Edge magnetization in Bernal-stacked trilayer zigzag graphene nanoribbons

We have used a tight-binding Hamiltonian of an ABA-stacked trilayer zigzag graphene nanoribbon with β-alignment edges to study the edge magnetizations. Our model includes the effect of the intralayer next-nearest-neighbor hopping, the interlayer hopping responsible for the trigonal warping and the interaction between electrons, which is considered by a single band Hubbard model in the mean field approximation. Firstly, in the neutral system we analyzed the two magnetic states in which both edge magnetizations reach their maximum value; the first one is characterized by an intralayer ferromagnetic coupling between the magnetizations at opposite edges, whereas in the second state that coupling is antiferromagnetic. The band structure, the location of the edge-state bands and the local density of states resolved in spin are calculated in order to understand the origins of the edge magnetizations. We have also introduced an electron doping so that the number of electrons in the ribbon unit cell is higher than in neutral case. As a consequence, we have obtained magnetization steps and charge accumulation at the edges of the sample, which are caused by the edge-state flat bands.     

The edge state of nanographene and the magnetism of the edge-state spins

Nanographene has unique edge-shape dependence of the electronic structure with non-bonding edge states being created in its zigzag edges. The presence of the edge state is experimentally confirmed in well-defined hydrogen-terminated zigzag edges by scanning tunneling microscopy/spectroscopy (STM/STS) observations. In the three-dimensional (3D) disordered network of nanographite domains in nanoporous carbon (activated carbon fibers), the localized edge-state spins are in a spin-glass-like ordered state at low temperatures with the aid of exchange interactions whose strengths varies randomly in space, when the strengths of inter-nanographene and nanographite interactions are tuned. Chemical and structural modifications of nanographene edges change the magnetism of edge-state spins through covalent bond formation and charge transfer.     

Magnetic potassium clusters in a nanographite host system

The magnetism and structure for potassium clusters physisorbed in nanographite-based nanoporous host are investigated. Potassium clusters are subjected to a slight charge transfer to a host nanographite and modify the magnetism of the edge-state spins of nanographite. The localized spins of 4s electrons in the potassium cluster interact with each other through a strong antiferromagnetic interaction. Finite size effect and structural disorder around the cluster surface are responsible for anomalous spin fluctuations in the magnetism.     

Magnetism of nanographene network influenced by the interaction with acid species

The magnetism of nanographite (stacked nanographene sheets)-based nanoporous carbon is investigated in relation to the interaction with acid guest species. The concentration of the localized spins of non-bonding π-electron state (edge state) localized in the nanographene edges decreases upon the sulfonation of nanographene edges through charge-transfer interaction with sulfonic groups. The sulfonation of nanographene edges enhances the hydrophilic nature of the edges, resulting in the easiness in the water adsorption into the nanopores. This enhances the mechanical compression effect of water molecules condensed in the nanopores on the nanographite domains, resulting in the decrease in the spin concentration. The change in the magnetism upon water uptake reveals ferrimagnetic nature of individual nanographene sheets. The adsorption of HCl having no oxidation ability shows a mechanical effect on the edge-state spins similar to water adsorption. The spin concentration is reduced in two-step manner by the charge-transfer interaction with guest concentrated HNO₃ that is strong oxidant. In the presence of H₂O molecules in diluted HNO₃ the cooperation of mechanical and charge-transfer interactions creates also a two-step change in the magnetism.     

Correlation effects in quantum spin-Hall insulators: a quantum Monte Carlo study

We consider the Kane-Mele model supplemented by a Hubbard U term. The phase diagram is mapped out using projective auxiliary field quantum Monte Carlo simulations. The quantum spin liquid of the Hubbard model is robust against weak spin-orbit interaction, and is not adiabatically connected to the spin-Hall insulating state. Beyond a critical value of U>U(c) both states are unstable toward magnetic ordering. In the quantum spin-Hall state we study the spin, charge, and single-particle dynamics of the helical Luttinger liquid by retaining the Hubbard interaction only on a ribbon edge. The Hubbard interaction greatly suppresses charge currents along the edge and promotes edge magnetism but leaves the single-particle signatures of the helical liquid intact.     

Circular photogalvanic effect caused by the transitions between edge and 2D states in a 2D topological insulator

The electron absorption and the edge photocurrent of a 2D topological insulator are studied for transitions between edge states to 2D states. The circular polarized light is found to produce the edge photocurrent, the direction of which is determined by light polarization and edge orientation. It is shown that the edge-state current is found to exceed the 2D current owing to the topological protection of the edge states.     

Persistent currents in a graphene ring with armchair edges

A graphene nanoribbon with armchair edges is known to have no edge state. However, if the nanoribbon is in the quantum spin Hall state, then there must be helical edge states. By folding a graphene ribbon into a ring and threading it by a magnetic flux, we study the persistent charge and spin currents in the tight-binding limit. It is found that, for a broad ribbon, the edge spin current approaches a finite value independent of the radius of the ring. For a narrow ribbon, inter-edge coupling between the edge states could open the Dirac gap and reduce the overall persistent currents. Furthermore, by enhancing the Rashba coupling, we find that the persistent spin current gradually reduces to zero at a critical value beyond which the graphene is no longer a quantum spin Hall insulator.     

Magnetic edge-state excitons in zigzag graphene nanoribbons

We present first-principles calculations of the optical properties of zigzag-edged graphene nanoribbons (ZGNRs) employing the GW-Bethe-Salpeter equation approach with the spin interaction included. Optical response of the ZGNRs is found to be dominated by magnetic edge-state-derived excitons with large binding energy. The absorption spectrum is composed of a characteristic series of exciton states, providing a possible signature for identifying the ZGNRs. The edge-state excitons are charge-transfer excitations with the excited electron and hole located on opposite edges; they moreover induce a spin transfer across the ribbon, resulting in a photoreduction of the magnetic ordering. These novel characteristics are potentially useful in the applications.     

Antiferromagnetic edge states in carbon nanotubes with hydrogen line defect abundancy

We have investigated the antiferromagnetic edge states in carbon nanotubes with hydrogen line defects by using the density functional theory calculations. As the hydrogen line defects increase, the exchange energy gain stabilizing the antiferromagnetic edge states increases in each graphenic ribbon produced by the line defects, indicating that the antiferromagnetic edge states can be realized at high temperatures regardless of the nanotube size. The exchange energy gain in each ribbon is determined by the ribbon width of the flat ribbon and apparently by the curvature of the curved ribbon. The exchange interaction between the ribbons is seen to be negligibly small even in the presence of a nonmagnetic inter-ribbon interaction that is sensitive to the ribbon width.     

Effects of electric and magnetic fields on electronic states and transport of a Hall bar

We study the edge-state band and transport property for a HgTe/CdTe quantum well Hall bar under the combined coupling of a transverse electric field and a perpendicular magnetic field. It is demonstrated that a weak magnetic field can protect one of the two edge states, open or enlarge a gap of the other edge state in the Hall bar. However, an appropriate electric field can remove the gap, restoring the quantum spin Hall effect. Using the scattering matrix method, we study the electronic transport of the system. We find that the electric field can not only make the switch from pure spin-up to spin-down current, but also open or close the edge-state channels in a narrow Hall bar under a weak magnetic field, which provides us with a new way to construct a topological insulator-based spin switch and charge switch.     

Edge currents in superconductors with a broken time-reversal symmetry

We analyze edge currents and edge bands at the surface of a time-reversal symmetry breaking dx2-y2 + id(xy) superconductor. We show that the currents have large Friedel oscillations with two interfering frequencies: square root of 2kF from subgap states, and 2kF from the continuum. The results are based independently on a self-consistent slave-boson mean-field theory for the t-J model on a triangular lattice, and on a T-matrix scattering theory calculation. The shape of the edge-state band, as well as the particular frequency square root of 2kF of the Friedel oscillations, are attributes unique for the dx2-y2 + id(xy) case, and may be used as a fingerprint for its identification. Extensions to different time-reversal symmetry breaking superconductors can be achieved within the same approach.     

Anisotropy Engineering Edge Magnetism in Zigzag Honeycomb Nanoribbons

It has been demonstrated that the zigzag honeycomb nanoribbons exhibit an intriguing edge magnetism. Here the effect of the anisotropy on the edge magnetism in zigzag honeycomb nanoribbons is investigated using two kinds of large-scale quantum Monte Carlo simulations. The anisotropy in zigzag honeycomb nanoribbons is characterized by the ratios of nearest-neighbor hopping integrals t_1 in one direction and t_2 in another direction. Considering the electron-electron correlation, it is shown that the edge ferromagnetism could be enhanced greatly as t_2/|t_1|increases from 1 to 3, which not only presents an avenue for the control of this magnetism but is also useful for exploring further novel magnetism in new nano-scale materials.     

Model Hamiltonian for the Quantum Anomalous Hall State in Iron-Halogenide

We examine quantum anomalous Hall(QAH) insulators with intrinsic magnetism displaying quantized Hall conductance at zero magnetic fields.The spin-momentum locking of the topological edge stats promises QAH insulators with great potential in device applications in the field of spintronics.Here,we generalize Haldane's model on the honeycomb lattice to a more realistic two-orbital case without the artificial real-space complex hopping.Instead,we introduce an intraorbital coupling,stemming directly from the local spin-orbit coupling(SOC).Our d_(xy)/d_(x~2-y~2) model may be viewed as a generalization of the bismuthene p_x/p_y-model for correlated d-orbitals.It promises a large SOC gap,featuring a high operating temperature.This two-orbital model nicely explains the low-energy excitation and the topology of two-dimensional ferromagnetic iron-halogenides.Furthermore,we find that electronic correlations can drive the QAH states to a c=0 phase,in which every band carries a nonzero Chern number.Our work not only provides a realistic QAH model,but also generalizes the nontrivial band topology to correlated orbitals,which demonstrates an exciting topological phase transition driven by Coulomb repulsions.Both the model and the material candidates provide excellent platforms for future study of the interplay between electronic correlations and nontrivial band topology.     

Spin polarized quantum pump effect in zigzag graphene nanoribbons

The spin polarized adiabatic quantum pump effect in zigzag graphene nanoribbons has been numerically analyzed. Since the ground state of such a ribbon is antiferromagnetic (the opposite spin electrons are located on the opposite edges of the ribbon), the spin currents can be generated in this system with the help of the quantum pump effect when symmetry between the opposite spin states is broken. Two methods of this breaking by means of defects at the ribbon edge and the transverse electric field have been proposed. It has been shown that the generation of not only the electron and spin currents, but also the purely spin current is possible in both cases.     

Localized electronic states on graphite edge

Examining the band structure of graphite ribbons with a typical edge shapes of armchair or zigzag, we find that minute graphite in a nanometer scale shows a striking contrast in the π electronic states depending on the edge shape. A wide armchair ribbon can reproduces the electronic state of graphite, but a zigzag ribbon shows a pair of partly flat bands which gives a remarkable peak of density of states at the Fermi level. We derive the analytic solution of this peculiar Edge State, disclosing the puzzle of its emergence.     

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.     

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.     

Decay and the double-decay properties of edge bands of phosphorene ribbons

Phosphorene (a monolayer of black phosphorus) recently spurred much attention due to its potential for application. We notice there are two types of zigzag edge and two types of armchair edge for phosphorene lattice. We study the winding number of various types of edge of phosphorene ribbons and conclude that, besides on the typical zigzag edge, the flat zero-energy edge band can be found in the ribbon of another nontypical armchair edge. The localization of these edge bands is investigated analytically. We find every single edge state of the atypical armchair edge decays to the bulk at two different decay rates.     

Coulomb-induced positive current-current correlations in normal conductors

In the white-noise limit current correlations measured at different contacts of a mesoscopic conductor are negative due to the antisymmetry of the wave function (Pauli principle). We show that current fluctuations at capacitive contacts induced via the long range Coulomb interaction due to charge fluctuations in the mesoscopic sample can be positively correlated. The positive correlations are a consequence of the extension of the wave functions into areas near both contacts. As an example we investigate in detail a quantum point contact in a high magnetic field under conditions in which transport is along an edge state.     

Plateau transitions in fractional quantum Hall liquids

Effects of backward scattering between fractional quantum Hall (FQH) edge modes are studied. Based on the edge-state picture for hierarchical FQH liquids, we discuss the possibility of the transitions between different plateaux of the tunneling conductance G. We find a selection rule for the sequence which begins with a conductance (m: integer, p: even integer) in units of e ²/h. The shot-noise spectrum as well as the scaling behavior of the tunneling current is calculated explicitly. Received 5 October 1999 and Received in final form 19 November 1999