Search

In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irreducible. Specifically, we analyze the spectrum on left-invariant Cayley graphs endowed with an invariant metric, and we give some criteria for generically irreducible eigenspaces. Additionally, we introduce an operator that is comparable to the Laplacian and show that the same criterion holds., Comment: 18 pages, 2 figures; typos corrected

We report compact, scalable, high-performance, waveguide integrated graphene-based photodetectors (GPDs) for telecom and datacom applications, not affected by dark current. To exploit the photothermoelectric (PTE) effect, our devices rely on a graphene-polymer-graphene stack with static top split gates. The polymeric dielectric, poly(vinyl alcohol) (PVA), allows us to preserve graphene quality and to generate a controllable p-n junction. Both graphene layers are fabricated using aligned single-crystal graphene arrays grown by chemical vapor deposition. The use of PVA yields a low charge inhomogeneity 8 x 10$^{10}$ $cm^{-2}$ at the charge neutrality point, and a large Seebeck coefficient 140 ${\mu}$V K$^{-1}$, enhancing the PTE effect. Our devices are the fastest GPDs operating with zero dark current, showing a flat frequency response up to 67 GHz without roll-off. This performance is achieved on a passive, low-cost, photonic platform, and does not rely on nanoscale plasmonic structures. This, combined with scalability and ease of integration, makes our GPDs a promising building block for next-generation optical communication devices., Comment: 15 pages, 11 figures. Published under ACS AuthorChoice license

Actuation of thin polymeric films via electron irradiation is a promising avenue to realize devices based on strain engineered two dimensional (2D) materials. Complex strain profiles demand a deep understanding of the mechanics of the polymeric layer under electron irradiation; in this article we report a detailed investigation on electron-induced stress on poly-methyl-methacrylate (PMMA) thin film material. After an assessment of stress values using a method based on dielectric cantilevers, we directly investigate the lateral shrinkage of PMMA patterns on epitaxial graphene, which reveals a universal behavior, independent of the electron acceleration energy. By knowing the stress-strain curve, we finally estimate an effective Young's modulus of PMMA on top of graphene which is a relevant parameter for PMMA based electron-beam lithography and strain engineering applications.

The effect of turbulence on snow precipitation is not incorporated into present weather forecasting models. Here we show evidence that turbulence is in fact a key influence on both fall speed and spatial distribution of settling snow. We consider three snowfall events under vastly different levels of atmospheric turbulence. We characterize the size and morphology of the snow particles, and we simultaneously image their velocity, acceleration, and relative concentration over vertical planes about 30 m2 in area. We find that turbulence-driven settling enhancement explains otherwise contradictory trends between the particle size and velocity. The estimates of the Stokes number and the correlation between vertical velocity and local concentration indicate that the enhanced settling is rooted in the preferential sweeping mechanism. When the snow vertical velocity is large compared to the characteristic turbulence velocity, the crossing trajectories effect results in strong accelerations. When the conditions of preferential sweeping are met, the concentration field is highly non-uniform and clustering appears over a wide range of scales. These clusters, identified for the first time in a naturally occurring flow, display the signature features seen in canonical settings: power-law size distribution, fractal-like shape, vertical elongation, and large fall speed that increases with the cluster size. These findings demonstrate that the fundamental phenomenology of particle-laden turbulence can be leveraged towards a better predictive understanding of snow precipitation and ground snow accumulation. They also demonstrate how environmental flows can be used to investigate dispersed multiphase flows at Reynolds numbers not accessible in laboratory experiments or numerical simulations., Comment: 22 pages, 13 figures

We propose a mathematical model to measure how multiple repetitions may influence in the ultimate proportion of the population never hearing a rumor during a given outbreak. The model is a multi-dimensional continuous-time Markov chain that can be seen as a generalization of the Maki-Thompson model for the propagation of a rumor within a homogeneously mixing population. In the well-known basic model, the population is made up of "spreaders", "ignorants" and "stiflers", and any spreader attempts to transmit the rumor to the other individuals via directed contacts. In case the contacted individual is an ignorant, it becomes a spreader, while in the other two cases the initiating spreader turns into a stifler. The process in a finite population will eventually reach an equilibrium situation, where individuals are either stiflers or ignorants. We generalize the model by assuming that each ignorant becomes a spreader only after hearing the rumor a predetermined number of times. We identify and analyze a suitable limiting dynamical system of the model, and we prove limit theorems that characterize the ultimate proportion of individuals in the different classes of the population., Comment: Revised version accepted for publication at SIAM Journal on Applied Dynamical Systems

Rhombohedral-stacked few-layer graphene (FLG) has been receiving an ever-increasing attention owing to its peculiar electronic properties that could lead to enticing phenomena such as superconductivity and magnetic ordering. Up to now, experimental studies on such material have been mainly limited by the difficulty in isolating it in thickness exceeding 3 atomic layers with device-compatible size. In this work, rhombohedral graphene with thickness up to 9 layers and areas up to ~50 micrometers square is grown via chemical vapor deposition (CVD) on suspended Cu foils and transferred onto target substrates via etch-free delamination. The domains of rhombohedral FLG are identified by Raman spectroscopy and are found to alternate with domains of Bernal-stacked FLG within the same crystal in a stripe-like configuration. A combined analysis of micro-Raman mapping, atomic force microscopy and optical microscopy indicates that the formation of rhombohedral-stacked FLG is strongly correlated to the copper substrate morphology. Cu step bunching results in bending of FLG and interlayer displacement along preferential crystallographic orientations, as determined experimentally by electron microscopy, thus inducing the stripe-like domains. The growth and transfer of rhombohedral FLG with the reported thickness and size shall facilitate the observation of predicted unconventional physics and ultimately add to its technological relevance., Comment: 27 pages, 4 Figures, 9 Supplementary Figures

The challenge of next generation datacom and telecom communication is to increase the available bandwidth while reducing the size, cost and power consumption of photonic integrated circuits. Silicon (Si) photonics has emerged as a viable solution to reach these objectives. Graphene, a single-atom thick layer of carbon5, has been recently proposed to be integrated with Si photonics because of its very high mobility, fast carrier dynamics and ultra-broadband optical properties. Here, we focus on graphene photodetectors for high speed datacom and telecom applications. High speed graphene photodetectors have been demonstrated so far, however the most are based on the photo-bolometric (PB) or photo-conductive (PC) effect. These devices are characterized by large dark current, in the order of milli-Amperes , which is an impairment in photo-receivers design, Photo-thermo-electric (PTE) effect has been identified as an alternative phenomenon for light detection. The main advantages of PTE-based photodetectors are the optical power to voltage conversion, zero-bias operation and ultra-fast response. Graphene PTE-based photodetectors have been reported in literature, however high-speed optical signal detection has not been shown. Here, we report on an optimized graphene PTE-based photodetector with flat frequency response up to 65 GHz. Thanks to the optimized design we demonstrate a system test leading to direct detection of 105 Gbit s-1 non-return to zero (NRZ) and 120 Gbit s-1 4-level pulse amplitude modulation (PAM) optical signals

We introduce a new random walk with unbounded memory obtained as a mixture of the Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic Elephant Random Walk (DERW). As a consequence of this mixture the distribution of the increments of the resulting random process is time dependent. We prove a strong law of large numbers for the DERW and, in a particular case, we provide an explicit expression for its speed. Finally, we give sufficient conditions for the central limit theorem and the law of the iterated logarithm to hold., Comment: We corrected a typo in the definition of the ERW

Metamaterials have recently established a new paradigm for enhanced light absorption in state-of-the-art photodetectors. Here, we demonstrate broadband, highly efficient, polarization-insensitive, and gate-tunable photodetection at room temperature in a novel metadevice based on gold/graphene Sierpinski carpet plasmonic fractals. We observed an unprecedented internal quantum efficiency up to 100% from the near-infrared to the visible range with an upper bound of optical detectivity of $10^{11}$ Jones and a gain up to $10^{6}$, which is a fingerprint of multiple hot carriers photogenerated in graphene. Also, we show a 100-fold enhanced photodetection due to highly focused (up to a record factor of $|E/E_{0}|\approx20$ for graphene) electromagnetic fields induced by electrically tunable multimodal plasmons, spatially localized in self-similar fashion on the metasurface. Our findings give direct insight into the physical processes governing graphene plasmonic fractal metamaterials. The proposed structure represents a promising route for the realization of a broadband, compact, and active platform for future optoelectronic devices including multiband bio/chemical and light sensors., Comment: 10 pages, 6 figures

Producing and manipulating graphene on fab-compatible scale, while maintaining its remarkable carrier mobility, is key to finalize its technological application. We show that a large-scale approach (chemical vapor deposition on Cu followed by polymer-mediated semi-dry transfer) yields single-layer graphene crystals fully comparable, in terms of electronic transport, to micro-mechanically exfoliated flakes. hBN is used to encapsulate the graphene crystals $-$ without taking part to their detachment from the growth catalyst $-$ and study their intrinsic properties in field-effect devices. At room temperature, the electron-phonon coupling sets the mobility to $\sim1.3 \times10^5$ cm$^2$V$^{-1}$s$^{-1}$ at $\sim10^{11}$ cm$^{-2}$ concentration. At cryogenic temperatures, the mobility ($ > 6\times10^5$ cm$^2$V$^{-1}$s$^{-1}$ at $\sim10^{11}$ cm$^{-2}$) is limited by the devices' physical edges, and charge fluctuations $ < 7\times10^9$ cm$^{-2}$ are detected. Under perpendicular magnetic fields, we observe early onset of Landau quantization ($B\sim50$ mT) and signatures of electronic correlation, including the fractional quantum Hall effect., Comment: This is the unedited authors' version of the submitted article; 24 pages, 4 figures and supplementary information

We consider two interacting random walks on $\mathbb{Z}$ such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter $\beta \geq 0$. When $\beta = 0$ both processes are independent symmetric random walks on $\mathbb{Z}$, and hence recurrent. We show that both random walks are further recurrent if $\beta \in (0,1]$. We also show that these processes are transient and diverge in opposite directions if $\beta > 2$. The case $\beta \in (1,2]$ remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations., Comment: 17 pages. Added references and corrected typos. Revised the argument for the convergence to equilibria of the vector field. Improved the proof for the recurrence when beta belongs to (0,1); leading to the removal of a previous conjecture

Several works reported increased differentiation of neuronal cells grown on graphene; however, the molecular mechanism driving axon elongation on this material has remained elusive. Here, we study the axonal transport of nerve growth factor (NGF), the neurotrophin supporting development of peripheral neurons, as a key player in the time course of axonal elongation of dorsal root ganglion neurons on graphene. We find that graphene drastically reduces the number of retrogradely transported NGF vesicles in favor of a stalled population in the first two days of culture, in which the boost of axon elongation is observed. This correlates with a mutual charge redistribution, observed via Raman spectroscopy and electrophysiological recordings. Furthermore, ultrastructural analysis indicates a reduced microtubule distance and an elongated axonal topology. Thus, both electrophysiological and structural effects can account for graphene action on neuron development. Unraveling the molecular players underneath this interplay may open new avenues for axon regeneration applications.

We report on a C-band double layer graphene electro-absorption modulator on a passive SOI platform showing 29GHz 3dB-bandwith and NRZ eye-diagrams extinction ratios ranging from 1.7 dB at 10 Gb/s to 1.3 dB at 50 Gb/s. Such high modulation speed is achieved thanks to the quality of the CVD pre-patterned single crystal growth and transfer on wafer method that permitted the integration of high-quality scalable graphene and low contact resistance. By demonstrating this high-speed CVD graphene EAM modulator integrated on Si photonics and the scalable approach, we are confident that graphene can satisfy the main requirements to be a competitive technology for photonics.

The artificial stacking of atomically thin crystals suffers from intrinsic limitations in terms of control and reproducibility of the relative orientation of exfoliated flakes. This drawback is particularly severe when the properties of the system critically depend on the twist angle, as in the case of the dodecagonal quasicrystal formed by two graphene layers rotated by 30$^\circ$. Here we show that large-area 30$^\circ$-rotated bilayer graphene can be grown deterministically by chemical vapor deposition on Cu, eliminating the need of artificial assembly. The quasicrystals are easily transferred to arbitrary substrates and integrated in high-quality hBN-encapsulated heterostructures, which we process into dual-gated devices exhibiting carrier mobility up to $10^5$ cm$^2$/Vs. From low-temperature magnetotransport, we find that the graphene quasicrystals effectively behave as uncoupled graphene layers, showing 8-fold degenerate quantum Hall states: this result indicates that the Dirac cones replica detected by previous photo-emission experiments do not contribute to the electrical transport., Comment: This is the unedited authors' version of the submitted article, published in its final form on Nano Letters 2020 https://doi.org/10.1021/acs.nanolett.0c00172 , 21 pages, 3 figures and supporting information

The synthesis of transition metals in a two-dimensional (2D) fashion has attracted growing attention for both fundamental and application-oriented investigations, such as 2D magnetism, nanoplasmonics and non-linear optics. However, the large-area synthesis of this class of materials in a single-layer form poses non-trivial difficulties. Here we present the synthesis of a large-area 2D gold layer, stabilized in between silicon carbide and monolayer (ML) graphene. We show that the 2D-Au ML is a semiconductor with the valence band maximum 50 meV below the Fermi level. The graphene and gold layers are largely non-interacting, thereby defining a novel class of van der Waals heterostructure. The 2D-Au bands, exhibit a 225 meV spin-orbit splitting along the {\Gamma K} direction, making it appealing for spin-related applications. By tuning the amount of gold at the SiC/graphene interface, we induce a semiconductor to metal transition in the 2D-Au, which was never observed before and hosts great interest for fundamental physics.

Paper is the ideal substrate for the development of flexible and environmentally sustainable ubiquitous electronic systems, which, combined with two-dimensional materials, could be exploited in many Internet-of-Things applications, ranging from wearable electronics to smart packaging. Here we report high-performance MoS2 field-effect transistors on paper fabricated with a channel-array approach, combining the advantages of two large-area techniques: chemical vapor deposition and inkjet-printing.The first allows the pre-deposition of a pattern of MoS2; the second, the printing of dielectric layers, contacts, and connections to complete transistors and circuits fabrication. Average ION/IOFF of 8 x 10^3 (up to 5 x 10^4) and mobility of 5.5 cm2 V-1 s-1 (up to 26 cm2 V-1 s-1) are obtained. Fully functional integrated circuits of digital and analog building blocks, such as logic gates and current mirrors, are demonstrated, highlighting the potential of this approach for ubiquitous electronics on paper.

The combination of the exciting properties of graphene with those of monolayer tungsten disulfide (WS2) makes this heterostack of great interest for electronic, optoelectronic and spintronic applications. The scalable synthesis of graphene/WS2 heterostructures on technologically attractive substrates like SiO2 would greatly facilitate the implementation of novel two-dimensional (2D) devices. In this work, we report the direct growth of monolayer WS2 via chemical vapor deposition (CVD) on single-crystal graphene arrays on SiO2. Remarkably, spectroscopic and microscopic characterization reveals that WS2 grows only on top of the graphene crystals so that the vertical heterostack is selectively obtained in a bottom-up fashion. Spectroscopic characterization indicates that, after WS2 synthesis, graphene undergoes compressive strain and hole doping. Tailored experiments show that such hole doping is caused by the modification of the SiO2 stoichiometry at the graphene/SiO2 interface during the WS2 growth. Electrical transport measurements reveal that the heterostructure behaves like an electron-blocking layer at large positive gate voltage, which makes it a suitable candidate for the development of unipolar optoelectronic components., Comment: 30 pages, main text and supplementary information

The use of graphene-based electrodes is burgeoning in a wide range of applications, including solar cells, light emitting diodes, touch screens, field-effect transistors, photodetectors, sensors and energy storage systems. The success of such electrodes strongly depends on the implementation of effective production and processing methods for graphene. In this work, we take advantage of two different graphene production methods to design an advanced, conductive oxide- and platinum-free, graphene-based counter electrode for dye-sensitized solar cells (DSSCs). In particular, we exploit the combination of a graphene film, produced by chemical vapor deposition (CVD) (CVD-graphene), with few-layer graphene (FLG) flakes, produced by liquid phase exfoliation. The CVD-graphene is used as charge collector, while the FLG flakes, deposited atop by spray coating, act as catalyst for the reduction of the electrolyte redox couple (i.e., I3-/I-- and Co+2/+3). The as-produced counter electrodes are tested in both I3-/I-- and Co+2/+3-based semitransparent DSSCs, showing power conversion efficiencies of 2.1% and 5.09%, respectively, under 1 SUN illumination. At 0.1 SUN, Co+2/+3-based DSSCs achieve a power conversion efficiency as high as 6.87%. Our results demonstrate that the electrical, optical, chemical and catalytic properties of graphene-based dual films, designed by combining CVD-graphene and FLG flakes, are effective alternatives to FTO/Pt counter electrodes for DSSCs for both outdoor and indoor applications.

In this work we study asymptotic properties of a long range memory random walk known as elephant random walk. First we prove recurrence and positive recurrence for the elephant random walk. Then, we establish the transience regime of the model. Finally, under the Poisson Hypothesis, we study the replica mean field limit for this random walk and we obtain an upper bound for the expected distance of the walker from the origin.