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Graphene nanoribbons (GNRs) with atomically precise widths and edge topologies have well-defined band gaps that depend on ribbon dimensions, making them ideal for room-temperature switching applications like field-effect transistors (FETs). For efficient device integration, it is crucial to optimize growth conditions to maximize GNR length and, consequently, device yield. Here, we investigate the growth and alignment of 9-atom-wide armchair graphene nanoribbons (9-AGNRs) on a vicinal gold substrate, Au(788), with varying molecular precursor doses (PD) and, therefore, different resulting GNR coverages. Our investigation reveals that GNR growth location on the Au(788) substrate is coverage-dependent. Furthermore, scanning tunneling microscopy shows a strong correlation between the GNR length evolution and both the PD and the GNR growth location on the substrate. Employing Raman spectroscopy, we analyze samples with eight different PDs on Au(788). We find that GNR alignment improves with length, achieving near-perfect alignment with an average GNR length of ~40 nm for GNRs growing solely at Au(788) step edges. To fully exploit GNR properties in device architectures, GNRs need to be transferred from the gold to semiconducting or insulating substrates. Upon substrate transfer, samples with higher PD present systematically better alignment preservation and less surface disorder, which we attribute to reduced GNR mobility during the transfer process. PD also affects the substrate transfer success rate, with higher success rates observed for samples with higher GNR coverages (77%) compared to those with lower GNR coverages (53%). Our findings characterize the important relationship between precursor dose, GNR length, alignment quality, and surface disorder during GNR growth and upon substrate transfer, offering crucial insights for the further development of GNR-based nanoelectronic devices.

Atomically precise graphene nanoribbons (GNRs) are increasingly attracting interest due to their largely modifiable electronic properties, which can be tailored by controlling their width and edge structure during chemical synthesis. In recent years, the exploitation of GNR properties for electronic devices has focused on GNR integration into field-effect-transistor (FET) geometries. However, such FET devices have limited electrostatic tunability due to the presence of a single gate. Here, we report on the device integration of 9-atom wide armchair graphene nanoribbons (9-AGNRs) into a multi-gate FET geometry, consisting of an ultra-narrow finger gate and two side gates. We use high-resolution electron-beam lithography (EBL) for defining finger gates as narrow as 12 nm and combine them with graphene electrodes for contacting the GNRs. Low-temperature transport spectroscopy measurements reveal quantum dot (QD) behavior with rich Coulomb diamond patterns, suggesting that the GNRs form QDs that are connected both in series and in parallel. Moreover, we show that the additional gates enable differential tuning of the QDs in the nanojunction, providing the first step towards multi-gate control of GNR-based multi-dot systems.

Atomically precise graphene nanoribbons are a promising emerging class of designer quantum materials with electronic properties that are tunable by chemical design. However, many challenges remain in the device integration of these materials, especially regarding contacting strategies. We report on the device integration of uniaxially aligned and non-aligned 9-atom wide armchair graphene nanoribbons (9-AGNRs) in a field-effect transistor geometry using electron beam lithography-defined graphene electrodes. This approach yields controlled electrode geometries and enables higher fabrication throughput compared to previous approaches using an electrical breakdown technique. Thermal annealing is found to be a crucial step for successful device operation resulting in electronic transport characteristics showing a strong gate dependence. Raman spectroscopy confirms the integrity of the graphene electrodes after patterning and of the GNRs after device integration. Our results demonstrate the importance of the GNR-graphene electrode interface and pave the way for GNR device integration with structurally well-defined electrodes.

Mapping the thermal transport properties of materials at the nanoscale is of critical importance for optimizing heat conduction in nanoscale devices. Several methods to determine the thermal conductivity of materials have been developed, most of them yielding an average value across the sample, thereby disregarding the role of local variations. Here, we present a method for the spatially-resolved assessment of the thermal conductivity of suspended graphene by using a combination of confocal Raman thermometry and a finite-element calculations-based fitting procedure. We demonstrate the working principle of our method by extracting the two-dimensional thermal conductivity map of one pristine suspended single-layer graphene sheet and one irradiated using helium ions. Our method paves the way for spatially resolving the thermal conductivity of other types of layered materials. This is particularly relevant for the design and engineering of nanoscale thermal circuits (e.g. thermal diodes).

Unsupervised machine learning, and in particular data clustering, is a powerful approach for the analysis of datasets and identification of characteristic features occurring throughout a dataset. It is gaining popularity across scientific disciplines and is particularly useful for applications without a priori knowledge of the data structure. Here, we introduce an approach for unsupervised data classification of any dataset consisting of a series of univariate measurements. It is therefore ideally suited for a wide range of measurement types. We apply it to the field of nanoelectronics and spectroscopy to identify meaningful structures in data sets. We also provide guidelines for the estimation of the optimum number of clusters. In addition, we have performed an extensive benchmark of novel and existing machine learning approaches and observe significant performance differences. Careful selection of the feature space construction method and clustering algorithms for a specific measurement type can therefore greatly improve classification accuracies.

Graphene nanoribbons (GNRs) have attracted a strong interest from researchers worldwide, as they constitute an emerging class of quantum-designed materials. The major challenges towards their exploitation in electronic applications include reliable contacting, complicated by their small size ($<$50 nm), as well as the preservation of their physical properties upon device integration. In this combined experimental and theoretical study, we report on the quantum dot (QD) behavior of atomically precise GNRs integrated in a device geometry. The devices consist of a film of aligned 5-atoms wide GNRs (5-AGNRs) transferred onto graphene electrodes with a sub 5-nm nanogap. We demonstrate that the narrow-bandgap 5-AGNRs exhibit metal-like behavior resulting in linear IV curves for low bias voltages at room temperature and single-electron transistor behavior for temperatures below 150~K. By performing spectroscopy of the molecular levels at 13~K, we obtain addition energies in the range of 200-300 meV. DFT calculations predict comparable addition energies and reveal the presence of two electronic states within the bandgap of infinite ribbons when the finite length of the 5-AGNRs is accounted for. By demonstrating the preservation of the 5-AGNRs electronic properties upon device integration, as demonstrated by transport spectroscopy, our study provides a critical step forward in the realisation of more exotic GNR-based nano-electronic devices., Comment: 18 pages, 5 figures

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 active low-energy vibrational mode that is present in atomically precise, bottom-up synthesized armchair graphene nanoribbons (AGNRs). Our Raman study demonstrates that this mode is present in all families of AGNRs and provides information on their length. Our spectroscopic findings are corroborated by scanning tunneling microscopy images and supported by first-principles calculations that allow us to attribute this mode to a longitudinal acoustic phonon. Finally, we show that this mode is a sensitive probe for the overall structural integrity of the ribbons and their interaction with technologically relevant substrates., Comment: Unedited author's version

The on-surface synthesis of graphene nanoribbons (GNRs) allows for the fabrication of atomically precise narrow GNRs. Despite their exceptional properties which can be tuned by ribbon width and edge structure, significant challenges remain for GNR processing and characterization. In this contribution, we use Raman spectroscopy to characterize different types of GNRs on their growth substrate and to track their quality upon substrate transfer. We present a Raman-optimized (RO) device substrate and an optimized mapping approach that allows for acquisition of high-resolution Raman spectra, achieving enhancement factors as high as 120 with respect to signals measured on standard SiO2/Si substrates. We show that this approach is well-suited to routinely monitor the geometry-dependent low-frequency modes of GNRs. In particular, we track the radial breathing-like mode (RBLM) and the shear-like mode (SLM) for 5-, 7- and 9-atom wide armchair GNRs (AGNRs) and compare their frequencies with first-principles calculations., Comment: *contributed equally 190722 - corrected typos

The rational invariants of the SL_2(q)-invariant quadratic forms on the real irreducible representations are determined. There is still one open question (see Remark 6.5) if q is an even square.

We describe an algorithm, meant to be very general, to compute a presentation of the group of units of an order in a (semi)simple algebra over Q. Our method is based on a generalisation of Vorono\"i's algorithm for computing perfect forms, combined with Bass-Serre theory. It differs essentially from previously known methods to deal with such questions, e.g. for units in quaternion algebras. We illustrate this new algorithm by a series of examples where the computations are carried out completely.

We present an adaptation of Voronoi theory for imaginary quadratic number fields of class number greater than 1. This includes a characterisation of extreme Hermitian forms which is analogous to the classic characterisation of extreme quadratic forms as well as a version of Voronoi's famous algorithm which may be used to enumerate all perfect Hermitian forms for a given imaginary quadratic number field in dimensions 2 and 3. We also present an application of the algorithm which allows to determine generators of the general linear group of an $\O_K$-lattice.

Single molecule pulling experiments provide information about interactions in biomolecules that cannot be obtained by any other method. However, the reconstruction of the molecule's free energy profile from the experimental data is still a challenge, in particular for the unstable barrier regions. We propose a new method for obtaining the full profile by introducing a periodic ramp and using Jarzynski's identity for obtaining equilibrium quantities from non-equilibrium data. Our simulated experiments show that this method delivers significant more accurate data than previous methods, under the constraint of equal experimental effort., Comment: 4 pages, 3 figures