Correlated Topological States in Graphene Nanoribbon Heterostructures

Deposition temperature-mediated growth of helically shaped polymers and chevron-type graphene nanoribbons from a fluorinated precursor

Graphene nanoribbons (GNRs) of precise size and shape, critical for controlling electronic properties and future device applications, can be realized via precision synthesis on surfaces using rationally designed molecular precursors. Fluorine-bearing precursors have the potential to form GNRs on nonmetallic substrates suitable for device fabrication. Here, we investigate the deposition temperature-mediated growth of a new fluorine-bearing precursor, 6,11-diiodo-1,4-bis(2-fluorophenyl)-2,3-diphenyltriphenylene (C42H24F2I2), into helically shaped polymer intermediates and chevron-type GNRs on Au(111) by combining scanning tunneling microscopy, X-ray photoelectron spectroscopy, and density functional theory simulations. The fluorinated precursors do not adsorb on the Au(111) surface at lower temperatures, necessitating an optimum substrate temperature to achieve maximum polymer and GNR lengths. We compare the adsorption behavior with that of pristine chevron precursors and discuss the effects of C-H and C-F bonds. The results elucidate the growth mechanism of GNRs with fluorine-bearing precursors and establish a foundation for future synthesis of GNRs on nonmetallic substrates.

Engineering Small HOMO-LUMO Gaps in Polycyclic Aromatic Hydrocarbons with Topologically Protected States

Topological phases in laterally confined low-dimensional nanographenes have emerged as versatile design tools that can imbue otherwise unremarkable materials with exotic band structures ranging from topological semiconductors and quantum dots to intrinsically metallic bands. The periodic boundary conditions that define the topology of a given lattice have thus far prevented the translation of this technology to the quasi-zero-dimensional (0D) domain of small molecular structures. Here, we describe the synthesis of a polycyclic aromatic hydrocarbon (PAH) featuring two localized zero modes (ZMs) formed by the topological junction interface between a trivial and nontrivial phase within a single molecule. First-principles density functional theory calculations predict a strong hybridization between adjacent ZMs that gives rise to an exceptionally small HOMO-LUMO gap. Scanning tunneling microscopy and spectroscopy corroborate the molecular structure of 9/7/9-double quantum dots and reveal an experimental quasiparticle gap of 0.16 eV, corresponding to a carbon-based small molecule long-wavelength infrared (LWIR) absorber.

Long-Range Effects in Topologically Defective Arm-Chair Graphene Nanoribbons

The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ=2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model.

Graphyne and graphdiyne nanoribbons: from their structures and properties to potential applications

Graphyne (GY) and graphdiyne (GDY) have properties including unique sp- and sp2-hybrid carbon atomic structures, natural non-zero band gaps, and highly conjugated π electrons. GY and GDY have good application prospects in many fields, including catalysis, solar cells, sensors, and modulators. Under the influence of the boundary effect and quantum size effect, quasi-one-dimensional graphyne nanoribbons (GYNRs) and graphdiyne nanoribbons (GDYNRs) show novel physical properties. The various structures available give GYNRs and GDYNRs greater band structure and electronic properties, and their excellent physical and chemical properties differ from those of two-dimensional GY and GDY. However, the development of GYNRs and GDYNRs still faces problems, including issues with accurate synthesis, advanced structural characterization, the structure-performance correlation of materials, and potential applications. In this review, the structures and physical properties of quasi-one-dimensional GYNRs and GDYNRs are reviewed, their advantages and disadvantages are summarized, and their potential applications are highlighted. This review provides a meaningful basis and research foundation for the design and development of high-performance materials and devices based on GYNRs and GDYNRs in the field of energy.

Thermal rectification through the topological states of asymmetrical length armchair graphene nanoribbons heterostructures with vacancies

We present a theoretical investigation of electron heat current in asymmetrical length armchair graphene nanoribbon (AGNR) heterostructures with vacancies, focusing on the topological states (TSs). In particular, we examine the 9-7-9 AGNR heterostructures where the TSs are well-isolated from the conduction and valence subbands. This isolation effectively mitigates thermal noise of subbands arising from temperature fluctuations during charge transport. Moreover, when the TSs exhibit an orbital off-set, intriguing electron heat rectification phenomena are observed, primarily attributed to inter-TS electron Coulomb interactions. To enhance the heat rectification ratio (ηQ), we manipulate the coupling strengths between the heat sources and the TSs by introducing asymmetrical lengths in the 9-AGNRs. This approach offers control over the rectification properties, enabling significant enhancements. Additionally, we introduce vacancies strategically positioned between the heat sources and the TSs to suppress phonon heat current. This arrangement effectively reduces the overall phonon heat current, while leaving the TSs unaffected. Our findings provide valuable insights into the behavior of electron heat current in AGNR heterostructures, highlighting the role of topological states, inter-TS electron Coulomb interactions, and the impact of structural modifications such as asymmetrical lengths and vacancy positioning. These results pave the way for the design and optimization of graphene-based devices with improved thermal management and efficient control of electron heat transport.

Relationship Between Stress Modulated Metallicity and Plasmon in Graphene Nanoribbons

Nanoscale quantum plasmon is an important technology that restricts the application of optics, electricity, and graphene photoelectric devices. Establishing a structure-effect relationship between the structure of graphene nanoribbons (GNRs) under stress regulation and the properties of plasmons is a key scientific issue for promoting the application of plasmons in micro-nano photoelectric devices. In this study, zigzag graphene nanoribbon (Z-GNR) and armchair graphene nanoribbon (A-GNR) models of specific widths were constructed, and density functional theory (DFT) was used to study their lattice structure, energy band, absorption spectrum, and plasmon effects under different stresses. The results showed that the Z-GNR band gap decreased with increasing stress, and the A-GNR band gap changed periodically with increasing stress. The plasmon effects of the A-GNRs and Z-GNRs appeared in the visible region, whereas the absorption spectrum showed a redshift trend, indicating the range of the plasmon spectrum also underwent significant changes. This study provides a theoretical basis for the application of graphene nanoribbons in the field of optoelectronics under strain-engineering conditions.

Effects of Coulomb Blockade on the Charge Transport through the Topological States of Finite Armchair Graphene Nanoribbons and Heterostructures

In this study, we investigate the charge transport properties of semiconducting armchair graphene nanoribbons (AGNRs) and heterostructures through their topological states (TSs), with a specific focus on the Coulomb blockade region. Our approach employs a two-site Hubbard model that takes into account both intra- and inter-site Coulomb interactions. Using this model, we calculate the electron thermoelectric coefficients and tunneling currents of serially coupled TSs (SCTSs). In the linear response regime, we analyze the electrical conductance (Ge), Seebeck coefficient (S), and electron thermal conductance (κe) of finite AGNRs. Our results reveal that at low temperatures, the Seebeck coefficient is more sensitive to many-body spectra than electrical conductance. Furthermore, we observe that the optimized S at high temperatures is less sensitive to electron Coulomb interactions than Ge and κe. In the nonlinear response regime, we observe a tunneling current with negative differential conductance through the SCTSs of finite AGNRs. This current is generated by electron inter-site Coulomb interactions rather than intra-site Coulomb interactions. Additionally, we observe current rectification behavior in asymmetrical junction systems of SCTSs of AGNRs. Notably, we also uncover the remarkable current rectification behavior of SCTSs of 9-7-9 AGNR heterostructure in the Pauli spin blockade configuration. Overall, our study provides valuable insights into the charge transport properties of TSs in finite AGNRs and heterostructures. We emphasize the importance of considering electron-electron interactions in understanding the behavior of these materials.

Carbon-based nanostructures as a versatile platform for tunableπ-magnetism

Emergence ofπ-magnetism in open-shell nanographenes has been theoretically predicted decades ago but their experimental characterization was elusive due to the strong chemical reactivity that makes their synthesis and stabilization difficult. In recent years, on-surface synthesis under vacuum conditions has provided unprecedented opportunities for atomically precise engineering of nanographenes, which in combination with scanning probe techniques have led to a substantial progress in our capabilities to realize localized electron spin states and to control electron spin interactions at the atomic scale. Here we review the essential concepts and the remarkable advances in the last few years, and outline the versatility of carbon-basedπ-magnetic materials as an interesting platform for applications in spintronics and quantum technologies.

Nanoconfined synthesis of conjugated ladder polymers

This review highlights recent advances in controlled synthesis of conjugated ladder polymers using templates.

Role Played by Edge-Defects in the Optical Properties of Armchair Graphene Nanoribbons

We explore the implementation of specific optical properties of armchair graphene nanoribbons (AGNRs) through edge-defect manipulation. This technique employs the tight-binding model in conjunction with the calculated absorption spectral function. Modification of the edge states gives rise to the diverse electronic structures with striking changes in the band gap and special flat bands at low energy. The optical-absorption spectra exhibit unique excitation peaks, and they strongly depend on the type and period of the edge extension. Remarkably, there exist the unusual transition channels associated with the flat bands for selected edge-modified systems. We discovered the special rule governing how the edge-defect influences the electronic and optical properties in AGNRs. Our theoretical prediction demonstrates an efficient way to manipulate the optical properties of AGNRs. This might be of importance in the search for suitable materials designed to have possible technology applications in nano-optical, plasmonic and optoelectronic devices.

Topological phase transition in chiral graphene nanoribbons: from edge bands to end states

Precise control over the size and shape of graphene nanostructures allows engineering spin-polarized edge and topological states, representing a novel source of non-conventional π-magnetism with promising applications in quantum spintronics. A prerequisite for their emergence is the existence of robust gapped phases, which are difficult to find in extended graphene systems. Here we show that semi-metallic chiral GNRs (chGNRs) narrowed down to nanometer widths undergo a topological phase transition. We fabricated atomically precise chGNRs of different chirality and size by on surface synthesis using predesigned molecular precursors. Combining scanning tunneling microscopy (STM) measurements and theory simulations, we follow the evolution of topological properties and bulk band gap depending on the width, length, and chirality of chGNRs. Our findings represent a new platform for producing topologically protected spin states and demonstrate the potential of connecting chiral edge and defect structure with band engineering.

Engineering plasmon modes and their loss in armchair graphene nanoribbons by selected edge-extended defects

The effect of edge modification of armchair graphene nanoribbons (AGNRs) on the collective excitations are theoretically investigated. The tight-binding method is employed in conjunction with the dielectric function. Unconventional plasmon modes and their association with the flat bands of the specially designed AGNRs are thoroughly studied. We demonstrate the robust relationship between the novel collective excitations and both the type and period of the edge modification. Additionally, we reveal that the main features displayed in the (momentum, frequency)-phase diagrams for both single-particle and collective excitations of AGNRs can be efficiently tuned by edge-extended defects. Our obtained plasmon modes are found to be analogous to magnetoplasmons associated with collective excitations of Landau-quantized electrons. This work provides a unique way to engineer discrete magnetoplasmon-like modes of AGNRs in the absence of magnetic field.

Atomically precise graphene nanoribbons: interplay of structural and electronic properties

Graphene nanoribbons hold great promise for future applications in nanoelectronic devices, as they may combine the excellent electronic properties of graphene with the opening of an electronic band gap - not present in graphene but required for transistor applications. With a two-step on-surface synthesis process, graphene nanoribbons can be fabricated with atomic precision, allowing precise control over width and edge structure. Meanwhile, a decade of research has resulted in a plethora of graphene nanoribbons having various structural and electronic properties. This article reviews not only the on-surface synthesis of atomically precise graphene nanoribbons but also how their electronic properties are ultimately linked to their structure. Current knowledge and considerations with respect to precursor design, which eventually determines the final (electronic) structure, are summarized. Special attention is dedicated to the electronic properties of graphene nanoribbons, also in dependence on their width and edge structure. It is exactly this possibility of precisely changing their properties by fine-tuning the precursor design - offering tunability over a wide range - which has generated this vast research interest, also in view of future applications. Thus, selected device prototypes are presented as well.

Charge localization and hopping in a topologically engineered graphene nanoribbon

Graphene nanoribbons (GNRs) are promising quasi-one-dimensional materials with various technological applications. Recently, methods that allowed for the control of GNR's topology have been developed, resulting in connected nanoribbons composed of two distinct armchair GNR families. Here, we employed an extended version of the Su-Schrieffer-Heeger model to study the morphological and electronic properties of these novel GNRs. Results demonstrated that charge injection leads to the formation of polarons that localize strictly in the 9-AGNRs segments of the system. Its mobility is highly impaired by the system's topology. The polaron displaces through hopping between 9-AGNR portions of the system, suggesting this mechanism for charge transport in this material.

Controlling the emission frequency of graphene nanoribbon emitters based on spatially excited topological boundary states

Graphene nanoribbons (GNRs) with atomically precise heterojunction interfaces are exploited as nanoscale light emitting devices with modulable emission frequencies. By connecting GNRs with different widths and lengths, topological boundary states can be formed and manipulated. Using first-principles-based atomistic simulations, we studied the luminescence properties of a STM GNR junction and explored the applications of these topological states as nanoscale light sources. Taking advantage of the ultrahigh resolution of the STM tip, direct injection of high energy carriers at selected boundary states can be achieved. In this way, the emission color can be controlled by precisely changing the tip position. The GNR heterojunction can therefore represent a robust and controllable light-emitting device that takes a step forward towards the fabrication of nanoscale graphene-based optoelectronic devices.