Properties in magnetic ordered states of graphene nanoribbons with zigzag shaped edges are investigated by applying mean-field approximation to the Hubbard model with on-site repulsion $U$. We observe that magnetic moments and critical temperature show anomalous power-law dependences as a function of $U$; the actual values of the power are determined by only the width of ribbons. Such singular behaviours are found to be due to localized nature of the electronic states close to Fermi energy.
Using the determinant quantum Monte-Carlo method, we elucidate the strain tuning of edge magnetism in zigzag graphene nanoribbons. Our intensive numerical results show that a relatively weak Coulomb interaction may induce a ferromagnetic-like behaviour with a proper strain, and the edge magnetism can be enhanced greatly as the strain along the zigzag edge increases, which provides another way to control graphene magnetism even at room temperature.
It have 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 by using two kinds of large-scale quantum Monte Carlo simulations. The anisotropy in zigzag honeycomb nanoribbons is characterized by the ratios of nearest-neighboring 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 $t_{2}/|t_{1}|$ increase from $1…
The topological phases of graphene with spin-orbit coupling, an exchange field, and a staggered-sublattice potential determine the properties of the edge states of the zigzag nanoribbon. In the presence of the Hubbard interaction, the spontaneous magnetization at the zigzag terminations induces sizable magnetic moments at the lattice sites in the bulk region. Thus, the exchange field and staggered-sublattice potential in the bulk region are effectively changed, which in turn change the topological phase. Within a certain parameter regime, quasi-stable excited states of the zigzag nanoribbon ex…
We present an analytical theory for the magnetic phase diagram for zigzag edge terminated honeycomb nanoribbons described by a Hubbard model with an interaction parameter U . We show that the edge magnetic moment varies as ln U and uncover its dependence on the width W of the ribbon. The physics of this owes its origin to the sensory organ like response of the nanoribbons, demonstrating that considerations beyond the usual Stoner-Landau theory are necessary to understand the magnetism of these systems. A first order magnetic transition from an anti-parallel orientation of the moments on opposi…
In contrast with carbon nanotubes, the absence of translational symmetry (or periodical boundary condition) in the restricted direction of zigzag graphene nanoribbon removes the selection rule of subband number conservation. However, zigzag graphene nanoribbons with even dimers do have the inversion symmetry. We, therefore, propose a selection rule of parity conservation for electron-phonon interactions. The electron-phonon scattering matrix in zigzag graphene nanoribbons is developed using the tight-binging model within the deformation potential approximation.
We theoretically examine the possible spin ordered states in zigzag graphene nanoribbon in a large supercell by the self-consistent mean field method as well as the first principle calculation. In addition to the well-known anti-ferromagnetic (AF) and ferromagnetic (FM) edge states, we find that there are also some excited spin density wave (ESDW) states, the energy of which are close to the AF edge state (ground state). We thus argue that these ESDW states may coexist in experiment when the temperature is not too low. Our numerical results indicate that the allowed ESDW are commensurate; and …
We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of …
The zigzag edge graphene nanoribbon, which is an antiferromagnetic insulator, is found from the density-function theory calculation to display a robust Dirac point after N and B doping at the zigzag edge. More interestingly, we found that the robust Dirac point is a common feature of the honeycomb structure nanoribbon with appropriate edge sites. The zigzag edge honeycomb nanoribbon is therefore expected to provide a very useful platform for material design and development.
Searching for room temperature ferromagnetic semiconductors has evolved into a broad field of material science and spintronics for decades, nevertheless, these novel states remain rare. Phosphorene, a monolayer black phosphorus with a puckered honeycomb lattice structure possessing a finite band gap and high carrier mobility, has been synthesized recently. Here we show, by means of two different large scale quantum Monte-Carlo methods, that relatively weak interactions can lead to remarkable edge magnetism in the phosphorene nanoribbons. The ground state constrained path quantum Monte-Carlo si…
This paper presents electronic spectra of zigzag and armchair graphene nanoribbons calculated within the tight-binding model for pi-electrons. Zigzag and armchair nanoribbons of different edge geometries are considered, with surface perturbation taken into account. The properties of surface states are discussed on the basis of their classification into Tamm states and Shockley states. In armchair nanoribbons surface states are shown to close the energy gap at the Dirac point for certain edge geometries.
We investigate the aspects of the electron transport in the zigzag graphene nanoribbons (ZGNRs) using the non-equilibrium Green's function (NEGF) formalism. The latter is an esoteric tool in mesoscopic physics and using this tool the analysis is performed by considering the potential well within the system. Within this potential well, the dependence of the transmission coefficient, local density of states (LDOS) and the electron transport properties on the number of atoms per unit cell is discussed. We observe that the electron and thermal conductance increases with the increase of the number …
Zigzag graphene nanoribbons can have magnetic ground states with ferromagnetic, antiferromagnetic, or canted configurations, depending on carrier density. We show that an electric field directed across the ribbon alters the magnetic state, favoring antiferromagnetic configurations. This property can be used to prepare ribbons with a prescribed spin-orientation on a given edge.
Zigzag nanoribbons of monolayer graphene-like two-dimensional materials host spontaneous edge magnetism at the zigzag terminations, whose configuration controls the band gap. In this article, the edge magnetism of zigzag nanoribbons of bilayer hexagonal crystals are studied. The specific models of bilayer graphene and bilayer silicene are both studied. As the gated voltage increases, the total energy level, magnetic structure and band structures of the ground state and the first quasi-stable excited state are tuned. For certain region of the gated voltage, the band gaps of spin up and down are…
We investigate the low-lying excitation spectrum and ground-state properties of narrow graphene nanoribbons with zigzag edge configurations. Nanoribbons of comparable widths have been synthesized very recently [P. Ruffieux, \emph{et al.} Nature \textbf{531}, 489 (2016)], and their descriptions require more sophisticated methods since in this regime conventional methods, like mean-field or density-functional theory with local density approximation, fail to capture the enhanced quantum fluctuations. Using the unbiased density-matrix renormalization group algorithm we calculate the charge gaps wi…
Based on ab-initio calculations we discuss Kondo effect due to Co adatom on graphene zigzag nanoribbon. Co atom located at hollow site behaves as spin S = 1/2 impurity with dxz and dyz orbitals contributing to magnetic moment. Dynamical correlations are analyzed with the use of complementary approximations: mean field slave boson approach, noncrossing approximation and equation of motion method. The impact of interplay between spin and orbital degrees of freedom together with the effect of peculiarities of electronic and magnetic structure of nanoribbon on many-body resonances is examined.
In the presence of the Hubbard interaction, graphene zigzag nanoribbons have spontaneous edge magnetism with anti-parallel configuration, whose amplitude can be tuned by a transversal electric field. As the electric field increases or decreases across a critical value, the edges are demagnetized or re-magnetized, respectively. A magnetic field at each edge determines the orientation of the re-magnetization. Thus, a combination of slowly varying transversal electric field and magnetic field in monolayer graphene zigzag nanoribbon could drive the quantum system into a bistability loop. The same …
Graphene nanoribbons with zigzag terminated edges have a magnetic ground state characterized by edge ferromagnetism and antiferromagnetic inter edge coupling. This broken symmetry state is degenerate in the spin orientation and we show that, associated with this degeneracy, the system has topological solitons. The solitons appear at the interface between degenerate ground states. These solitons are the relevant charge excitations in the system. When charge is added to the nanoribbon, the system energetically prefers to create magnetic domains and accommodate the extra electrons in the interfac…
An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g., the bulk-edge correspondence between the Zak phase and the existence of edge states, along with the presence of chiral boundary states, which are important for charge fractionalization. In polyacetylene, a fermion mass potential in the Dirac equation produces an excitation gap, and a twist in this scalar potential produces a zero-energy chiral so…
Using a tight binding model, we theoretically study the electronic properties of zigzag boron-carbon-nitride (BCN) nanoribbons where the outermost C atoms of zigzag graphene nanoribbons are replaced with B and N atoms. We show that the flat bands and edge states appear at the Fermi level when the number of B and N atoms are equal except the case of six times supercell. To investigate the origin of the edge states in BCN nanoribbons, we consider the semi-infinite graphene sheet with zigzag edge where outermost C atoms are replaced with B and N atoms. We analytically demonstrate the presence of …
We study spin-orbit torques and charge pumping in magnetic quasi-one dimensional zigzag nanoribbons with hexagonal lattice, in the presence of large intrinsic spin-orbit coupling. Such a system experiences topological phase transition from a trivial band insulator to a quantum spin Hall insulator either by tuning the magnetization direction or the intrinsic spin-orbit coupling. We find that spin-charge conversion efficiency (i.e. spin-orbit torque and charge pumping) is dramatically enhanced at the topological transition, displaying a substantial angular anisotropy.
Profiles of the spin and orbital angular momentum accumulations induced by a longitudinally applied electric field are explored in nanoribbons of $p$-band systems with a honeycomb lattice. We show that nanoribbons with zigzag borders can exhibit orbital magnetoelectric effects. More specifically, we have found that purely orbital magnetization oriented perpendicularly to the ribbon may be induced in these systems by means of the external electric field, when sublattice symmetry is broken. The effect is rather general and may occur in other multi-orbital materials.
In this article, we report band structure studies of zigzag graphene nanoribbons (ZGNRs) on introducing defects (sp_3 hybridized carbon atoms) in different concentrations at edges by varying the ratio of sp_3 to sp_2 hybridized carbon atoms. On the basis of theoretical analyses, band gap values of ZGNRs are found to be strongly dependent on relative arrangement of sp3 to sp2 hybridized carbon atoms at the edges for a defect concentration; so the findings would greatly help in understanding band gap of nanoribbons for their electronic applications.
Using full-band electron and phonon dispersion relation, we investigate the temperature dependence of Joule heating in Zigzag Graphene Nanoribbons under high-field. At different temperatures of 300 K, 600 K, and 900 K, the Joule heating always increases linearly with time or the power is a constant. Although the scattering rates at 900 K and 600 K are 113 and 55 times higher than that of 300 K, the Joule heating power of 900 K and 600 K are just 12.6 and 6.7 timers higher than that of 300 K.
We investigate transport properties of the junctions in which the graphene nanoribbon with the zigzag shaped edges consisting of the $N$ legs is sandwiched by the two normal metals by means of recursive Green's function method. The conductance and the transmission probabilities are found to have the remarkable properties depending on the parity of $N$. The singular behaviors close to E=0 with $E$ being the Fermi energy are demonstrated. The channel filtering is shown to occur in the case with $N=$ even.
An interesting property of zigzag graphene nanoribbons is the presence of edge states which are extended along its borders but localized in the transverse direction. We show that because of this property, electron transport through an externally induced potential well displays two-paths-interference oscillations when subject either to a magnetic or a transverse electric field. This effect does not require the existence of an actual `hole' in the nanoribbon's geometry. Moreover, since edge states are spin polarized, having opposite polarization on opposite sides, such interference effect can be…
The electronic and magnetic properties of zigzag graphene nanoribbons with asymmetric notches along their edges are investigated by first principle density functional theory calculations. It is found that the electronic and magnetic properties of the asymmetrically-notched graphene nanoribbons are closely related with the depth of notches, but weekly dependent on the length of notches. As the relative depth of notch increases, the energy level of spin-up and spin-down becomes greatly shifted, associated with the gradual increase of magnetic momentum. The asymmetric band shift allows the asymme…
The influence of carrier density on magnetism in a zigzag graphene nanoribbon is studied in a $π$-orbital Hubbard-model mean-field approximation. Departures from half-filling alter the magnetism, leading to states with charge density variation across the ribbon and parallel spin-alignment on opposite edges. Finite carrier densities cause the spin-density near the edges to decrease steadily, leading eventually to the absence of magnetism. At low doping densities the system shows a tendency to multiferroic order in which edge charges and spins are simultaneously polarized.
We investigate electron and phonon transport through edge disordered zigzag graphene nanoribbons based on the same methodological tool of nonequilibrium Green functions. We show that edge disorder dramatically reduces phonon thermal transport while being only weakly detrimental to electronic conduction. The behavior of the electronic and phononic elastic mean free paths points to the possibility of realizing an electron-crystal coexisting with a phonon-glass. The calculated thermoelectric figure of merit (ZT) values qualify zigzag graphene nanoribbons as a very promising material for thermoele…
The Dirac electrons of graphene, an intrinsic zero gap semiconductor, uniquely carry spin and pseudospin that give rise to many fascinating electronic and transport properties. While isolated zigzag graphene nanoribbons are antiferromagnetic semiconductors, we show by means of first-principles and tight-binding calculations that zigzag graphene nanoribbons supported on graphene are half-metallic as a result of spin- and pseudospin-symmetry breaking. In particular, half-metallic Dirac cones are formed at K (K') near the Fermi level. The present results demonstrate that the unique combination of…
We study the role of non-locality of exchange in a neutral zigzag graphene nanoribbon within the $π$-orbital unrestricted Hartree-Fock approximation. Within this theory we find that the magnetic features are further stabilized for both the intra-edge and inter-edge exchange compared to mean field theories of zigzag ribbon based on local exchange (like the Hubbard model or the ab-initio Local Density Approximation). The inter-edge exchange produces an enhancement of the band-gap of the magnetic ground-state solutions. The effect of this enhanced exchange on the edge states can not be satisfacto…
Using first principles pseudopotential density functional theory calculations, we find that terminating zigzag graphene nanoribbons (ZGNR) with monovalent alkali atoms at a reduced concentration has a dramatic impact on their properties. In particular, using sodium atoms for the saturation of ZGNR edges at half the concentration of edge-carbon atoms make it a one dimensional, perfect semimetal, where the valance and conduction bands meet at only a single, Dirac-like point. Unlike pristine graphene, the Dirac-"cones" of Na-ZGNR is not symmetric with respect to wave vector, but rather it is tilt…
Effects of electron-electron and spin-orbit interactions on the ground-state magnetic configuration and on the corresponding thermoelectric and spin thermoelectric properties in zigzag nanoribbons of two-dimensional hexagonal crystals are analyzed theoretically. Thermoelectric properties of quasi-stable magnetic states are also considered. Of particular interest is the influence of Coulomb and spin-orbit interactions on the topological edge states and on the transition between the topological insulator and conventional gap insulator states. It is shown that the interplay of both interactions h…
We investigate spin transport in diffusive graphene nanoribbons with both clean and rough zigzag edges, and long-range potential fluctuations. The long-range fields along the ribbon edges cause the local doping to come close to the charge neutrality point forming $p$-$n$ junctions with localized magnetic moments, similar to the predicted magnetic edge of clean zigzag graphene nanoribbons. The resulting random edge magnetization polarizes charge currents and causes sample-to-sample fluctuations of the spin currents obeying universal predictions. We show furthermore that, although the average sp…
We study electronic properties of graphene derivatives which have closed edges. They are finite-length graphene nanoribbons and graphene nanodisks. No metallic states are found in finite-length zigzag nanoribbons though all infinite-length zigzag nanoribbons are metallic. We also study hexagonal, parallelogrammic and trigonal nanodisks with zigzag or armchair edges. No metallic states are found in these nanodisks either except trigonal zigzag nanodisks. It is interesting that we can design the degeneracy of the metallic states arbitrarily in trigonal zigzag nanodisks by changing the size.
The electronic nonlinear transport through ultra narrow graphene nanoribbons (sub-$10nm$) is studied. A stable region of negative differential resistance (NDR) appears in the I-V characteristic curve of {\it odd} zigzag graphene nanoribbons (ZGNRs) in both positive and negative polarity. This NDR originates from a transport gap inducing by a selection rule which blocks electron transition between disconnecting energy bands of ZGNR. Based on this transition rule, on/off ratio of the current increases exponentially with the ribbon length up to $10^5$. In addition, charging effects and also spati…
We report on the possibility for a spin valve effect driven by edge defect engineering of zigzag graphene nanoribbons. Based on a mean-field spin unrestricted Hubbard model, electronic band structures and conductance profiles are derived, using a self-consistent scheme to include gate-induced charge density. The use of an external gate is found to trigger a semiconductor-metal transition in clean zigzag graphene nanoribbons, whereas it yields a closure of the spin-split bandgap in the presence of Klein edge defects. These features could be exploited to make novel charge and spin based switches…
Conductance fluctuations produced by the presence of disorder in zigzag and armchair graphene nanoribbons are studied. We show that quantum transport in zigzag nanoribbons takes place via edge states which are exponentially localized, as in the standard Anderson localization problem, whereas for armchair nanoribbons the symmetry of the graphene sublattices produces anomalous localization, or delocalization. We show that these two different electron localizations lead to significant differences of the conductance statistics between zigzag and armchair nanoribbons. In particular, armchair nanori…
We study the low energy spin excitations of zigzag graphene nanoribbons of varying width. We find their energy dispersion at small wave vector to be dominated by antiferromagnetic correlations between the ribbon's edges, in accrodance with previous calculations. We point out that spin wave lifetimes are very long due to the semi-conducting nature of the electrically neutral nanoribbons. However, application of very modest gate voltages cause a discontinuous transition to a regime of finite spin wave lifetime. By further increasing doping the ferromagnetic alignments along the edge become unsta…
We performed electronic structure calculations based on the first-principles many-body theory approach in order to study quasiparticle band gaps, and optical absorption spectra of hydrogen-passivated zigzag SiC nanoribbons. Self-energy corrections are included using the GW approximation, and excitonic effects are included using the Bethe-Salpeter equation. We have systematically studied nanoribbons that have widths between 0.6 $\text{nm}$ and 2.2 $\text{nm}$. Quasiparticle corrections widened the Kohn-Sham band gaps because of enhanced interaction effects, caused by reduced dimensionality. Zig…
We investigate the effects of randomly distributed atomic defects on the magnetic properties of graphene nanoribbons with zigzag edges using an extended mean-field Hubbard model. For a balanced defect distribution among the sublattices of the honeycomb lattice in the bulk region of the ribbon, the ground state antiferromagnetism of the edge states remains unaffected. By analyzing the excitation spectrum, we show that while the antiferromagnetic ground state is susceptible to single spin flip excitations from edge states to magnetic defect states at low defect concentrations, it's overall stabi…
The simple Hubbard Hamiltonian with the mean field approximation is used to know about the energy bands and spin susceptibilities of zigzag graphene nanoribbons. Depending on the electron doping, antiferromagnetic or ferromagnetic configurations are possible; in the former, an energy gap exits which is proportional to the Hubbard parameter, while in the latter the up and down spin bands intersect the Fermi level. Due to the two dimensional nature of the system, a susceptibility square matrix is necessary to explain the self-correlations and correlations between spins in the ribbon unit cell. T…
By combining Floquet theory with Green's function formalism, we present non-adiabatic quantum spin and charge pumping through a zigzag ferromagnetic graphene nanoribbon including a double-barriers structure driven weakly by two local $ac$ gate voltages operating with a phase-lag. Over a wide range of Fermi energies, interesting quantum pumping such as i) pure spin pumping with zero net charge pumping, ii) pure charge pumping and iii) fully spin polarized pumping can be achieved by tuning and manipulating driving frequency in the non-adiabatic regime. Spin polarized pumping which is measurable …
Thermoelectric properties of finite graphene nanoribbons (GNRs) coupled to metallic electrodes are theoretically studied in the framework of tight-binding model and Green's function approach. When the zigzag sides are coupled to the electrodes, the electron transport through the localized edge states can occur only if the channel length between electrodes is smaller than the decay length of these localized zigzag edge states. When the armchair edges are coupled to the electrodes, there is an interesting thermoelectric behavior associated with the mid-gap states when the GNR is in the semicondu…
Using a continuum Dirac theory, we study the density and spin response of zigzag edge terminated graphene ribbons subjected to edge potentials and Zeeman fields. Our analytical calculations of the density and spin responses of the closed system (fixed particle number) to the static edge fields, show a highly nonlinear Weber-Fechner type behavior where the response depends logarithmically on the edge potential. The dependence of the response on the size of the system (e.g. width of a nanoribbon) is also uncovered. Zigzag edge graphene nanoribbons, therefore, provide a realization of response of…
We study the conductivity of disordered zigzag graphene nanoribbons in the incoherent regime by using the Boltzmann equation approach. The band structure of zigzag nanoribbons contains two energy valleys, and each valley has an excess one-way channel. The crucial point is that the numbers of conducting channels for two propagating directions are imbalanced in each valley due to the presence of an excess one-way channel. It was pointed out that as a consequence of this imbalance, a perfectly conducting channel is stabilized in the coherent regime if intervalley scattering is absent. We show tha…
It is shown that apart from well-known factors, like temperature, substrate, and edge reconstruction effects, also the presence of external contacts is destructive for the formation of magnetic moments at the edges of graphene nanoribbons. The edge magnetism gradually decreases when graphene/electrode interfaces become more and more transparent for electrons. In addition to the graphene/electrode coupling strength, also the aspect ratio parameter, i.e. a width/length ratio of the graphene nanoribbon, is crucial for the suppression of edge magnetism. The present theory uses a tight-binding meth…
It is known that there is a wide class of quasi-two-dimensional graphenelike nanomaterials which in many respects can outperform graphene. So, here in addition to graphene, the attention is directed to stanene (buckled honeycomb structure) and phosphorene (puckered honeycomb structure). It is shown that, depending on the doping, these materials can have magnetically ordered edges. Computed diagrams of magnetic phases illustrate that, on the one hand, n-type doped narrow zigzag nanoribbons of graphene and stanene have antiferromagnetically aligned magnetic moments between the edges. On the othe…
Molybdenum disulfide nanoribbons with zigzag edges show ferromagnetic and metallic properties based on previous \emph{ab-initio} calculations. The investigation of the role of disorder on the magnetic properties is, however, still lacking due to the computational costs of these methods. In this work we fill this gap by studying the magnetic and electronic properties of several nanometer long MoS$_2$ zigzag nanoribbons using tight-binding and Hubbard Hamiltonians. Our results reveal that proper tight-binding parameters for the edge atoms are crucial to obtain quantitatively the metallic states …
Electronic properties of zigzag boron-carbon-nitride (BCN) nanoribbons, where the outermost C atoms on the edges of graphene nanoribbons are replaced by B or N atoms, are theoretically studied using the first-principles calculations. We show that BCN nanoribbons are metallic, since several bands cross the Fermi level. For BCN nanoribbons in a rich H$_2$ environment, the so-called nearly free electron state appears just above the Fermi level because of the intrinsic giant Stark effect due to the internal electric field of a transverse dipole moment. The position of the nearly free electron stat…
We study the influence of ripple waves originating from the electromechanical effects on spin relaxation caused by electromagnetic fields in armchair and zigzag graphene nanoribbons (GNRs). By utilizing analytical expressions supported by numerical simulations, we show that it is possible to tune the spin flip behaviors ON and OFF due to ripple waves in GNRs for potential applications in straintronic devices. This finding is similar to recently made observations on the design of spintronic devices in III-V semiconductor quantum dots, where the sign change in the effective Land$\mathrm{\acute{e…
Properties of bulk and boundaries of materials can, in general, be quite different, both for topological and non-topological reasons. One of the simplest boundary problems to pose is the tight-binding problem of noninteracting electrons on a finite honeycomb lattice. Despite its simplicity, the problem is quite rich and directly related to the physics of graphene. We revisit this long-studied problem and present an analytical derivation of the electron spectrum and wave functions for graphene rectangular derivatives. We provide an exact analytical description of extended and localized states, …
The influence of periodic edge vacancies and antidot arrays on the thermoelectric properties of zigzag graphene nanoribbons is investigated. Using the Green's function method, the tight-binding approximation for the electron Hamiltonian and the 4th nearest neighbor approximation for the phonon dynamical matrix, we calculate the Seebeck coefficient and the thermoelectric figure of merit. It is found that, at a certain periodic arrangement of vacancies on both edges of zigzag nanoribbon, a finite band gap opens and almost twofold degenerate energy levels appear. As a result, a marked increase in…
We study the interaction energy between two graphene nanoribbons by first principles calculations, including van der Waals interactions and spin polarization. For ultranarrow zigzag nanoribbons, the direct stacking is even more stable than Bernal, competing in energy for wider ribbons. This behavior is due to the magnetic interaction between edge states. We relate the reduction of the magnetization in zigzag nanoribbons with increasing ribbon width to the structural changes produced by the magnetic interaction, and show that when deposited on a substrate, zigzag bilayer ribbons remain magnetic…
We numerically compute the density of states (DOS) of interacting disordered zigzag graphene nanoribbon (ZGNR) having midgap states showing $e/2$ fractional edge charges. The computed Hartree-Fock DOS is linear at the critical disorder strength where the gap vanishes. This implies an $I\mbox{-}V$ curve of $I\propto V^2$. Thus, $I\mbox{-}V$ curve measurement may yield evidence of fractional charges in interacting disordered ZGNR. We show that even a weak disorder potential acts as a singular perturbation on zigzag edge electronic states, producing drastic changes in the energy spectrum. Spin-ch…
We provide a systematic quantitative description of spin polarization in armchair and zigzag graphene nanoribbons in a perpendicular magnetic field. We first address spinless electrons within the Hartree approximation studying the evolution of the magnetoband structure and formation of the compressible strips. We discuss the potential profile and the density distribution near the edges and the difference and similarities between armchair and zigzag edges. Accounting for the Zeeman interaction and describing the spin effects via the Hubbard term we study the spin-resolved subband structure and …
The nonequilibrium time-dependent fluctuations of charge current have recently emerged as a sensitive experimental tool to probe ballistic transport through evanescent wave functions introduced into clean wide and short graphene strips by the attached metallic electrodes. We demonstrate that such "pseudo-diffusive" shot noise can be substantially modified in zigzag graphene nanoribbon (ZGNR) due to the topology of its edges responsible for localized states that facilitate ferromagnetic ordering along the edge when Coulomb interaction is taken into account. Thus, the shot noise enhancement of u…
We have carried out an ab initio study of the structural, electronic and magnetic properties of zigzag graphene nanoribbons on Cu(111), Ag(111) and Au(111). Both, H-free and H-terminated nanoribbons are considered revealing that the nanoribbons invariably possess edge states when deposited on these surfaces. In spite of this, they do not exhibit a significant magnetization at the edge, with the exception of H-terminated nanoribbons on Au(111), whose zero-temperature magnetic properties are comparable to those of free-standing nanoribbons. These results are explained by the different hybridizat…
We unveil the nature of the structural disorder in bottom-up zigzag graphene nanoribbons along with its effect on the magnetism and electronic transport on the basis of scanning probe microscopies and first-principles calculations. We find that edge-missing m-xylene units emerging during the cyclodehydrogenation step of the on-surface synthesis are the most common point defects. These "bite'' defects act as spin-1 paramagnetic centers, severely disrupt the conductance spectrum around the band extrema, and give rise to spin-polarized charge transport. We further show that the electronic conduct…
