice 2D materials. We investigated the valley degree of freedom of GaX and Janus GaXY (X, Y = S, Se, Te). By considering the spin-orbit coupling (SOC) effect in the band structure calculations, we identified the Rashba-type spin splitting in band structures of Janus Ga2SSe and Ga2STe. Further, we confirmed that the Zeeman-type spin splitting at the K and K' valleys of GaX and Janus Ga2XY show opposite spin contributions. We also calculated the Berry curvatures of GaX and Janus GaXY. In this study, we find that GaX and Janus Ga2XY have a similar magnitude of Berry curvatures, while having opposite signs at the K and K' points. In particular, GaTe and Ga2SeTe have relatively larger Berry curvatures of about 3.98 Å2 and 3.41 Å2, respectively, than other GaX and Janus Ga2XY.

Maximizing Potential Applications of MAX Phases: Sustainable Synthesis of Multielement Ti3AlC2.

This study employs the molten-salt-shielded method to dope the Ti3AlC2 MAX phase with Nb and Mo, aiming to expand the intrinsic potential of the material. X-ray diffraction confirms the preservation of the hexagonal lattice structure of Ti3AlC2, while Raman and X-ray photoelectron spectroscopic analyses reveal the successful incorporation of dopants with subtle yet significant alterations in the vibrational modes and chemical environment. Scanning electron microscopy with energy-dispersive X-ray spectroscopy characterizations illustrate the characteristic layered morphology and uniform dopant distribution. Density functional theory simulations provide insights into the modified electronic structure, displaying changes in carrier transport mechanisms and potential increases in metallic conductivity, particularly when doping occurs at both the M and A sites. The computational findings are corroborated by the experimental results, suggesting that the enhanced material may possess improved properties for electronic applications. This comprehensive approach not only expands the MAX phase family but also tailors its functionality, which could allow for the production of hybrid materials with novel functionalities not present in the pristine form.

Topological states in Penrose-square photonic crystals

Topological edge states (TESs) and topological corner states (TCSs) in photonic crystals (PCs) provide an effective way to control the propagation and localization of light. The topological performance of integrated photonic devices can be improved by introducing the basic structural unit of photonic quasicrystals (PQCs) into PCs. However, the previous works arranged the basic structural unit of Stampfli-type and 12-fold Penrose-type photonic quasicrystals into triangular lattices, which have a complex structure and allow light to only propagate around 60° or 120° corners, limiting their applications. In this paper, a Penrose-square PC is proposed, which realizes both TESs and TCSs, and light successfully propagates around 90° corners. This work may reduce the difficulties encountered in the preparation of topological photonic crystals (TPCs) structured by arranging the basic structural units of PQCs periodically. It also provides a new, to the best of our knowledge, platform for studying TPCs and new ideas for improving the performance of integrated photonic devices.

Achievement splitting for topological states with pseudospin in phase modulation by using gyromagnetic photonic crystals

As we know, valley-Hall kink states or pseudospin helical edge states are excited by polarized-momentum-locking [left-handed circular polarization (LCP) and right-handed circular polarization (RCP)] because the valley-Hall kink modes or pseudospin polarized modes have intrinsic and local chirality, which is difficult for these states to achieve phase modulation. Here we theoretically design and study a compatible topological photonic system with coexistence of photonic quantum Hall phase and pseudospin Hall phase, which is composed of gyromagnetic photonic crystals with a deformed honeycomb lattice containing six cylinders. A typical kind of hybrid topological waveguide states with pseudospin-characteristic, magnetic field-dependent, and strong robustness against backscattering and perfect electric conductor (PEC) is realized in the present system. Furthermore, we re-design a structure with intersection-liked, achieve splitting for one-way pseudospin quantum Hall edge states by using phase modulation. Robustness of the one-way pseudospin-quantum Hall edge states in splitting has been demonstrated as well. Additionally, PEC inserted in transport channel brings optical path difference in waveguide transmission, which would influence splitting for hybrid topological waveguide states in phase difference modulation. This work not only provides a new way for manipulation (i.e., phase modulation) of hybrid topological waveguide states in compatible topological photonic system from distinct topological classes but also has potential in various applications, such as sensing, signal processing, and on-chip communications.