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In the case of spherical varieties with reductive general isotropy group we prove a conjecture of G. Gagliardi and J. Hofscheier, which implies the generalized Mukai conjecture of L. Bonavero, C. Casagrande, O. Debarre and S. Druel for these varieties.

Atomically thin materials offer multiple opportunities for layer-by-layer control of their electronic properties. While monolayer graphene (MLG) is a zero-gap system, Bernal-stacked bilayer graphene (BLG) acquires a finite band gap when the symmetry between the layers' potential energy is broken, usually, via a displacement electric field applied in double-gate devices. Here, we introduce a twistronic stack comprising both MLG and BLG, synthesized via chemical vapor deposition, showing a Bernal gap in the absence of external fields. Although a large ($\sim30^{\circ}$) twist angle decouples the MLG and BLG electronic bands near Fermi level, proximity-induced energy shifts in the outermost layers result in a built-in asymmetry, which requires a displacement field of $0.14$ V/nm to be compensated. The latter corresponds to a $\sim10$ meV intrinsic BLG gap, a value confirmed by our thermal-activation measurements. The present results highlight the role of structural asymmetry and encapsulating environment, expanding the engineering toolbox for monolithically-grown graphene multilayers., Comment: 25 pages, 4 figures and supplementary information

The expanding solar wind plasma ubiquitously exhibits anisotropic non-thermal particle velocity distributions. Typically, proton Velocity Distribution Functions (VDFs) show the presence of a core and a field-aligned beam. Novel observations made by Parker Solar Probe (PSP) in the innermost heliosphere have revealed new complex features in the proton VDFs, namely anisotropic beams that sometimes experience perpendicular diffusion. In this study, we use a 2.5D fully kinetic simulation to investigate the stability of proton VDFs with anisotropic beams observed by PSP. Our setup consists of a core and an anisotropic beam populations that drift with respect to each other. This configuration triggers a proton-beam instability from which nearly parallel fast magnetosonic modes develop. Our results demonstrate that before this instability reaches saturation, the waves resonantly interact with the beam protons, causing perpendicular heating at the expense of the parallel temperature.

In this paper, we introduce and discuss an exactly energy-conserving Particle-in-Cell method for arbitrary curvilinear coordinates. The flexibility provided by curvilinear coordinates enables the study of plasmas in complex-shaped domains by aligning the grid to the given geometry, or by focusing grid resolution on regions of interest without overresolving the surrounding, potentially uninteresting domain. We have achieved this through the introduction of the metric tensor, the Jacobian matrix, and contravariant operators combined with an energy-conserving fully implicit solver. We demonstrate the method's capabilities using a Python implementation to study several one- and two-dimensional test cases: the electrostatic two-stream instability, the electromagnetic Weibel instability, and the geomagnetic environment modeling (GEM) reconnection challenge. The test results confirm the capability of our new method to reproduce theoretical expectations (e.g. instability growth rates) and the corresponding results obtained with a Cartesian uniform grid when using curvilinear grids. Simultaneously, we show that the method conserves energy to machine precision in all cases., Comment: 14 pages, 5 figures

Two-dimensional (2D) materials have received extensive research attentions over the past two decades due to their intriguing physical properties (such as the ultrahigh mobility and strong light-matter interaction at atomic thickness) and a broad range of potential applications (especially in the fields of electronics and optoelectronics). The growth of single-crystal 2D materials is the prerequisite to realize 2D-based high-performance applications. In this review, we aim to provide an in-depth analysis of the state-of-the-art technology for the growth and applications of 2D materials, with particular emphasis on single crystals. We first summarize the major growth strategies for monolayer 2D single crystals. Following that, we discuss the growth of multilayer single crystals, including the control of thickness, stacking sequence, and heterostructure composition. Then we highlight the exploration of 2D single crystals in electronic and optoelectronic devices. Finally, a perspective is given to outline the research opportunities and the remaining challenges in this field.

Graphene-hexagonal boron nitride (hBN) scalable heterostructures are pivotal for the development of graphene-based high-tech applications. In this work, we demonstrate the realization of high-quality graphene-hBN heterostructures entirely obtained with scalable approaches. hBN continuous films were grown via ion beam-assisted physical vapor deposition directly on commercially available $SiO_2/Si$ and used as receiving substrates for graphene single-crystal matrixes grown by chemical vapor deposition on copper. The structural, chemical, and electronic properties of the heterostructure were investigated by atomic force microscopy, Raman spectroscopy, and electrical transport measurements. We demonstrate graphene carrier mobilities exceeding $10,000 cm^2/Vs$ in ambient conditions, 30% higher than those directly measured on $SiO_{2}/Si$. We prove the scalability of our approach by measuring more than 100 transfer length method devices over a centimeter scale, which present an average carrier mobility of $7500 \pm 850 cm^{2}/Vs$. The reported high-quality all-scalable heterostructures are of relevance for the development of graphene-based high-performing electronic and optoelectronic applications.

The quantum Hall (QH) effect in two-dimensional electron systems (2DESs) is conventionally observed at liquid-helium temperatures, where lattice vibrations are strongly suppressed and bulk carrier scattering is dominated by disorder. However, due to large Landau level (LL) separation (~2000 K at B = 30 T), graphene can support the QH effect up to room temperature (RT), concomitant with a non-negligible population of acoustic phonons with a wave-vector commensurate to the inverse electronic magnetic length. Here, we demonstrate that graphene encapsulated in hexagonal boron nitride (hBN) realizes a novel transport regime, where dissipation in the QH phase is governed predominantly by electron-phonon scattering. Investigating thermally-activated transport at filling factor 2 up to RT in an ensemble of back-gated devices, we show that the high B-field behaviour correlates with their zero B-field transport mobility. By this means, we extend the well-accepted notion of phonon-limited resistivity in ultra-clean graphene to a hitherto unexplored high-field realm., Comment: 17 pages, 4 figures. Supplementary information available at https://doi.org/10.1038/s41467-023-35986-3

To realize the applicative potential of 2D twistronic devices, scalable synthesis and assembly techniques need to meet stringent requirements in terms of interface cleanness and twist-angle homogeneity. Here, we show that small-angle twisted bilayer graphene assembled from separated CVD-grown graphene single-crystals can ensure high-quality transport properties, determined by a device-scale-uniform moire\'e potential. Via low-temperature dual-gated magnetotransport, we demonstrate the hallmarks of a $2.4^\circ$ -twisted superlattice, including tunable regimes of interlayer coupling, reduced Fermi velocity, large interlayer capacitance, and density-independent Brown-Zak oscillations. The observation of these moir\'e-induced electrical transport features establishes CVD-based twisted bilayer graphene as an alternative to 'tear-and-stack' exfoliated flakes for fundamental studies, while serving as a proof-of-concept for future large-scale assembly., Comment: This is the unedited authors' version of the submitted article, published in its final form on Nano Letters 2022 at https://pubs.acs.org/doi/full/10.1021/acs.nanolett.2c01114 , main text, 17 pages, 4 figures

Recently hBN has become an interesting platform for quantum optics due to the peculiar defect-related luminescence properties. Concomitantly, hBN was established as the ideal insulating support for realizing 2D materials device, where, on the contrary, defects can affect the device performance. In this work, we study the light emission properties of hBN flakes obtained by mechanical exfoliation with particular focus on extended defects generated in the process. In particular, we tackle different issues as the light emission in hBN flakes of different thicknesses in the range of hundreds of nm, revealing a higher concentration of deep level emission in thinner area of the flake. We recognize the effect of crystal deformation in some areas of the flake with an important blue-shift (130 meV) of the room temperature near band edge emission of hBN and the concurrent presence of a novel emission at 2.36 eV related to the formation of array of dislocations. We studied the light emission properties by means of cathodoluminescence and sub-bandgap excitation photoluminescence of thickness steps with different crystallographic orientations, revealing the presence of different concentration of radiative centers. CL mapping allows to detect buried thickness steps, invisible to the SEM and AFM morphological analysis., Comment: 27 pages, 6 figures, 1 table

We employ dual-gated 30{\deg}-twisted bilayer graphene to demonstrate simultaneous ultra-high mobility and conductivity (up to 40 mS at room temperature), unattainable in a single-layer of graphene. We find quantitative agreement with a simple phenomenology of parallel conduction between two pristine graphene sheets, with a gate-controlled carrier distribution. Based on the parallel transport mechanism, we then introduce a method for in situ measurements of the chemical potential of the two layers. This twist-enabled approach, neither requiring a dielectric spacer, nor separate contacting, has the potential to greatly simplify the measurement of thermodynamic quantities in graphene-based systems of high current interest., Comment: This is the unedited authors' version of the submitted article, published in Phys. Rev. B 104, L241410 (2021), 23 pages, main text and supplementary information

Graphene and related materials can lead to disruptive advances in next generation photonics and optoelectronics. The challenge is to devise growth, transfer and fabrication protocols providing high (>5,000 cm2 V-1 s-1) mobility devices with reliable performance at the wafer scale. Here, we present a flow for the integration of graphene in photonics circuits. This relies on chemical vapour deposition (CVD) of single layer graphene (SLG) matrices comprising up to ~12000 individual single crystals (SCs), grown to match the geometrical configuration of the devices in the photonic circuit. This is followed by a transfer approach which guarantees coverage over ~80% of the device area, and integrity for up to 150 mm wafers, with room temperature mobility ~5000 cm2 V-1 s-1. We use this process flow to demonstrate double SLG electro-absorption modulators with modulation efficiency ~0.25, 0.45, 0.75, 1 dB V-1 for device lengths ~30, 60, 90, 120 {\mu}m. The data rate is up to 20 Gbps. Encapsulation with single-layer hBN is used to protected SLG during plasma-enhanced CVD of Si3N4, ensuring reproducible device performance. Our full process flow (from growth to device fabrication) enables the commercial implementation of graphene-based photonic devices., Comment: 30 pages, 9 Figures

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

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

Given a connected simply connected semisimple group G and a connected spherical subgroup K we determine the generators of the extended weight monoid of G/K, based on the homogeneous spherical datum of G/K. Let H be a reductive subgroup of G and let P be a parabolic subgroup of H for which G/P is spherical. A triple (G,H,P) with this property is called multiplicity free system and we determine the generators of the extended weight monoid of G/P explicitly in the cases where (G,H) is strictly indecomposable. The extended weight monoid of G/P describes the induction from H to G of an irreducible H-representation V whose lowest weight is a character of P. The space of regular End(V)-valued functions on G that satisfy F(hgk)=hF(g)k for all h,k in H and all g in G, is a module over the algebra of H-biinvariant regular functions on G. We show that under a mild assumption this module is freely and finitely generated. As a consequence the spherical functions of such a type V can be described as a family of matrix-valued orthogonal polynomials., Comment: v1: 65 pages, 1 figure; v2: minor corrections, computations of extended weight monoids moved to appendices, 67 pages, 1 figure

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 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.

Unambiguous and complete determination of the Fermi surface is a primary step in understanding the electronic properties of topical metals and semi-metals, but only in a relatively few cases has this goal been realized. In this work, we present a systematic high-field quantum oscillation study up to 35 T on ZrSiS, a textbook example of a nodal-line semimetal with only linearly dispersive bands crossing the Fermi energy. The topology of the Fermi surface is determined with unprecedented precision and all pockets are identified by comparing the measured angle dependence of the quantum oscillations to density functional theory calculations. Comparison of the Shubnikov-de Haas and de Haas-van Alphen oscillations at low temperatures and analysis of the respective Dingle plots reveal the presence of significantly enhanced scattering on the electron pocket. Above a threshold field that is aligned along the c-axis of the crystal, the specific cage-like Fermi surface of ZrSiS allows for electron-hole tunneling to occur across finite gaps in momentum space leading to quantum oscillations with a complex frequency spectrum. Additional high-frequency quantum oscillations signify magnetic breakdown orbits that encircle the entire Dirac nodal loop. We suggest that the persistence of quantum oscillations in the resistivity to high temperatures is caused by Stark interference between orbits of nearly equal masses., Comment: 14 pages, 13 figures

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 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

We report on high-field magnetotransport (B up to 35 T) on a gated superlattice based on single-layer graphene aligned on top of hexagonal boron nitride. The large-period moir\'e modulation (15 nm) enables us to access the Hofstadter spectrum in the vicinity of and above one flux quantum per superlattice unit cell (Phi/Phi_0 = 1 at B = 22 T). We thereby reveal, in addition to the spin-valley antiferromagnet at nu = 0, two insulating states developing in positive and negative effective magnetic fields from the main nu = 1 and nu = -2 quantum Hall states respectively. We investigate the field dependence of the energy gaps associated with these insulating states, which we quantify from the temperature-activated peak resistance. Referring to a simple model of local Landau quantization of third generation Dirac fermions arising at Phi/Phi_0 = 1, we describe the different microscopic origins of the insulating states and experimentally determine the energy-momentum dispersion of the emergent gapped Dirac quasi-particles.

We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This enables us to derive a classification of these varieties, without specifying the open orbit, as well as a classification of all Fano spherical varieties. In the setting of multiplicity free compact and connected Hamiltonian manifolds, we obtain a necessary and sufficient condition involving momentum polytopes for such manifolds to be K\"ahler and classify the invariant compatible complex structures of a given K\"ahler multiplicity free compact and connected Hamiltonian manifold., Comment: v1: 32 pages. v2: 47 pages, fixed errors, improved exposition, expanded Section 7. v3: 47 pages, implemented changes and corrections requested by referee

The motivation to search for signatures of superconductivity in Weyl semi-metals and other topological phases lies in their potential for hosting exotic phenomena such as nonzero-momentum pairing or the Majorana fermion, a viable candidate for the ultimate realization of a scalable quantum computer. Until now, however, all known reports of superconductivity in Weyl semimetals have arisen through surface contact with a sharp tip, focused ion-beam surface treatment or the application of high pressures. Here, we demonstrate the observation of superconductivity in single crystals, even an as-grown crystal, of the Weyl semi-metal tantalum phosphide (TaP), at ambient pressure. A superconducting transition temperature, $Tc$, varying between 1.7 and 5.3 K, is observed in different samples, both as-grown and microscopic samples processed with focused ion beam (FIB) etching. Our data show that the superconductivity present in the as-grown crystal is inhomogeneous yet exists in the bulk. For samples fabricated with FIB, we observe, in addition to the bulk superconductivity, a second superconducting state that resides on the sample surface. Through measurements of the characteristic fields as a function of temperature and angle, we are able to confirm the dimensionality of the two distinct superconducting phases., Comment: 17 pages, 3 figures