First-principles study on the structural and electronic properties of AlNCx nanosheet

The structural and electronic properties of a hydrogen terminated hexagonally AlN nanoribbon with 6 zigzag Al-N chains across the ribbon width (6-ZAlNNR) and the hexagonally bonded hetero-sheets AlNC_x (x=2,4,6) consisting of AlN and graphite strips with zigzag shaped borders have been investigated systemically by using the first-principles. The results show that in 6-ZAlNNR, the states of the lowest unoccupied conduction band (LUCB) and the highest occupied valence band (HOVB) at zone boundary Z are edge states whose charges are localized at edge Al and N atoms, respectively. Introducing the graphite strip C_x and increasing its width lead to the LUCB and HOVB getting closer with each other especially in flat dispersion region around the zone boundary J_y, thus decreasing in the energy gap of the hetero-sheets AlNC₂, AlNC₄ and AlNC₆ successively. Similar to the edge states existing in zigzag edged AlNNR, the flat dispersion border states also exist in the zigzag borders of hexagonally networked hetero-sheets AlNC_x. Unlike the edge states whose charges are localized at one of the edge atoms, the border states are localized at two atoms of the borders with either bonding or antibonding character.     

First-principles study on structural and electronic properties of AlNSix heterosheet

Under generalized gradient approximation (GGA), the structural and electronic properties of AlN and Si sheets, hydrogen terminated AlN and Si nanoribbons with hexagonal morphology and 2, 4, 6 zigzag chains across the ribbon width and the hexagonally bonded heterosheets AlNSi_x (x=2, 4, and 6) consisting of hexagonal networks of AlN (h-AlN) strips and silicene sheets with zigzag shaped borders have been investigated using the first-principles projector-augmented wave (PAW) formalism within the density function theory (DFT) framework. The AlN sheet is an indirect semiconductor with a band gap of 2.56 eV, while the Si sheet has a metallic character since the lowest unoccupied conduction band (LUCB) and the highest occupied valence band (HOVB) meet at one k point from Γ to Z. In the semiconductor 6-ZAlNNR, for example, the states of LUCB and HOVB at zone boundary Z are edge states whose charges are localized at edge Al and N atoms, respectively. In metallic 6-ZSiNR, a flat edge state is formed at the Fermi level E_F near the zone boundary Z because its charges are localized at edge Si atoms. The hybridizations between the edge states of h-AlN strips and silicene sheets result in the appearance of border states in the zigzag borders of heterosheets AlNSi_x whose charges are localized at two atoms of the borders with either bonding or antibonding π character.     

Tunable magnetism through edge functionalization in zigzag green phosphorene nanoribbons

Ab initio density-functional theory calculations with spin polarization are performed to explore magnetic properties in zigzag green phosphorene nanoribbons (ZGPNRs) with no passivation or edge-saturated by H, OH and O chemical species. It is found that antiferromagnetic order at intra-edges is the most energetically favorable for the pristine and oxygen passivated ribbons, while H- or OH-saturated ZGPNRs show nonmagnetic order. It indicates that edge states arising from the unsaturated bonds are vital for the formation of the magnetic moment in the ZGPNRs. The magnitude of the edge magnetism in the pristine and O-saturated ZGPNRs is comparable to that in zigzag black phosphorene nanoribbons. Electronic band structures, spin densities and spd-orbital projected density of states for the studied pristine and O-passivated ZGPNRs are further analyzed to study their electronic properties. The magnetic and electronic properties discovered in the ZGPNRs may suggest potential applications in future spintronics and electronics.     

Snake states along graphene p-n junctions

We investigate transport in locally gated graphene devices, where carriers are injected and collected along, rather than across, the gate edge. Tuning densities into the p-n regime significantly reduces resistance along the p-n interface, while resistance across the interface increases. This provides an experimental signature of snake states, which zigzag along the p-n interface and remain stable as applied perpendicular magnetic field approaches zero. Snake states appear as a peak in transverse resistance measured along the p-n interface. The generic role of snake states in disordered graphene is also discussed.     

Carbon nanoribbons and nanotubes based on δ-graphyne: A first-principles study

As a stable allotropy of two-dimensional (2D) carbon materials, δ-graphyne has been predicted to be superior to graphene in many aspects. Using first-principles calculations, we investigated the electronic properties of carbon nanoribbons (CNRs) and nanotubes (CNTs) formed by δ-graphyne. It is found that the electronic band structures of CNRs depend on the edge structure and the ribbon width. The CNRs with zigzag edges (Z-CNRs) have spin-polarized edge states with ferromagnetic (FM) ordering along each edge and anti-ferromagnetic (AFM) ordering between two edges. The CNRs with armchair edges (A-CNRs), however, are semiconductors with the band gap oscillating with the ribbon width. For the CNTs built by rolling up δ-graphyne with different chirality, the electronic properties are closely related to the chirality of the CNTs. Armchair (n, n) CNTs are metallic while zigzag (n, 0) CNTs are semiconducting or metallic. These interesting properties are quite crucial for applications in δ-graphyne-based nanoscale devices.     

Edge states and distributions of edge currents in semi-infinite graphene

The distributions of edge currents in semi-infinite graphene under a uniform perpendicular magnetic field are investigated. We show unambiguously that the edge current is finite at the armchair edge but vanishes at the zigzag edge. It is shown that the current density oscillates with the distance away from the boundary and tends to zero deep inside the graphene. The study shows that the total current is independent of edge configurations. The interplay of the bulk and edge contributions to the total current is presented. The quantized plateaus of Hall conductivity at (4e ²/h)(n+1/2) provide a direct evidence of the connection between the edge states and topological properties of relativistic fermions in a magnetic field.     

Relative stability of armchair,zigzag and reczag graphene edges on the Ru(0001) surface

The relative stability of armchair, zigzag, and the reconstructed zigzag (reczag) graphene edges was studied using density functional theory with the Perdew, Burke, and Ernzerhof (PBE) exchange correlation functional for graphene nanoribbons in vacuo and on the Ru(0001) surface. Although the reczag edge was found to be more stable in vacuo confirming previous predictions of Koskinen et al. [Phys. Rev. Lett. 101 (2008) 115502], the relative stability reverses upon adsorption on the Ru(0001) surface. The zigzag edge is more stable than the reczag edge on the surface by about 0.15 eV/Å and the armchair ribbon was found to be approximately isoenergetic with the zigzag ribbon. For all three types of edges, strong edge–Ru interactions are observed that cause the edges to buckle down. The lowered edge height may facilitate C attachments at graphene edges during graphene synthesis.     

Magnetic structure of graphite ribbon

Anoble mechanism of spin polarization is proposed for finite graphite sheet with edge. For graphite ribbon with zigzag edge, there appear peculiar ‘edge states’. These localized states comprise nearly flat band at the Fermi level, which easily causes magnetic instability. Magnetic structure is suggested from Hartree-Fock analysis of the Hubbard model, where huge magnetic moments are induced at around both of edges by weak HubbardU and are coupled antiferromagnetically with each other.     

First-principles calculations of magnetic edge states in zigzag CrI3 nanoribbons

CrI₃ monolayer has recently drawn much attention due to its two-dimensional long range ferromagnetic order. We find that CrI₃ nanoribbons, which are strips of CrI₃ monolayer, can be used as building blocks of nanodevices. In this paper, we studied the atomic and electronic structures of CrI₃ zigzag nanoribbons by using first-principles calculations. CrI₃ zigzag nanoribbons are also ferromagnet. Interestingly, edge states exist in the system and play an important role in their electronic structures. They dominate the band structures around Fermi level and can be tuned by edge atomic structures. The intrinsic ferromagnetism and rich electronic structures enable CrI₃ zigzag nanoribbons a group of promising candidate materials for spintronics.     

Energy gap modulation of graphene nanoribbons by F termination

Under the generalized gradient approximation (GGA), the electronic properties are studied for the F-terminated graphene nanoribbons (GNRs) with either zigzag edge (ZGNRs) or armchair edge (AGNRs) by using the first-principles projector augmented wave potential within the density function theory (DFT) framework. The results show that an edge state appears at the Fermi level E_F in the broader F-terminated ZGNRs, but does not appear in all the F-terminated AGNRs due to their dimerized C-C bonds at edge. The density of states (DOS) and projected DOS (PDOS) analyses show that the F-terminated ZGNRs are metallic and have a sharp peak at the Fermi level when the width is large enough. In contrast, the AGNRs are always semiconductors independent of their width. The charge density contours analyses shows that the C-F bond is an ionic bond due to a much stronger electronegativity of the F atom than that of the C atom. However, all kinds of the C-C bonds display a typical nonpolar covalent bonding feature.     

Symmetrical metallic and magnetic edge states of nanoribbon from semiconductive monolayer PtS2

Transition metal dichalcogenides (TMD) MoS₂ or graphene could be designed to metallic nanoribbons, which always have only one edge show metallic properties due to symmetric protection. In present work, a nanoribbon with two parallel metallic and magnetic edges was designed from a noble TMD PtS₂ by employing first-principles calculations based on density functional theory (DFT). Edge energy, bonding charge density, band structure, density of states (DOS) and simulated scanning tunneling microscopy (STM) of four possible edge states of monolayer semiconductive PtS₂ were systematically studied. Detailed calculations show that only Pt-terminated edge state among four edge states was relatively stable, metallic and magnetic. Those metallic and magnetic properties mainly contributed from 5d orbits of Pt atoms located at edges. What's more, two of those central symmetric edges coexist in one zigzag nanoribbon, which providing two atomic metallic wires thus may have promising application for the realization of quantum effects, such as Aharanov–Bohm effect and atomic power transmission lines in single nanoribbon.     

Hydrogen passivation tunes edge magnetism in the ZMoS2NR with a sulfur vacancy

We performed density functional theory study on electronic structure, magnetic properties and stability of zigzag MoS₂ nanoribbons with a S vacancy (ZMoS₂NRs-V_S) and considered their different edge passivation. The ZMoS₂NR-V_S systems are magnetic metals with ferromagnetic (FM) edge states. The magnetic moments are greatly influenced by the site of S vacancy and edge passivation because the vacancy and edge states significantly change the structure of the systems. Importantly, we can achieve distinct FM states such as both edge FM and single edge FM states in the ZMoS₂NRs-V_S by tuning edge passivated pattern. Additionally, edge passivation can not only tune the magnetism of the ZMoS₂NRs-V_S but also enhance their stability by eliminating dangling bonds. These interesting findings on the ZMoS₂NRs may open the possibility of their application in nanodevices and spintronics.     

Manipulating edge current spin polarization in zigzag MoS2 nanoribbons

The electronic structure and quantum transport of a zigzag monolayer molybdenum disulfide (MoS₂) nanoribbon are investigated using a six-band tight-binding model. For metallic edge modes, considering both an intrinsic spin–orbit coupling and local exchange field effects, spin degeneracy and spin inversion symmetry are broken and spin selective transport is possible. Our model is a three-terminal field effect transistor with a circular-shaped gate voltage in the middle of scattering region. One terminal measures the top edge current and the other measures the bottom edge current separately. By controlling the circular gate voltage, each terminal can detect a totally spin-polarized edge current. The radius of the circular gate and the strength of the exchange field are important, because the former determines the size of the channel in both S-terminated (top) and Mo-terminated (bottom) edges and the latter is strongly related to unbalancing of the density of spin states. The results presented here suggest that it should be possible to construct spin filters using implanted MoS₂ nanoribbons.     

Effect of interface roughness on the density of states of finite barrier height quantum wells

We calculate the density of states of a 2D electron gas in finite barrier height quantum wells with the explicit inclusion of the interface roughness effect. By using Feynman path-integral method, the analytic expression is derived. The results show that the 2D density of states is dependent on the RMS of the fluctuation potential. The interface roughness causes localized states below the subband edge. We also apply the theory to model the finite barrier height quantum wells in Al_xGa_1?xAs/GaAs.     

Comparison of Raman spectra and vibrational density of states between graphene nanoribbons with different edges

Vibrational properties of graphene nanoribbons are examined with density functional based tight-binding method and non-resonant bond polarization theory. We show that the recently discovered reconstructed zigzag edge can be identified from the emergence of high-energy vibrational mode due to strong triple bonds at the edges. This mode is visible also in the Raman spectrum. Total vibrational density of states of the reconstructed zigzag edge is observed to resemble the vibrational density of states of armchair, rather than zigzag, graphene nanoribbon. Edge-related vibrational states increase in energy which corroborates increased rigidity of the reconstructed zigzag edge.     

Magnetic and charge orders in zigzag nanographene ribbons

We theoretically study the electronic states in graphene ribbons which are strongly affected by the edge states, the peculiar non-bonding molecular orbitals localized along the zigzag edges of the ribbons. New kinds of edge localized electronic states with spin and charge polarizations are found in the mean field solutions of the extended Hubbard model with onsite and nearest-neighbor Coulomb repulsions. These novel states appear due to the interplay between the edge states and the Fermi instabilities. We also examine the competition between the charge polarized state and the spin polarized state to draw a phase diagram depending on Coulomb parameters. The results obtained by the mean field calculations with the extended Hubbard model modified to include Coulomb integrals provide useful insights to understand and functionalize the nanoscale materials.     

Charge fractionalization in biased bilayer graphene

Fractional charge may arise when fermionic zero modes exist in a topological background field. In biased bilayer graphene (BBLG), the bias plays the role of the nontrivial background field. When semi-infinite BBLG with a zigzag edge is used, the dynamics induces an odd number of zero-energy modes, which, together with the conjugation symmetry between positive-?and negative-energy states, are the requisite conditions for fractionalization. Exploiting the trigonal interaction to isolate a given zero-energy mode on the zigzag edge, we consider extended and localized modes (the latter being obtained from a localized wavepacket generated by prior irradiation of the sample with an electromagnetic vortex). The valley degeneracy is lifted by a layer asymmetry, while an edge-induced spin polarization breaks the spin degeneracy. We describe scenarios for the detection of charge-[Formula: see text] edge states.     

Acoustic analog of monolayer graphene and edge states

Acoustic analog of monolayer graphene has been designed by using silicone rubber spheres of honeycomb lattices embedded in water. The dispersion of the structure has been studied theoretically using the rigorous multiple-scattering method. The energy spectra with the Dirac point have been verified and zigzag edge states have been found in ribbons of the structure, which are analogous to the electronic ones in graphene nanoribbons. The guided modes along the zigzag edge excited by a point source have been numerically demonstrated. The open cavity and “Z” type edge waveguide with 60° corners have also been realized by using such edge states.     

Edge states and topological properties of electrons on the bismuth on silicon surface with giant spin-orbit coupling

We derive a model of localized edge states in a finite-width strip for the two-dimensional electron gas formed in the hybrid system of a bismuth monolayer deposited on the silicon interface and described by the nearly free electron model with giant spin-orbit splitting. The edge states have the energy dispersion in the bulk energy gap with a Dirac-like linear dependence on the quasimomentum and the spin polarization coupled to the direction of propagation, demonstrating the properties of a topological insulator. The topological stability of edge states is confirmed by the calculations of the Z ₂ invariant taken from the structure of the Pfaffian for the time reversal operator for the filled bulk bands in the surface Brillouin zone, which is shown to have a stable number of zeros with the variations of material parameters. The proposed properties of the edge states may support future advances in experimental and technological applications of this new material in nanoelectronics and spintronics.