Graphene Sublattices Research Articles

Regioselective On-Surface Synthesis of [3]Triangulene Graphene Nanoribbons.

The integration of low-energy states into bottom-up engineered graphene nanoribbons (GNRs) is a robust strategy for realizing materials with tailored electronic band structure for nanoelectronics. Low-energy zero-modes (ZMs) can be introduced into nanographenes (NGs) by creating an imbalance between the two sublattices of graphene. This phenomenon is exemplified by the family of [n]triangulenes (n ∈ ). Here, we demonstrate the synthesis of [3]triangulene-GNRs, a regioregular one-dimensional (1D) chain of [3]triangulenes linked by five-membered rings. Hybridization between ZMs on adjacent [3]triangulenes leads to the emergence of a narrow band gap, Eg,exp ∼ 0.7 eV, and topological end states that are experimentally verified using scanning tunneling spectroscopy. Tight-binding and first-principles density functional theory calculations within the local density approximation corroborate our experimental observations. Our synthetic design takes advantage of a selective on-surface head-to-tail coupling of monomer building blocks enabling the regioselective synthesis of [3]triangulene-GNRs. Detailed ab initio theory provides insights into the mechanism of on-surface radical polymerization, revealing the pivotal role of Au-C bond formation/breakage in driving selectivity.

Quantum transport of massless Dirac fermions through wormhole-shaped curved graphene in presence of constant axial magnetic flux

In this work, we have studied the spin-dependent quantum transport of charged fermion on (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-dimensional spacetime, whose spatial part is described by a wormhole-type geometry in the presence of constant axial magnetic flux. Choosing the solutions of the Dirac equation associated with real energy and momentum, we explored the spin-dependent transmission probabilities and giant magnetoresistance (GMR) through a single layer of wormhole graphene with an external magnetic field, using the transition matrix (T-Matrix) approach. The spin-up and spin-down components within the A and B sublattices of graphene in the matrix of 4×1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\ imes 1$$\\end{document} wave function are coupled to each other due to the wormhole structure and the magnetic field. We have found that transport properties strongly depend on the magnetic field, incident energy, and geometric parameters of the system. We observed that the transmission probability increases as the radius of the wormhole increases, and the length of the wormhole decreases. The higher energies lead to a decrease in the transmission probabilities of particles. Furthermore, we observed that the probability of the spin-flip effect is almost larger than that of the non-spin-flip effect, illustrating that electrons lose their spins during transmission. These findings highlight the complex and interesting behavior of wormhole graphene in the presence of external magnetic fields and suggest that these nano structures can have potential applications in electronic and spintronic devices.

Functional nanoporous graphene superlattice

Two-dimensional (2D) superlattices, formed by stacking sublattices of 2D materials, have emerged as a powerful platform for tailoring and enhancing material properties beyond their intrinsic characteristics. However, conventional synthesis methods are limited to pristine 2D material sublattices, posing a significant practical challenge when it comes to stacking chemically modified sublattices. Here we report a chemical synthesis method that overcomes this challenge by creating a unique 2D graphene superlattice, stacking graphene sublattices with monodisperse, nanometer-sized, square-shaped pores and strategically doped elements at the pore edges. The resulting graphene superlattice exhibits remarkable correlations between quantum phases at both the electron and phonon levels, leading to diverse functionalities, such as electromagnetic shielding, energy harvesting, optoelectronics, and thermoelectrics. Overall, our findings not only provide chemical design principles for synthesizing and understanding functional 2D superlattices but also expand their enhanced functionality and extensive application potential compared to their pristine counterparts.

Atomically Thin Current Pathways in Graphene through Kekulé-O Engineering.

We demonstrate that the current flow in graphene can be guided on atomically thin current pathways by the engineering of Kekulé-O distortions. A grain boundary in these distortions separates the system into topologically distinct regions and induces a ballistic domain-wall state. The state is independent of the orientation of the grain boundary with respect to the graphene sublattice and permits guiding the current on arbitrary paths. As the state is gapped, the current flow can be switched by electrostatic gates. Our findings are explained by a generalization of the Jackiw-Rebbi model, where the electrons behave in one region of the system as Fermions with an effective complex mass, making the device not only promising for technological applications but also a test-ground for concepts from high-energy physics. An atomic model supported by DFT calculations demonstrates that the system can be realized by decorating graphene with Ti atoms.

Valley filtering and valley-polarized collective modes in bulk graphene monolayers

The presence of two sublattices in hexagonal graphene brings two energetically degenerate extremes in the conduction and valence bands, which are identified by the valley quantum number. Recently, this valley degree of freedom has been suggested to encode and process information, which develops a new carbon-based electronics named graphene valleytronics. In this topical review, we present and discuss valley-related transport properties in bulk graphene monolayers, which are due to strain-induced pseudomagnetic fields and associated vector potential, sublattice-stagger potential, and the valley-Zeeman effect. These valley-related interactions can be utilized to obtain valley filtering, valley spatial separation, valley-resolved guiding modes, and valley-polarized collective modes such as edge or surface plasmons. The present challenges and the perspectives on graphene valleytronics are also provided in this review.

Topological origin of flat bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions

Flat bands play a central role in the presence of correlated phases in moir\'e and other modulated two-dimensional systems. In this paper, flat bands are shown to exist in uniaxially periodic strained graphene. Such strain should be produced for example by a substrate. The model is thus mapped into a one-dimensional effective Hamiltonian and this allows to find the conditions for having flat bands, i.e., a long-wavelength modulation only on each one of the bipartite graphene sublattices, while having a tagged strain field between neighboring carbon atoms. The origin of such flat bands is thus tracked down to the existence of topological localized wavefunctions at domain walls separating different regions, each with a nonuniform Su-Schriffer-Hegger model (SSH) type of coupling. Thereafter, the system is mapped into a continuum model allowing to explain the numerical results in terms of the Jackiw-Rebbi model and of pseudo-Landau levels. Finally, the interplay between the obtained flat bands and electron-electron interaction is explored through the Hubbard model. The numerical results within the mean-field approximation indicate that the flat bands induce N\'eel antiferromagnetic and ferromagnetic domains even for a very weak Hubbard interaction, while the repulsive Hubbard interaction results in an effective electron-electron attraction. Thus this paper provides a simple, analytically solvable but realistic model to understand the physical origin of flat bands, pseudo-Landau levels and their effects on the effective electron-electron interaction.

Photoreduced graphene oxide recovers graphene hot electron cooling dynamics

Reduced graphene oxide (rGO) is a bulk-processable quasi-amorphous 2D material with broad spectral coverage and fast electronic response. rGO sheets are suspended in a polymer matrix and sequentially photoreduced while measuring the evolving optical spectra and ultrafast electron relaxation dynamics. Photoreduced rGO yields optical absorption spectra that fit with the same Fano lineshape parameters as monolayer graphene. With increasing photoreduction time, rGO transient absorption kinetics accelerate monotonically, reaching an optimal point that matches the hot electron cooling in graphene. All stages of rGO ultrafast kinetics are simulated with a hot-electron cooling model mediated by disorder-assisted supercollisions. While the rGO room temperature 0.31 ps$^{-1}$ electronic cooling rate matches monolayer graphene, subsequent photoreduction can rapidly increase the rate by ~10-12$\times$. Such accelerated supercollision rates imply a reduced mean-free scattering length caused by photoionized point-defects on the rGO sp$^2$ sub-lattice. For visible range excitations of rGO, photoreduction shows three increasing spectral peaks that match graphene quantum dot (GQD) transitions, while a broad peak from oxygenated defect edge states shrinks. These three confined GQD states donate their hot carriers to the graphene sub-lattice with a 0.17 ps rise-time that accelerates with photoreduction. Collectively, many desirable photophysical properties of 2D graphene are replicated through selectively reducing rGO scaffolded within a 3D bulk polymeric network.

Metalloids (B, Si) and non-metal (N, P, S) doped graphene nanosheet as a supercapacitor electrode: A density functional theory study

Metalloids [Boron (B), Silicon (Si)] and Non -metals [Nitrogen (N), Phosphorus (P), Sulfur (S)] doped graphene nanosheets were considered for alternative lightweight electrode materials in energy storage device applications. The density functional theory studies were performed to investigate the structural stability, charge density distribution, excessive surface charge density, and quantum capacitance of doped graphene nanosheets. It is found that the structures are stable with negative formation energy, and the graphene nanosheet doped with P and S shows protrusion forming a pyramidal shape along the planar graphene nanosheet to maintain stability. Further, the doping of atoms into the graphene nanosheet introduced a minimal bandgap with a shift in the Fermi level, either into the conduction band or valence band, depending on the dopant type. This appearance of bandgap is attributed to the breaking of the symmetry in the graphene sublattice. Meanwhile, based on the type and concentration of dopant, localized and delocalized states are formed near the Fermi level. It is also found that the formation of a localized state near the Fermi level has profoundly improved the excessive surface charge density and quantum capacitance. The S – doped graphene nanosheet was observed to exhibit an excellent quantum capacitance of 38.88 μFcm−2 compared to all other structures and it can be used as a suitable light-weight electrode for asymmetric supercapacitors.

Density functional theory study on the electronic, optical and adsorption properties of Ti-, Fe- and Ni- doped graphene

Graphene has attracted widespread attention for its excellent physicochemical properties and a bright application prospect. However, the zero bandgap of graphene limits its application in optoelectronic devices. The Ti-, Fe- and Ni-doped graphene (Ti-G, Fe-G and Ni-G) with a non-zero bandgap catches our eyes. Therefore, the geometrical structures, electronic, optical and adsorption properties of Ti-G, Fe-G and Ni-G configurations are systematically investigated. Our results show that Ti-G, Fe-G and Ni-G systems are nonmagnetic semiconductors with the bandgaps of 0.441/0.443/0.338 eV. The reasons of the systems own bandgaps mainly originate from the hybridization between the d orbital of Ti/Fe/Ni atoms and p orbital of C atoms, which break the equivalent sublattices of intrinsic graphene. Furthermore, the doped systems exhibit good thermal stability, high Young's modulus and remarkable charge transfer. Optical adsorption spectrum reveals that Ti-G, Fe-G and Ni-G systems occur redshift and possess large light absorption range (up to 3000 nm). Adsorption energies demonstrate that they are highly sensitive to SO2, NO and NO2. The work provides a theoretical guidance for developing Ti-G, Fe-G and Ni-G systems with flexible application in optoelectronic devices and efficient gas detectors.

Strong-Magnetic-Field Magnon Transport in Monolayer Graphene

At high magnetic fields, monolayer graphene hosts competing phases distinguished by their breaking of the approximate SU(4) isospin symmetry. Recent experiments have observed an even denominator fractional quantum Hall state thought to be associated with a transition in the underlying isospin order from a spin-singlet charge density wave at low magnetic fields to an antiferromagnet at high magnetic fields, implying that a similar transition must occur at charge neutrality. However, this transition does not generate contrast in typical electrical transport or thermodynamic measurements and no direct evidence for it has been reported, despite theoretical interest arising from its potentially unconventional nature. Here, we measure the transmission of ferromagnetic magnons through the two-dimensional bulk of clean monolayer graphene. Using spin polarized fractional quantum Hall states as a benchmark, we find that magnon transmission is controlled by the detailed properties of the low-momentum spin waves in the intervening Hall fluid, which is highly density dependent. Remarkably, as the system is driven into the antiferromagnetic regime, robust magnon transmission is restored across a wide range of filling factors consistent with Pauli blocking of fractional quantum Hall spin-wave excitations and their replacement by conventional ferromagnetic magnons confined to the minority graphene sublattice. Finally, using devices in which spin waves are launched directly into the insulating charge-neutral bulk, we directly detect the hidden phase transition between bulk insulating charge density wave and a canted antiferromagnetic phase at charge neutrality, completing the experimental map of broken-symmetry phases in monolayer graphene.3 MoreReceived 6 February 2021Revised 22 February 2022Accepted 28 April 2022DOI:https://doi.org/10.1103/PhysRevX.12.021060Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFractional quantum Hall effectSpintronicsPhysical SystemsGrapheneCondensed Matter, Materials & Applied Physics

Nanodiamond islands confined between two graphene sheets as perspective 2D quantum materials

Based on direct space DFT PBE0/6-31G* electronic structure calculations, the structure and properties of nanodiamond islands confined between two finite graphene fragments (NDI-c2G) was proposed and theoretically explored. DFT simulations revealed that fusion of planar aromatic molecules with two parent graphene fragments may form either cubic or hexagonal allotropes of NDI-c2Gs lattices accompanied with formation of local corrugated sp3 sites with substituted dangling bonds embedded into graphene sublattices. It was shown that at the DFT level of theory, low distortion energies of NDI-c2Gs lattices are comparable or smaller than the energy of van-der-Waals interactions, which allows the NDI-c2G lattices to be stabilized by a support and finally synthesized. The Nuclear Independent Chemical Shift calculations, shows that in the vicinity of NDI regions, graphene lattices are estimated to be either low-, or anti-aromatic. Furthermore, the formation of NDI-c2Gs leads to localization of HOMO and LUMO states at different sites of the NDI-c2Gs lattices. The NDI-c2G regions with confined frontier orbitals can be considered as arrays of quantum dots isolated from each other by NDI scattering centres of 3.82 Å dimension. The results demonstrates that NDI-c2G should be considered as strongly-correlated entangled hybrid quantum dots which may form extended quantum ensembles with great potential for advanced quantum applications.

Rhombohedral trilayer graphene is more stable than its Bernal counterpart.

Stackings in graphene have a pivotal role in properties that could be useful in the future, as seen in the recently found superconductivity of twisted bilayer graphene. Beyond bilayer graphene, the stacking order of multilayer graphene can be rhombohedral, which shows flat bands near the Fermi level that are associated with interesting phenomena, such as tunable conducting surface states that can be expected to exhibit spontaneous quantum Hall effect, surface superconductivity, and even topological order. However, the difficulty in exploring rhombohedral graphenes is that in experiments, the alternating, hexagonal stacking is the most commonly found geometry and has been considered to be the most stable configuration for many years. Here we reexamine this stability issue in line with current ongoing studies in various laboratories. We conducted a detailed investigation of the relative stability of trilayer graphene stackings and showed how delicate this aspect is. These few-layer graphenes appear to have two basic stackings with similar energies. The rhombohedral and Bernal stackings are selected using not only compressions but anisotropic in-plane distortions. Furthermore, switching between stable stackings is more clearly induced by deformations such as shear and breaking of the symmetries between graphene sublattices, which can be accessed during selective synthesis approaches. We seek a guide on how to better control - by preserving and changing - the stackings in multilayer graphene samples.

Quantum Interferences of Pseudospin-Mediated Atomic-Scale Vortices in Monolayer Graphene.

A vortex is a universal and significant phenomenon that has been known for centuries. However, creating vortices to the atomic limit has remained elusive. Very recently, it was demonstrated that intervalley scattering induced by the single carbon defect of graphene leads to phase winding over a closed path surrounding the defect. Motivated by this, we demonstrate that the single carbon defects at A and B sublattices of graphene can be regarded as pseudospin-mediated atomic-scale vortices with angular momenta l = +2 and -2, respectively. The quantum interference measurements of the vortices indicate that the vortices cancel each other, resulting in zero total angular momentum, in the |A| = |B| case, and they show aggregate chirality and angular momenta similar to a single vortex of the majority in the |A| ≠ |B| case, where |A| (|B|) is the number of vortices with angular momenta l = +2 (l = -2).

Tracking atomic structure evolution during directed electron beam induced Si-atom motion in graphene via deep machine learning

Using electron beam manipulation, we enable deterministic motion of individual Si atoms in graphene along predefined trajectories. Structural evolution during the dopant motion was explored, providing information on changes of the Si atom neighborhood during atomic motion and providing statistical information of possible defect configurations. The combination of a Gaussian mixture model and principal component analysis applied to the deep learning-processed experimental data allowed disentangling of the atomic distortions for two different graphene sublattices. This approach demonstrates the potential of e-beam manipulation to create defect libraries of multiple realizations of the same defect and explore the potential of symmetry breaking physics. The rapid image analytics enabled via a deep learning network further empowers instrumentation for e-beam controlled atom-by-atom fabrication. The analysis described in the paper can be reproduced via an interactive Jupyter notebook at https://git.io/JJ3Bx

Vacancies in graphene: Dirac physics and fractional vacuum charges

The study of vacancies in graphene is a topic of growing interest. A single vacancy induces a localized stable charge of order unity interacting with other charges of the conductor through an unscreened Coulomb potential. It also breaks the symmetry between the two triangular graphene sublattices hence inducing zero energy states at the Dirac points. Here we show the fractional and pseudoscalar nature of this vacancy charge. A continuous Dirac model is presented which relates zero modes to vacuum fractional charge and to a parity anomaly. This relation constitutes an index theorem and is achieved by using particular chiral boundary conditions, which map the vacancy problem onto edge state physics. Vacancies in graphene thus allow us to realize prominent features of $2+1$ quantum electrodynamics but without coupling to a gauge field. This essential difference makes vacancy physics relatively easy to implement and an interesting playground for topological state switching.

Magnetic Spin Susceptibility of Graphene in Ferromagnetic State: A Tight-Binding Model Study

We report here a tight-binding model study of frequency-dependent ferromagnetic spin susceptibility of the graphene system. The tight-binding Hamiltonian consists of electron hoppings up to third-nearest-neighbors, substrate and impurity effects in the presence of Coulomb interaction of electrons separately at two in-equivalent A and B sub-lattices of graphene. To calculate magnetic susceptibility, we calculate the two-particle electron Green’s functions by using Zubarev’s double time Green’s function technique. The electron occupations at A and B sub-lattices for both up and down spins are computed numerically and self-consistently. The frequency-dependent real part of ferromagnetic susceptibility of the system is computed numerically by taking [Formula: see text] grid points of the electron momentum. The susceptibility displays a sharp peak at the neutron momentum transfer energy at low energies and another higher energy resonance peak appearing at substrate-induced gap. The [Formula: see text]-peak shifts to a higher energy with the increase of momentum [Formula: see text]. The susceptibility shows that the high energy peak shifts to higher energies due to the corresponding increase of substrate-induced gap observed experimentally. It is observed that the Coulomb interaction suppresses the substrate-induced gap, but the impurity doping at A site enhances the substrate-induced gap, while doping at B site suppresses it.

The reconstruction of the symmetry between sublattices: a strategy to improve the transport properties of edge-defective graphene nanoribbon transistors.

A numerical study that combines device simulation and first-principle calculations is performed, aiming to alleviate the performance degradation of graphene nanoribbon field-effect devices with edge defects. We believe that investigating the symmetry between the sublattices of graphene is a novel approach to understand this key problem. The results show that the edge defects that break the symmetry between the sublattices of graphene cause more severe degradation of the device performance because they induce highly localized electronic states, which dramatically affect the transport of carriers. We propose a strategy to alleviate the localization of electronic states by rebuilding the symmetry between the sublattices. This strategy can be realized by introducing foreign radicals to modify the defective edge. A stability analysis is performed to find the most stable modified structures. The final effect of our strategy on the corresponding devices demonstrates that it can effectively address specific edge defects and remarkably improve the ON-state current and subthreshold swing.

Resonant optical second harmonic generation in graphene-based heterostructures

An optical Second-Harmonic Generation (SHG) allows to probe various structural and symmetry-related properties of materials, since it is sensitive to the inversion symmetry breaking in the system. Here, we investigate the SHG response from a single layer of graphene disposed on an insulating hexagonal Boron Nitride (hBN) and Silicon Carbide (SiC) substrates. The considered systems are described by a non-interacting tight-binding model with a mass term, which describes a non-equivalence of two sublattices of graphene when the latter is placed on a substrate. The resulting SHG signal linearly depends on the degree of the inversion symmetry breaking (value of the mass term) and reveals several resonances associated with the band gap, van Hove singularity, and band width. The difficulty in distinguishing between SHG signals coming from the considered heterostrusture and environment (insulating substrate) can be avoided applying a homogeneous magnetic field. The latter creates Landau levels in the energy spectrum and leads to multiple resonances in the SHG spectrum. Position of these resonances explicitly depends on the value of the mass term. We show that at energies below the band-gap of the substrate the SHG signal from the massive graphene becomes resonant at physically relevant values of the applied magnetic field, while the SHG response from the environment stays off-resonant.

Tunable 2D-gallium arsenide and graphene bandgaps in a graphene/GaAs heterostructure: an ab initio study

The bandgap behavior of 2D-GaAs and graphene have been investigated with van der Waals heterostructured into a yet unexplored graphene/GaAs bilayer, under both uniaxial stress along c axis and different planar strain distributions. The 2D-GaAs bandgap nature changes from -K indirect in isolated monolayer to - direct in graphene/GaAs bilayer. In the latter, graphene exhibits a bandgap of 5 meV. The uniaxial stress strongly affects the graphene electronic bandgap, while symmetric in-plane strain does not open the bandgap in graphene. Nevertheless, it induces remarkable changes on the GaAs bandgap-width around the Fermi level. However, when applying asymmetric in-plane strain to graphene/GaAs, the graphene sublattice symmetry is broken, and the graphene bandgap is open at the Fermi level to a maximum width of 814 meV. This value is much higher than that reported for just graphene under asymmetric strain. The - direct bandgap of GaAs remains unchanged in graphene/GaAs under different types of applied strain. The analyses of phonon dispersion and the elastic constants yield the dynamical and mechanical stability of the graphene/GaAs system, respectively. The calculated mechanical properties for bilayer heterostructure are better than those of their constituent monolayers. This finding, together with the tunable graphene bandgap not only by the strength but also by the direction of the strain, enhance the potential for strain engineering of ultrathin group-III-V electronic devices hybridized by graphene.

Interaction of two symmetric monovacancy defects in graphene**Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0202300 and 2018YFA0305800), the National Natural Science Foundation of China (Grant Nos. 61622116, 61474141, 61390501, and 11604373), and the Pioneer Hundred Talents Program, Chinese Academy of Sciences.

We investigate the interactions between two symmetric monovacancy defects in graphene grown on Ru (0001) after silicon intercalation by combining first-principles calculations with scanning tunneling microscopy (STM). First-principles calculations based on free-standing graphene show that the interaction is weak and no scattering pattern is observed when the two vacancies are located in the same sublattice of graphene, no matter how close they are, except that they are next to each other. For the two vacancies in different sublattices of graphene, the interaction strongly influences the scattering and new patterns’ emerge, which are determined by the distance between two vacancies. Further experiments on silicon intercalated graphene epitaxially grown on Ru (0001) shows that the experiment results are consistent with the simulated STM images based on free-standing graphene, suggesting that a single layer of silicon is good enough to decouple the strong interaction between graphene and the Ru (0001) substrate.