Edge States In Graphene Nanoribbons Research Articles

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.

Erratum to “Floquet bands and photon-induced topological edge states of graphene nanoribbons”

Figures 2(a) and 2(b) in the original paper [Chin. Phys. B 30 066701 (2021)] are replaced by the new ones.

Floquet bands and photon-induced topological edge states of graphene nanoribbons* *Project supported by the starting foundation of Chongqing University (Grant No. 0233001104429), the National Natural Science Foundation of China (Grant No. 11847301), and the Fundamental Research Funds for the Central Universities, China (Grant No. 2020CQJQY-Z003).

Floquet theorem is widely used in the light-driven systems. But many 2D-materials models under the radiation are investigated with the high-frequency approximation, which may not be suitable for the practical experiment. In this work, we employ the non-perturbative Floquet method to strictly investigate the photo-induced topological phase transitions and edge states properties of graphene nanoribbons under the light irradiation of different frequencies (including both low and high frequencies). By analyzing the Floquet energy bands of ribbon and bulk graphene, we find the cause of the phase transitions and its relation with edge states. Besides, we also find the size effect of the graphene nanoribbon on the band gap and edge states in the presence of the light.

Observing photo-induced chiral edge states of graphene nanoribbons in pump-probe spectroscopies

Photo-induced edge states in low-dimensional materials have attracted considerable attention due to the tunability of topological properties and dispersion. Specifically, graphene nanoribbons have been predicted to host chiral edge modes upon irradiation with circularly polarized light. Here, we present numerical calculations of time-resolved angle resolved photoemission spectroscopy and trRIXS of a graphene nanoribbon. We characterize pump-probe spectroscopic signatures of photo-induced edge states, illustrate the origin of distinct spectral features that arise from Floquet topological edge modes, and investigate the roles of incoming photon energies and finite core–hole lifetime in RIXS. With momentum, energy, and time resolution, pump-probe spectroscopies can play an important role in understanding the behavior of photo-induced topological states of matter.

Engineering Edge States of Graphene Nanoribbons for Narrow-Band Photoluminescence.

Solid-state narrow-band light emitters are on-demand for quantum optoelectronics. Current approaches based on defect engineering in low-dimensional materials usually introduce a broad range of emission centers. Here, we report narrow-band light emission from covalent heterostructures fused to the edges of graphene nanoribbons (GNRs) by controllable on-surface reactions from molecular precursors. Two types of heterojunction (HJ) states are realized by sequentially synthesizing GNRs and graphene nanodots (GNDs) and then coupling them together. HJs between armchair GNDs and armchair edges of the GNR are coherent and give rise to narrow-band photoluminescence. In contrast, HJs between the armchair GNDs and the zigzag ends of GNRs are defective and give rise to nonradiative states near the Fermi level. At low temperatures, sharp photoluminescence emissions with peak energy range from 2.03 to 2.08 eV and line widths of 2-5 meV are observed. The radiative HJ states are uniform, and the optical transition energy is controlled by the band gaps of GNRs and GNDs. As these HJs can be synthesized in a large quantity with atomic precision, this finding highlights a route to programmable and deterministic creation of quantum light emitters.

Graphene Diamagnetism: Levitation, transport, rotation, and orientation alignment of graphene flakes in a magnetic field

Magnetic edge states of graphene nanoribbons have attracted much attention resulting from their potential applications in spintronics and quantum computing. Despite recent progress in graphene synthesis, the predicted ferromagnetic state has not been observed due to the challenge of the precise control of zigzag edge termination. In the meantime, more people have begun to recognize a different magnetic property, i.e., diamagnetism of graphene. Fundamentally, graphene diamagnetism arises from orbital or Landau magnetization of p electrons, and it is strongly related to the Dirac cone band structure and Fermi level.

Quantum Transport by Spin‐Polarized Edge States in Graphene Nanoribbons in the Quantum Spin Hall and Quantum Anomalous Hall Regimes

Using the non‐equilibrium Green's function method and the Keldysh formalism, we study the effects of spin–orbit interactions and time‐reversal symmetry breaking exchange fields on non‐equilibrium quantum transport in graphene armchair nanoribbons. We identify signatures of the quantum spin Hall (QSH) and the quantum anomalous Hall (QAH) phases in non‐equilibrium edge transport by calculating the spin‐resolved real space charge density and local currents at the nanoribbon edges. We find that the QSH phase, which is realized in a system with intrinsic spin–orbit coupling, is characterized by chiral counter‐propagating local spin currents summing up to a net charge flow with opposite spin polarization at the edges. In the QAH phase, emerging in the presence of Rashba spin–orbit coupling and a ferromagnetic exchange field, two chiral edge channels with opposite spins propagate in the same direction at each edge, generating an unpolarized charge current and a quantized Hall conductance G = 2e2/h. Increasing the intrinsic spin–orbit coupling causes a transition from the QAH to the QSH phase, evinced by characteristic changes in the non‐equilibrium edge transport. In contrast, an antiferromagnetic exchange field can coexist with a QSH phase, but can never induce a QAH phase due to a symmetry that combines time‐reversal and sublattice translational symmetry.

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

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 intra-edge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the inter-edge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intra-edge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intra-chain couplings. The results for the critical exponents are compared also to several recent renormalization group calculations for related long-ranged interacting quantum systems.

Effects of edge magnetism on the Kohn anomalies of zigzag graphene nanoribbons

The effects of edge magnetism on the Kohn anomaly (KA) of the G-band phonons of zigzag graphene nanoribbons (ZGNRs) are studied using a combination of the tight-binding and mean-field Hubbard models. We show that the opening of an energy gap, induced by magnetic ordering, significantly changes the KA effects, particularly for narrow ribbons in which the gap is larger than the phonon energy. Therefore, the G-band phonon frequency and lifetime are altered for a magnetically-ordered edge state with respect to an unpolarized edge state. The effects of temperature, ZGNR width, doping and transverse electric fields are systematically investigated. We propose using this effect to probe the magnetic order of edge states in graphene nanoribbons using Raman spectroscopy.

Structural and Electronic Properties of Zigzag Graphene Nanoribbons on Si(001) Substrates

We study the adsorption of zigzag graphene nanoribbons (GNRs) on Si(001) substrates using the first-principles density functional theory, exploring the effects of the interface interaction on the structural and electronic properties of both GNRs and the substrate. By comparing the adsorption structures predicted by the local density approximation, the generalized gradient approximation, and the DFT-D2 approach, we confirm that both edge and inner C atoms of GNRs can form covalent bonds with the substrate. The GNR/substrate interaction destroys the antiferromagnetic coupling of the edge states in GNRs. The charge transfer from the substrate to GNRs exhibits a complicated pattern and is mainly localized near the C–Si bonds. We also observe a strong perturbation of the surface states and a surface reconstruction transition induced by the GNR adsorption.

Lanczos transformation for quantum impurity problems ind-dimensional lattices: Application to graphene nanoribbons

We present a completely unbiased and controlled numerical method to solve quantum impurity problems in d-dimensional lattices. This approach is based on a canonical transformation, of the Lanczos form, where the complete lattice Hamiltonian is exactly mapped onto an equivalent one dimensional system, in the same spirit as Wilson's numerical renormalization. The method is particularly suited to study systems that are inhomogeneous, and/or have a boundary. As a proof of concept, we use the density matrix renormalization group to solve the equivalent one-dimensional problem. The resulting dimensional reduction translates into a reduction of the scaling of the entanglement entropy by a factor $L^{d-1}$, where L is the linear dimension of the original d-dimensional lattice. This allows one to calculate the ground state of a magnetic impurity attached to an LxL square lattice and an LxLxL cubic lattice with L up to 140 sites. We also study the localized edge states in graphene nanoribbons by attaching a magnetic impurity to the edge or the center of the system. For armchair metallic nanoribbons we find a slow decay of the spin correlations as a consequence of the delocalized metallic states. In the case of zigzag ribbons, the decay of the spin correlations depends on the position of the impurity. If the impurity is situated in the bulk of the ribbon, the decay is slow as in the metallic case. On the other hand, if the adatom is attached to the edge, the decay is fast, within few sites of the impurity, as a consequence of the localized edge states, and the short correlation length. The mapping can be combined with ab-initio band structure calculations to model the system, and to understand correlation effects in quantum impurity problems from first principles.

Edge-states in graphene nanoribbons: a combined spectroscopy and transport study

Graphene structures of finite size are expected to reveal exceptional electronic and magnetic properties which are highly attractive for future nano-technological applications. In this study we have looked at the edge-states in graphene nanoribbons (GNR) grown by self-assembly on mesa structured SiC(0001) templates. By means of a 4-tip STM/SEM system, both local spectroscopy and lateral transport have been performed in situ on the same nanostructures. The conductance in these structures was found to be e2/h for temperatures up to 400 K. Scanning tunneling spectroscopy clearly reveals edge-localized states on these ribbons. The local bonding of these ribbons to their support turns out to be essential in order to preserve the metallicity of the edge-states.

Ab Initio Study of the Edge States of Graphene Nanoribbons in the Presence of Electrodes

Thankstoitsoutstandingelectronicproperties, likeveryhighmobilityofcarriers, graphenehasemergedinrecentyearsasexcitingcandidateforuseinnewelectronicdevices. Whenitispatternedintheformofribbonswith widths in the range of nanometers, its transport properties become strongly influenced by the presence ofthestateslocalizedattheedgesoftheribbon. Usingfirstprinciplescalculationswestudythepropertiesofthesestates for both isolated ribbons and in the presence of metallic electrodes. The calculations were performed forend contacted geometry i.e. for graphene sheets at right angle to the electrodes. Both para- and ferromagneticelectrodeswereconsidered.PACSnumbers:73.20.At,73.40.Ns

Selection rule for the optical absorption of graphene nanoribbons

We demonstrate that the optical absorption of zigzag-edge graphene nanoribbons is qualitatively different from that of armchair nanotubes. Unlike the selection rule for nanotubes, when the incident beam is polarized along the longitudinal direction, the interband transitions at direct gaps are forbidden for graphene nanoribbons. This selection rule is due to the finite width of graphene nanoribbons. We also demonstrate that the edge states of graphene nanoribbons play an important role in the optical absorption. They are involved in many of the absorption peaks within optical range $(\ensuremath{\hbar}\ensuremath{\omega}l0.12\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.})$ and have no contribution to the absorption peaks beyond optical range.