Armchair Boundaries Research Articles

Evaluation of topological protection in kagome lattice-based thermal diffusion systems

We evaluated topological protection for edge and higher-order corner states in topological diffusion systems based on the breathing kagome lattice. In the kagome lattice, the corner states appear at the corner boundary where all three Wannier centers in nontrivial unit cells are located. The three Wannier centers in a unit cell can be placed on the obtuse- and acute-corner boundaries utilizing the armchair boundary, generating topological acute- and obtuse-corner states. For another representative zigzag boundary, only the acute-corner unit cell has three Wannier centers located at the boundary; hence, only the acute-corner state appears. Our band analysis and numerical studies show that the topologically protected decay behavior for armchair boundaries is as robust as that for zigzag boundaries, unlike wave phenomena with space and time periodicities. Our findings can guide the flexible design of topological diffusion applications such as heat localization and recovery systems.

Fracture behaviour of bicrystalline graphene characterized via freestanding indentation

Using molecular mechanics (MM) simulations, the failure stress of bicrystalline graphene with different tilt angles is investigated using their free-standing indentation behaviour, in which two types of grain boundaries, including armchair (ac) and zigzag (zz) grain boundaries, and two types of indenter tip, including cylindrical and spherical tips are considered. For reference purposes, the corresponding results under inplane stretching are also examined. It is found that the failure stress of grain boundary (GB) in bicrystalline graphene decreases with the decrease of the GB tilt angle [Formula: see text], which is similar to that determined in inplane stretching. In indentation, the stress concentration under the indenter tip will decrease the failure stress of graphene; in addition, the out-of-plane deformation of graphene in indentation can partially release the pretension induced by the GB in bicrystalline graphene. For the GB with a small prestress, the effect of the former is larger than that of the latter; but for the GB with a larger prestress, the effect of the latter is larger than that of the former. Consequently, the effect of tilt angle [Formula: see text] on the GB strength of bicrystalline graphene is lower in indentation than that given by inplane stretching.

Nernst and seebeck effects in α−T3 lattice

By using the tight-binding Hamiltonian and non-equilibrium Green’s function methods, the Seebeck and Nernst effects of α−T3 lattice are investigated, in which the lattice interpolates between graphene and the dice lattice via the parameter α. For α = 0 (graphene), flat bands are always present in the band structure. The Seebeck and Nernst coefficients are consistent with those in graphene. When α is non-zero at zero magnetic field, the Seebeck coefficient is an odd function of the Fermi energy. It produces a very large and wide first peak within the band gap for the zigzag boundary. Under the influence of magnetic fields, the first peak of the Seebeck coefficient in the gap region increases with α increasing. The Nernst effect occurs under the influence of a magnetic field. The height of the zeroth peak of the Nernst coefficient increases with α increasing. When α reaches a certain value, the zeroth peak splits. The post-split peak decreases with α increasing for the zigzag boundary, but continues to become wider and higher for the armchair boundary.

Topological phases, local magnetic moments, and spin polarization triggered by C558-line defects in armchair graphene nanoribbons.

The topological and magnetic properties induced by topological defects in graphene have attracted attention. Here, we study a novel topological defect structure for graphene nanoribbons interspersed with C558-line defects along the armchair boundary, which possesses topological properties and is tritopic. Using strain engineering to regulate the magnitude of hopping at defects, the position of the energy level can be easily changed to achieve a topological phase transition. We also discuss the local magnetic moment and the ferromagnetic ground state in the context of line defects. This leads to spin polarization of the whole system. Finally, when C558 graphene nanoribbons are controlled by a nonlocal exchange magnetic field, spin-polarized quantum conductivity occurs near the Fermi level. Consequently, spin filtering can be achieved by varying the incident energy of the electrons. Our results provide new insights into realizing topological and spin electronics in low-dimensional quantum devices.

Detecting the spin-polarization of edge states in graphene nanoribbons

Low dimensional carbon-based materials can show intrinsic magnetism associated to p-electrons in open-shell π-conjugated systems. Chemical design provides atomically precise control of the π-electron cloud, which makes them promising for nanoscale magnetic devices. However, direct verification of their spatially resolved spin-moment remains elusive. Here, we report the spin-polarization of chiral graphene nanoribbons (one-dimensional strips of graphene with alternating zig-zag and arm-chair boundaries), obtained by means of spin-polarized scanning tunnelling microscopy. We extract the energy-dependent spin-moment distribution of spatially extended edge states with π-orbital character, thus beyond localized magnetic moments at radical or defective carbon sites. Guided by mean-field Hubbard calculations, we demonstrate that electron correlations are responsible for the spin-splitting of the electronic structure. Our versatile platform utilizes a ferromagnetic substrate that stabilizes the organic magnetic moments against thermal and quantum fluctuations, while being fully compatible with on-surface synthesis of the rapidly growing class of nanographenes.

Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry

Studying the edge states of a topological system and extracting their topological properties is of great importance in understanding and characterizing these systems. In this paper, we present a novel analytical approach for obtaining explicit expressions for the edge states in the Kane-Mele model within a ribbon geometry featuring armchair boundaries. Our approach involves a mapping procedure that transforms the system into an extended Su–Schrieffer–Heeger model, specifically a two-leg ladder, in momentum space. Through rigorous derivation, we determine various analytical properties of the edge states, including their wave functions and energy dispersion. Additionally, we investigate the condition for topological transition by solely analyzing the edge states, and we elucidate the underlying reasons for the violation of the bulk-edge correspondence in relatively narrow ribbons. Our findings shed light on the unique characteristics of the edge states in the quantum spin Hall phase of the Kane–Mele model and provide valuable insights into the topological properties of such systems.

Domain nucleation kinetics and polarization-texture-dependent electronic properties in two-dimensional α-In2Se3 ferroelectrics.

Two-dimensional (2D) ferroelectric semiconductors, such as α-In2Se3 with switchable spontaneous polarization and superior optoelectronic properties, exhibit large potential for functional device applications. The electric transport properties and device performance of 2D α-In2Se3 are strongly sensitive to the ferroelectric domain structures and polarization textures, but they are rarely explored at the atomic scale. Herein, by a combination of first-principles calculations and a developed domain switching theory, we report the domain nucleation kinetics and polarization-texture dependent electronic properties in α-In2Se3 ferroelectrics. Our calculated results reveal that the reversed domains characterized by armchair boundaries tend to form triangular or stripped shape. The energy barrier for propagating domain boundaries is ∼1.42 eV and can be reduced by loading external electric field, which is responsible for driving the evolution of domain structures. Moreover, the domain switching leads to notable changes in the band gap and carrier spatial distribution of α-In2Se3 monolayer, resulting in higher electric resistance of multi-polarization domain structures than that of single-polarization state. The domain structures of multilayer α-In2Se3 follow a layer-by-layer switching mechanism, which causes the transition of electronic structures from self-doped p-n junctions to type-II semiconductor homojunctions. This study not only provides an in-depth insight into the domain switching mechanisms of α-In2Se3 but also opens up the possibility to tailor their electronic and transport properties.

Vacancy clustering effect on the electronic and transport properties of bilayer graphene nanoribbons

Experimental realizations of two-dimensional materials are hardly free of structural defects such as e.g. vacancies, which, in turn, modify drastically its pristine physical defect-free properties. In this work, we explore effects due to point defect clustering on the electronic and transport properties of bilayer graphene nanoribbons, for AA and AB stacking and zigzag and armchair boundaries, by means of the tight-binding approach and scattering matrix formalism. Evident vacancy concentration signatures exhibiting a maximum amplitude and an universality regardless of the system size, stacking and boundary types, in the density of states around the zero-energy level are observed. Our results are explained via the coalescence analysis of the strong sizeable vacancy clustering effect in the system and the breaking of the inversion symmetry at high vacancy densities, demonstrating a similar density of states for two equivalent degrees of concentration disorder, below and above the maximum value.

Electronic and optical properties of Janus black arsenic-phosphorus AsP quantum dots under magnetic field

By utilizing the tight-binding method, the electronic spectrum and states distribution of square Janus monolayer black arsenic phosphorus (b-AsP) quantum dots (QDs) in the presence of a perpendicular magnetic field are explored. Strong in-gap states of b-AsP QDs, whose probability densities are distributed on the armchair boundary (armchair edge states) appear in the energy gap of host perfect two-dimensional b-AsP. The corresponding energy levels of the armchair edge states can degenerate to the Landu energy levels upon applying a perpendicular magnetic field. When an in-plane polarized light is introduced, due to the presence of armchair edge states, the edge-to-edge transitions are mainly induced from the armchair edge (hole) states to zigzag edge (electron) states. The optical absorption undergoes blue shift as a function of the magnetic field. Our work suggests tunable optical properties via modulating the armchair edge states of a b-AsP QD and provides a theoretical basis for the design of b-AsP-based optoelectronic devices.

Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots

We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of electrostatic quantum dots. We provide an analytically feasible model where some bound states can be found explicitly. We show that the energies of these bound states belong either to the gap of valence and conducting bands or they represent bound states in the continuum whose energies are embedded in the continuous spectrum. The solutions satisfying armchair boundary conditions are found in an elegant manner with the use of specific projection operators.

Electronic characteristics of SbBi binary nanoflakes

The structural and electronic characteristics of the Antimony–Bismuth binary monolayer is presented here. The electronic gap is reported as a function of the nanoflake dimensions. Tunable photocatalytic properties are observed. The stability of the SbBi binary nanoflakes falls by widening the nanosheet from both sides of the Zigzag and Armchair edges. The dependency of the energy bandgap between frontier orbital levels concerning the nanoflakes width across either of the Zigzag and Armchair boundaries are explored for structures having maximum of 388 atoms. Regions of chemical activity in SbBi monolayers are mainly focused on their middling points, leading to negligible chemical activity along the edges. Furthermore, some of the considered nanoflakes ions exhibit strong spin-exchange splitting.

Current distribution and group velocities for electronic states on lattice ribbons in a magnetic field

We study the group velocities of electronic states and distributions of currents in lattice ribbons under a uniform perpendicular magnetic field. Using the effective low-energy model we analyze all possible simple configurations of lattice termination with zigzag and armchair boundaries. We show that the edge current depends on the type of zigzag termination, and can be zero or finite near the edge. Also similar dependence is observed in the case of armchair termination and is related to the size of the ribbon. The nonzero current flowing along the edge can be used a signature of formation of propagating edge states. In addition, we show the qualitative difference in the distribution of the edge current between the case of α = 1 (dice model) and other values of model parameter α ≠ 1 for armchair-terminated ribbons.

Electronic structures and transport properties of low-dimensional GaN nanoderivatives: A first-principles study

Low-dimensional gallium nitride (GaN) nanoderivatives have recently attracted great attention, and they are one of the most attractive fields for future development of microelectronic devices. Here, the electronic structures and transport properties of GaN nanoderivatives were investigated by density functional theory. For two-dimensional bilayer GaN nanosheets, we found that AA-NN(GaGa) is the most stable structure among the five GaN stacking structures, and the stacking arrangement does not change the wide and indirect band gap of these two-dimensional bilayer stacked nanosheets. The transport properties of one-dimensional GaN nanoribbons were also investigated. The current in the bilayer GaN nanodevices was about twice that in the monolayer GaN nanodevices regardless of the nanoribbon morphology. That is, the bilayer GaN nanodevices show the current superposition law, like a parallel circuit, compared with their respective monolayer GaN model devices. The one-dimensional armchair boundary GaN nanoribbon devices showed the width effect because the width had a great effect on the current–voltage (I-V) curve and transport characteristics, but the one-dimensional zigzag boundary GaN nanoribbon devices did not and the I-V characteristic curves for different nanoribbon widths were similar. These extraordinary electronic structures indicate that GaN is promising for application in microelectronic devices.

Quadratic Dirac point and valley topological phases in acoustic analogues of AB-stacked bilayer graphene

The concepts of Dirac point and valley have been extended to phononic crystals, inspired by the development of valleytronic materials. Usually, the valley topological phases are induced by opening the gap of the linear Dirac points. In this work, we investigate the valley topological phases by breaking the quadratic Dirac point in two-dimensional bilayer phononic crystals, as analogues of the AB-stacked bilayer graphene. The acoustic edge states exist at the zigzag boundary of a single valley phase, attributed to the integer valley Chern number. In the domain wall between two distinct valley phases, the numbers of the acoustic edge states double in both the zigzag and armchair boundaries. Our work provides a macroscopic platform to explore the intriguing properties of the bilayer graphene.

Quantum effects on the mechanical properties of fine-scale CNTs: an approach based on DFT and molecular mechanics model

The quantum effects of fine scaling on the properties of nanostructures are studied in this paper. After studying the dimensional effects of nanosheets on the structural energy of materials using the density functional theory and determining the effective parameters on the structural energy of materials, the mechanical properties of the nanosheets are computed. The results showed that for carbon structures with lengths less than 20 angstroms, dimensional changes have significant effects on the structural energy. Then, by obtaining the coefficients of the molecular mechanics related to the size of structure, the mechanical properties of nanotubes, such as their Young’s modulus, shear modulus and Poisson’s ratio, are calculated. It is seen that the dimensional changes cause significant changes on Young’s and shear moduli, while Poisson’s ratio is affected the most. For example, Young’s moduli of nanosheets with the zigzag boundary atoms arrangement for two widths of 7.1043 and 36.9423 angstroms are 431.28 and 352.21 $$ {\text{GPa}}\;{\text{nm}} $$ , respectively, which have 23.22 and 0.63 percent difference compared to Young’s modulus of graphene which is 350 $$ {\text{GPa}}\;{\text{nm}} $$ , respectively. In addition, Poisson’s ratio for the mentioned structures is equal to 0.41 and 0.22, respectively, which have a difference of 156.25 and 37.5 percent as compared to Poisson’s ratio of graphene, which is 0.16. Moreover, a comparison study is presented on the mechanical properties of finite elemental structures and their maximum lengths, and the differences caused by dimensional changes are reported. The results show that dimensional changes have a significant effect on the properties of nanostructures with certain sizes. For example, for a zigzag nanotube with the length of 7.10431 angstrom and two diameters of 2.349 and 10.96 angstroms, Young’s moduli of nanotube are 354.95 and 425.89 $$ {\text{GPa}}\;{\text{nm}} $$ , respectively. The difference in the diameters results in the change of Young’s modulus for the amount of 19.99 percent. The results also reveal that in addition to the structural dimensions, the layout of structural atoms and the arrangement of boundary atoms has major influences on the mechanical properties of structure. For example, Poisson’s ratio of nanosheets with the of armchair boundary atoms arrangement the for two widths of 7.3830 and 36.9150 angstroms is equal to 0.56 and 0.30, respectively, and Poisson’s ratio for the same width and zigzag boundary atom arrangement is 0.41 and 0.22, respectively, which has the difference of 36.58 and 36.36, respectively.

Vibrational Characteristics of Two-Dimensional Composite Structures of Hexagonal Boron Nitride and Graphene

We use an eigenmode analysis to investigate normal mode vibrations of hexagonal boron nitride (h-BN) and of various types of graphene and h-BN composites. The vibrational spectrum of pristine h-BN structure was a rescaled one of pristine graphene. The vibrational spectra of graphene and h-BN composites with zigzag and with armchair boundaries were just mixtures of the vibrational spectra of the pristine structures of graphene and h-BN, respectively. The vibrational spectrum of h-BN doped with a graphene quantum dot was similar to that of h-BN, and the vibrational spectrum of graphene doped with a small piece of boron nitride was similar to that of graphene. We found that the resemblance of the vibrational spectra was closely related to the similarities of the lattice structures. Using the amplitude analysis, we were able to identify the eigenmodes of the various composites as motions of nodes in the graphene region or in the h-BN region or at the interfacial boundaries between them.

Granular graphene: Direct observation of edge states on zigzag and armchair boundaries

We propose a mechanical graphene analog which is made of stainless steel beads placed in a periodic magnetic field by a proper design. A stable, free of mechanical borders granular structure with well-predicted wave dynamics is experimentally constructed. First, we report the dispersion relation in conjunction with the evidence of the Dirac points. Theoretical analysis shows that, compared to genuine or other artificial graphene analogs, edge modes exist in the free zigzag and armchair boundaries together with bulk modes composed of in-plane extended translations but localized rotations at the edges. We observe the existence of edge modes in free zigzag boundary, and we reveal an experimental turning effect of edge waves from the zigzag to the armchair/zigzag boundary, even in the absence of a full band gap for bulk modes. Our work shows that granular graphene can serve as an excellent experimental platform to study Dirac, topological, and nonlinear wave phenomena.

Valley isospin of interface states in a graphene pn junction in the quantum Hall regime

In the presence of crossed electric and magnetic fields, a graphene ribbon has chiral states running along sample edges and along boundaries between $p$-doped and $n$-doped regions. We here consider the scattering of edge states into interface states, which takes place whereever the $pn$ interface crosses the sample boundary, as well as the reverse process. For a graphene ribbon with armchair boundaries, the evolution of edge states into interface states and {\em vice versa} is governed by the conservation of valley isospin. Although valley isospin is not conserved in simplified models of a ribbon with zigzag boundaries, we find that arguments based on isospin conservation can be applied to a more realistic modeling of the graphene ribbon, which takes account of the lifting of electron-hole degeneracy. The valley isospin of interface states is an important factor determining the conductance of a graphene $pn$ junction in a quantizing magnetic field.

The Thermal, Electrical and ThermoelectricProperties of Graphene Nanomaterials.

Graphene, as a typical two-dimensional nanometer material, has shown its unique application potential in electrical characteristics, thermal properties, and thermoelectric properties by virtue of its novel electronic structure. The field of traditional material modification mainly changes or enhances certain properties of materials by mixing a variety of materials (to form a heterostructure) and doping. For graphene as well, this paper specifically discusses the use of traditional modification methods to improve graphene’s electrical and thermoelectrical properties. More deeply, since graphene is an atomic-level thin film material, its shape and edge conformation (zigzag boundary and armchair boundary) have a great impact on performance. Therefore, this paper reviews the graphene modification field in recent years. Through the change in the shape of graphene, the change in the boundary structure configuration, the doping of other atoms, and the formation of a heterostructure, the electrical, thermal, and thermoelectric properties of graphene change, resulting in broader applications in more fields. Through studies of graphene’s electrical, thermal, and thermoelectric properties in recent years, progress has been made not only in experimental testing, but also in theoretical calculation. These aspects of graphene are reviewed in this paper.

Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure

We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface. Our method builds on the generalized Bloch theorem [A. Alase et al., Phys. Rev. B 96, 195133 (2017)] and the fact that the bulk-boundary separation of the Schrodinger equation is compatible with a partial Fourier transform operation. Bulk equations may display unusual features because they are relative eigenvalue problems for non-Hermitian, bulk-projected Hamiltonians. Nonetheless, they admit a rich symmetry analysis that can simplify considerably the structure of energy eigenstates, often allowing a solution in fully analytical form. We illustrate our extension of the generalized Bloch theorem to multicomponent systems by determining the exact Andreev bound states for a simple SNS junction. We then analyze the Creutz ladder model, by way of a conceptual bridge from one to higher dimensions. Upon introducing a new Gaussian duality transformation that maps the Creutz ladder to a system of two Majorana chains, we show how the model provides a first example of a short-range chiral topological insulator hosting topological zero modes with a power-law profile. Additional applications include the complete analytical diagonalization of graphene ribbons with both zigzag-bearded and armchair boundary conditions, and the analytical determination of the edge modes in a chiral $p+ip$ two-dimensional topological superconductor. Lastly, we revisit the phenomenon of Majorana flat bands and anomalous bulk-boundary correspondence in a two-band gapless $s$-wave topological superconductor. We analyze the equilibrium Josephson response of the system, showing how the presence of Majorana flat bands implies a substantial enhancement in the $4\pi$-periodic supercurrent.