We studied the Klein paradox in zigzag (ZNR) and anti-zigzag (AZNR) graphene nanoribbons. Due to the fact that ZNR (the number of lattice sites across the nanoribbon (N is even) and AZNR (N is odd) configurations are indistinguishable when treated by the Dirac equation, we supplemented the model with a pseudo-parity operator whose eigenvalues correctly depend on the sublattice wavefunctions for the number of carbon atoms across the ribbon, in agreement with the tight-binding model. We have shown that the Klein tunneling in zigzag nanoribbons is related to conservation of the pseudo-parity rather than pseudo-spin in infinite graphene. The perfect transmission in the case of head-on incidence is replaced by perfect transmission at the center of the ribbon and the chirality is interpreted as the projection of the pseudo-parity on momentum at different corners of the Brillouin zone.
A theory is developed for interband tunneling in semiconducting carbon nanotube and graphene nanoribbon p-n junction diodes. Characteristic length and energy scales that dictate the tunneling probabilities and currents are evaluated. By comparing the Zener tunneling processes in these structures to traditional group IV and III-V semiconductors, it is proved that for identical bandgaps, carbon based 1D structures have higher tunneling probabilities. The high tunneling current magnitudes for 1D carbon structures suggest the distinct feasibility of high-performance tunneling-based field-effect tr…
Tunneling field-effect transistors (FETs) have been intensely explored recently due to its potential to address power concerns in nanoelectronics. The recently discovered graphene nanoribbon (GNR) is ideal for tunneling FETs due to its symmetric bandstructure, light effective mass, and monolayer-thin body. In this work, we examine the device physics of p-i-n GNR tunneling FETs using atomistic quantum transport simulations. The important role of the edge bond relaxation in the device characteristics is identified. The device, however, has ambipolar I-V characteristics, which are not preferred f…
We investigate theoretically resonant tunneling through double-bended graphene nanoribbon structures, i.e., armchair-edged graphene nanoribbons (AGNRs) in between two semi-infinite zigzag graphene nanoribbon (ZGNR) leads. Our numerical results demonstrate that the resonant tunneling can be tuned dramatically by the Fermi energy and the length and/or widths of the AGNR for both the metallic and semiconductor-like AGNRs. The structure can also be use to control the valley polarization of the tunneling currents and could be useful for potential application in valleytronics devices.
Usually, graphene is used in its horizontal directions to design novel concept devices. Here, we report a single electron tunneling diode based on quantum tunneling through a vertical graphene two-barrier junction. The junction is formed by positioning a scanning tunnelling microscopy (STM) tip above a graphene nanoribbon that was deposited on a graphite surface. Because of the asymmetry of the two-barrier junction, the electrons can unidirectional transfer from the tip to the graphene nanoribbon but not from the graphene to the tip. This result opens intriguing opportunities for designing new…
Spin-dependent electronic transport properties of Fe-terminated zig-zag graphene nanoribbons (zGNR) have been studied using first-principles transport simulations. The spin configuration of proposed zGNR junction can be controlled with external magnetic field, and the tunneling junction show MR>1000 at small bias and is a perfect spin-filter by applying uniform external magnetic filed at small bias.
Metallic graphene nanoribbons (GNRs) represent a critical component in the toolbox of low-dimensional functional materials technolo-gy serving as 1D interconnects capable of both electronic and quantum information transport. The structural constraints imposed by on-surface bottom-up GNR synthesis protocols along with the limited control over orientation and sequence of asymmetric monomer building blocks during the radical step-growth polymerization has plagued the design and assembly of metallic GNRs. Here we report the regioregular synthesis of GNRs hosting robust metallic states by embedding…
The fabrication of atomically precise structures with designer electronic properties is one of the emerging topics in condensed matter physics. The required level of structural control can either be reached through atomic manipulation using the tip of a scanning tunneling microscope (STM) or by bottom-up chemical synthesis. In this review, we focus on recent progress in constructing novel, atomically precise artificial materials: artificial lattices built through atom manipulation and graphene nanoribbons (GNRs) realized by on-surface synthesis. We summarize the required theoretical background…
Graphene nanoribbons (GNRs) have attracted considerable interest as their atomically tunable structure makes them promising candidates for future electronic devices. However, obtaining detailed information about the length of GNRs has been challenging and typically relies on low-temperature scanning tunneling microscopy. Such methods are ill-suited for practical device application and characterization. In contrast, Raman spectroscopy is a sensitive method for the characterization of GNRs, in particular for investigating their width and structure. Here, we report on a length-dependent, Raman ac…
Results of quantum mechanical simulations of the influence of edge disorder on transport in graphene nanoribbon metal oxide semiconductor field-effect transistors (MOSFETs) are reported. The addition of edge disorder significantly reduces ON-state currents and increases OFF-state currents, and introduces wide variability across devices. These effects decrease as ribbon widths increase and as edges become smoother. However the bandgap decreases with increasing width, thereby increasing the band-to-band tunneling mediated subthreshold leakage current even with perfect nanoribbons. These results …
Stacking two-dimensional layered materials such as graphene and transitional metal dichalcogenides with nonzero interlayer twist angles has recently become attractive because of the emergence of novel physical properties. Stacking of one-dimensional nanomaterials offers the lateral stacking offset as an additional parameter for modulating the resulting material properties. Here, we report that the edge states of twisted bilayer zigzag graphene nanoribbons (TBZGNRs) can be tuned with both the twist angle and the stacking offset. Strong edge state variations in the stacking region are first reve…
By using analytical solution of a tight-binding model for armchair nanoribbons, it is confirmed that the solution represents the standing wave formed by intervalley scattering and that pseudospin is invariant under the scattering. The phase space of armchair nanoribbon which includes a single Dirac singularity is specified. By examining the effects of boundary perturbations on the wave function, we suggest that the existance of a strong boundary potential is inconsistent with the observation in a recent scanning tunneling microscopy. Some of the possible electron-density superstructure pattern…
We report on the on-surface synthesis of 7 armchair graphene nanoribbons (7-AGNRs) substituted with nitrile (CN) functional groups. The CN groups are attached to the GNR backbone by modifying the 7-AGNR precursor. While many of these groups survive the on-surface synthesis, the reaction process causes the cleavage of some CN from the ribbon backbone and the on-surface cycloisomerization of few nitriles onto pyridine rings. Scanning Tunneling Spectroscopy and Density Functional Theory reveal that CN groups behave as very efficient n-dopants, significantly downshifting the bands of the ribbon, a…
Excitonic emission from atomically precise graphene nanoribbons (GNRs) synthesised on a metal surface is probed with atomic-scale spatial resolution using a scanning tunneling microscopy (STM) approach. A STM-based strategy to transfer the GNRs to a partially insulating surface is used to prevent light emission quenching of the ribbons by the metal substrate. Sub-nanometer resolved STM-induced fluorescence spectra reveal emission from localized dark excitons build upon the topological end states of the GNRs. A low frequency vibronic emission comb whose characteristics change with the GNR lengt…
The challenge of synthesizing graphene nanoribbons (GNRs) with atomic precision is currently being pursued along a one-way road, based on the synthesis of adequate molecular precursors that react in predefined ways through self-assembly processes. The synthetic options for GNR generation would multiply by adding a new direction to this readily successful approach, especially if both of them can be combined. We show here how GNR synthesis can be guided by an adequately nanotemplated substrate instead of by the traditionally designed reactants. The structural atomic precision, unachievable to da…
We show that Clar's theory of the aromatic sextet is a simple and powerful tool to predict the stability, the π-electron distribution, the geometry, the electronic/magnetic structure of graphene nanoribbons with different hydrogen edge terminations. We use density functional theory to obtain the equilibrium atomic positions, simulated scanning tunneling microscopy (STM) images, edge energies, band gaps, and edge-induced strains of graphene ribbons that we analyze in terms of Clar formulas. Based on their Clar representation, we propose a classification scheme for graphene ribbons that groups c…
The impact of electrostatic doping level on the dissipative transport of Armchair GNR-TFET is studied using the Quantum Perturbation Theory (QPT) with the Extended Lowest Order Expansion (XLOE) implementation method. Results show that the doping level of the source and drain sides of the GNR-TFET has a significant impact on the phonon contribution to the carrier transport process. Unlike in other similar studies, where phonons are believed to have a constant detrimental influence on the ION/IOFF ratio and Subthreshold Swing (SS) of the TFET devices due to the phonon absorption-assisted tunneli…
We study the electronic structure of finite armchair graphene nanoribbons using density-functional theory and the Hubbard model, concentrating on the states localized at the zigzag termini. We show that the energy gaps between end-localized states are sensitive to doping, and that in doped systems, the gap between the end-localized states decreases exponentially as a function of the ribbon length. Doping also quenches the antiferromagnetic coupling between the end-localized states leading to a spin-split gap in neutral ribbons. By comparing dI/dV maps calculated using the many-body Hubbard mod…
We study the band gap of finite $N_A=7$ armchair graphene nanoribbons (7-AGNRs) on Au(111) through scanning tunneling microscopy/spectroscopy combined with density functional theory calculations. The band gap of 7-AGNRs with lengths of 6 nm and more is converged to within 0.1 eV of its bulk value of 2.3 eV, while the band gap opens by several hundred meV in very short 7-AGNRs. The termination has a significant effect on the band gap, doubly hydrogenated termini yielding a lower band gap than singly hydrogenated ones.
The wavefunction of a massless fermion consists of two chiralities, left-handed and right-handed, which are eigenstates of the chiral operator. The theory of weak interactions of elementally particle physics is not symmetric about the two chiralities, and such a symmetry breaking theory is referred to as a chiral gauge theory. The chiral gauge theory can be applied to the massless Dirac particles of graphene. In this paper we show within the framework of the chiral gauge theory for graphene that a topological soliton exists near the boundary of a graphene nanoribbon in the presence of a strain…
We report on the energy level alignment evolution of valence and conduction bands of armchair-oriented graphene nanoribbons (aGNR) as their band gap shrinks with increasing width. We use 4,4-dibromo-para-terphenyl as molecular precursor on Au(111) to form extended poly-para-phenylene nanowires, which can be fused sideways to form atomically precise aGNRs of varying widths. We measure the frontier bands by means of scanning tunneling spectroscopy, corroborating that the nanoribbons band gap is inversely proportional to their width. Interestingly, valence bands are found to show Fermi level pinn…
Here we present a flexible strategy to realize robust nanomaterials exhibiting valence electronic structures whose fundamental physics is described by the SSH-Hamiltonian. These solid-state materials are realized using atomically precise graphene nanoribbons (GNR). We demonstrate the controlled periodic coupling of topological boundary states at junctions of armchair GNRs of different widths to create quasi-1D trivial and non-trivial electronic quantum phases. Their topological class is experimentally determined by drawing upon the bulk-boundary correspondence and measuring the presence (non-t…
The design and fabrication of robust metallic states in graphene nanoribbons (GNRs) is a significant challenge since lateral quantum confinement and many-electron interactions tend to induce electronic band gaps when graphene is patterned at nanometer length scales. Recent developments in bottom-up synthesis have enabled the design and characterization of atomically-precise GNRs, but strategies for realizing GNR metallicity have been elusive. Here we demonstrate a general technique for inducing metallicity in GNRs by inserting a symmetric superlattice of zero-energy modes into otherwise semico…
The effects of lattice distortion and chemical disorder on charge transport properties of two-terminal zigzag phosphorene nanoribbons (zPNRs), which shows resonant tunneling behavior under an electrical applied bias, are studied. Our comprehensive study is based on an {\it ab~initio} quantum transport calculations on the basis of the Landauer theory. We use nitrogen and silicon substitutional dopant atoms, and employ different physical quantities such as $I-V$ curve, voltage drop behavior, transmission spectrum, transmission pathway, and atomic current, to explore the transport mechanism of zP…
The magnetoelectronic properties of quasi-one-dimensional zigzag graphene nanoribbons are investigated by using the Peierls tight-binding model. Quasi-Landau levels (QLLs), dispersionless Landau subbands within a certain region of k-space, are resulted from the competition between magnetic and quantum confinement effects. In bilayer system, the interlayer interactions lead to two groups of QLLs, one occurring at the Fermi level and the other one occurring at higher energies. Transverse electric fields are able to distort energy spectrum, tilt two groups of QLLs and cause semiconductor-metal tr…
Thanks to their highly tunable band gaps, graphene nanoribbons (GNRs) with atomically precise edges are emerging as mechanically and chemically robust candidates for nanoscale light emitting devices of modulable emission color. While their optical properties have been addressed theoretically in depth, only few experimental studies exist, limited to ensemble measurements and without any attempt to integrate them in an electronic-like circuit. Here we report on the electroluminescence of individual GNRs suspended between the tip of a scanning tunneling microscope (STM) and a Au(111) substrate, c…
Zigzag edges of graphene nanostructures host localized electronic states that are predicted to be spin-polarized. However, these edge states are highly susceptible to edge roughness and interaction with a supporting substrate, complicating the study of their intrinsic electronic and magnetic structure. Here, we focus on atomically precise graphene nanoribbons whose two short zigzag edges host exactly one localized electron each. Using the tip of a scanning tunneling microscope, the graphene nanoribbons are transferred from the metallic growth substrate onto insulating islands of NaCl in order …
Ferromagnetic Insulator to Metal Transition in Non-Centrosymmetric Graphene Nanoribbons
University of California, Berkeley（加州大学伯克利分校）；Kavli Energy NanoSciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory（加州大学伯克利分校卡弗里纳米科学能源研究所与劳伦斯伯克利国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Interfacial Coupling and Sparse Intercalation of 7-Atom-Wide Armchair Graphene Nanoribbons by N-Heterocyclic Carbene Monolayers
Empa - Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科学与技术研究院）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微观结构物理研究所）；Technische Universität Dresden（德累斯顿工业大学）；University of Chinese Academy of Science（中国科学院大学）
Spin-ordered electronic states in hydrogen-terminated zigzag nanographene give rise to magnetic quantum phenomena that have sparked renewed interest in carbon-based spintronics. Zigzag graphene nanoribbons (ZGNRs), quasi one-dimensional semiconducting strips of graphene featuring two parallel zigzag edges along the main axis of the ribbon, are predicted to host intrinsic electronic edge states that are ferromagnetically ordered along the edges of the ribbon and antiferromagnetically coupled across its width. Despite recent advances in the bottom-up synthesis of atomically-precise ZGNRs, their …
Guanine-quadruplex, consisting of several stacked guanine-quartets (GQs), has emerged as an important category of novel molecular targets with applications from nanoelectronic devices to anticancer drugs. Incorporation of metal cations into GQ structure is utilized to form stable G-quadruplexes, while no other passage has been reported yet. Here we report the room temperature (RT) molecular self-assembly of extensive metal-free GQ networks on Au(111) surface. Surface defect induced by an implanted molybdenum atom within Au(111) surface is used to nucleate and stabilize the cation-free GQ netwo…
The surface bound electronic states of three-dimensional topological insulators, as well as the edge states in two-dimensional topological insulators, are investigated in the presence of a circularly polarized light. The strong coupling between electrons and photons is found t o give rise to an energy gap as well as a unique energy dispersion of the dressed states, different from both graphene and conventional two-dimensional electron gas (2DEG). The effects of electron-photon interaction, barrier height and width on the electron tunneling through a p-n junction and on the ballistic conductanc…
Length-independent quantum transport through topological band states of graphene nanoribbons
Université de Strasbourg（斯特拉斯堡大学）；CNRS（法国国家科学研究中心）；Empa - Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科技与工程研究所）；Max Planck Institute for Polymer Research（马克斯·普朗克聚合物研究所）；Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学）；University of Bern（伯尔尼大学）；Donostia International Physics Center (DIPC) – UPV/EHU（圣塞巴斯蒂安国际物理中心（巴斯克国立大学））；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基克，巴斯克科学基金会）；Materials Genome Institute, Shanghai University（上海大学材料基因组研究院）；Department of Materials, University of Oxford（牛津大学材料系）
Multiproperty Atomistic Characterization of a Synthesized Pyrazinic Nitrogen-Doped Porous Armchair Graphene Nanoribbon
Laboratory of NanoEngineering, College of Technology, University of Brasília（巴西利亚大学技术学院纳米工程实验室）；Graduate Program in Physics, Institute of Physics, University of Brasília（巴西利亚大学物理研究所物理研究生项目）；Center for Agri-Food Science and Technology, Federal University of Campina Grande（坎皮纳格兰德联邦大学农业食品科学与技术中心）；Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学物理研究所）；Department of Applied Physics, Gleb Wataghin Institute of Physics, University of Campinas（坎皮纳斯大学格列布·瓦塔金物理研究所应用物理系）；Department of Electrical Engineering, College of Technology, University of Brasília（巴西利亚大学技术学院电气工程系）
Topological insulators (TIs) are an emerging class of materials that host highly robust in-gap surface/interface states while maintaining an insulating bulk. While most notable scientific advancements in this field have been focused on TIs and related topological crystalline insulators in 2D and 3D, more recent theoretical work has predicted the existence of 1D symmetry-protected topological phases in graphene nanoribbons (GNRs). The topological phase of these laterally-confined, semiconducting strips of graphene is determined by their width, edge shape, and the terminating unit cell, and is c…
Massless Dirac fermions in graphene provide unprecedented opportunities to realize the Klein paradox, which is one of the most exotic and striking properties of relativistic particles. In the seminal theoretical work [Katsnelson et al., Nat. Phys. 2 620 (2006)], it was predicted that the massless Dirac fermions can pass through one-dimensional (1D) potential barriers unimpededly at normal incidence. Such a result seems to preclude confinement of the massless Dirac fermions in graphene by using 1D potential barriers. Here, we demonstrate, both experimentally and theoretically, that massless Dir…
Atomic-scale imaging of graphene nanoribbons on graphene after polymer-free substrate transfer
Universidad de Granada（格拉纳达大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；Max Planck Institute for Polymer Research（马克斯·普朗克聚合物研究所）；University of Bern（伯尔尼大学）；Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学）
Synthesis of Metal-Semiconductor Heterojunctions in Single Graphene Nanoribbons
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Kavli Energy NanoSciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory（加州大学伯克利分校与劳伦斯伯克利国家实验室卡弗里能源纳米科学研究所）；Department of Chemistry, Columbia University（哥伦比亚大学化学系）；Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）；Department of Physics, Cornell University（康奈尔大学物理系）；Department of Materials Science and Nanoengineering, Rice University（莱斯大学材料科学与纳米工程系）
