We use density functional theory to determine the equilibrium shape of graphene flakes, through the calculation of the edge orientation dependence of the edge energy and edge stress of graphene nanoribbons. The edge energy is a nearly linear function of edge orientation angle; increasing from the armchair orientation to the zigzag orientation. Reconstruction of the zigzag edge lowers its energy to less than that of the armchair edge. The edge stress for all edge orientations is compressive, however, reconstruction of the zigzag edge reduces this edge stress to near zero. Hydrogen adsorption is favorable for all edge orientations; dramatically lowering all edge energies and all edge stresses. It also removes the reconstruction of the zigzag edge. Using the new edge energy data, we determine the equilibrium shape of a graphene sheet (with unreconstructed edges) to be hexagonal with straight armchair edges in the presence and absence of hydrogen. However, zigzag edge reconstruction produces graphene flakes with a six-fold symmetry, but with rounded edges. This shape is dominated by near zigzag edges. The compressive edge stresses will lead to edge buckling (out-of-the-plane of the graphene sheet) for all edge orientations, in the absence of hydrogen. Exposing the graphene flake to hydrogen dramatically decreases the buckling amplitude.
High-Yield Production and Transfer of Graphene Flakes Obtained by Anodic Bonding
我们报告了通过阳极键合在玻璃上大产量地生产石墨烯薄片。在最佳条件下，我们计数了几十个横向尺寸在20-30 μm左右的薄片和几十个较大尺寸的薄片。60-70%的薄片具有可忽略的D峰。我们表明，这是可能的，很容易转移的薄片楔技术。硅上的转移不会损坏石墨烯并降低掺杂。转移到硅上的薄片的电荷迁移率约为6000 cm ^2/V·s（载流子浓度为10^12 cm^-2），这对于在该衬底上用剥离的石墨烯制备的器件是典型的。
Localisation and finite-size effects in graphene flakes
我们表明，在无序的石墨烯，现场电位，诱导谷间散射的电子状态，是本地化的所有能量在无序小至1/6的带宽度的干净的石墨烯。我们澄清，为了使这种安德森型局部化得以体现，需要尺寸约为200 x 200 nm^2或更大的石墨烯薄片。对于较小的样品，由于电子波函数的范围令人惊讶的大，一个政权显然扩展（甚至临界）的状态被确定。我们的研究结果补充了宏观大样品的早期研究，并可以解释有限尺寸石墨烯片的结果的分歧。
We calculate the friction of fully mobile graphene flakes sliding on graphite. For incommensurately stacked flakes, we find a sudden and reversible increase in friction with load, in agreement with experimental observations. The transition from smooth sliding to stick-slip and the corresponding increase in friction is neither due to rotations to commensurate contact nor to dislocations but to a pinning caused by vertical distortions of edge atoms also when they are saturated by Hydrogen. This behavior should apply to all layered materials with strong in-plane bonding.
Twisted bilayer graphene (TBG) exhibits a wide range of intriguing physical properties, such as superconductivity, ferromagnetism, and superlubricity. Depending on the twist angle, periodic moiré superlattices form in twisted bilayer graphene, with inhomogeneous interlayer coupling and lattice deformation. For a small twist angle (typically <2°), each moiré supercell contains a large number of atoms (>10,000), making it computationally expensive for first-principles and atomistic modeling. In this work, a finite element method based on a continuum model is used to simulate the inhomogeneous in…
A method of regulating spin dynamics of the so-called magnetic graphene is analyzed. Magnetic moments can be incorporated into graphene flakes and graphene ribbons through defects, such as adatoms and vacancies. Local spins can also be attached to graphene at hydrogenated zigzag edges. Spin flips can be produced by transverse pulses and by connecting the sample to a resonance electric coil. The action of the resonator feedback field strongly accelerates spin reversal. The possibility of fast spin reversal is important for spintronics and for quantum information processing allowing for an effic…
We show how the magnetization of nano-objects can be efficiently regulated. Several types of nanosystems are considered: magnetics nanomolecules, magnetic nanoclusters, polarized nanomolecules, and magnetic graphene. These nano-objects and the structures composed of them enjoy many common properties, with the main difference being in the type of particle interactions. The possibility of governing spin dynamics is important for spintronics.
We investigate topological properties of models that describe graphene on realistic substrates which induce proximity spin-orbit coupling in graphene. A $\mathbb{Z}_2$ phase diagram is calculated for the parameter space of (generally different) intrinsic spin-orbit coupling on the two graphene sublattices, in the presence of Rashba coupling. The most fascinating case is that of staggered intrinsic spin-orbit coupling which, despite being topologically trivial, $\mathbb{Z}_2 = 0$, does exhibit edge states protected against time-reversal scattering for zigzag ribbons as wide as micrometers. We c…
It has been shown recently [J. L. Lado et al., Phys. Rev. Lett. 113, 027203 (2014)] that edge magnetic moments in graphene-like nanoribbons are strongly influenced by the intrinsic spin-orbit interaction. Due to this interaction an anisotropy comes about which makes the in-plane arrangement of magnetic moments energetically more favorable than that corresponding to the out-of-plane configuration. In this paper we raise both the edge magnetism problem as well as differential conductance and shot noise Fano factor issues, in the context of finite-size flakes within the Coulomb blockade (CB) tran…
We investigate the Josephson effect in a bilayer graphene flake contacted by two monolayer sheet deposited by superconducting electrodes. It is found that when the electrodes are attached to the different layers of the bilayer, the Josephson current is in a $π$ state when the bilayer region is undoped and in the absence of vertical bias. Applying doping or bias to the junction reveals $π-0$ transitions which can be controlled by varying the temperature and the junction length. The supercurrent reversal here is very different from the ferromagnetic Josephson junctions where the spin degree of f…
We investigate the coupling of spin and thermal currents as a means to rise the thermoelectric efficiency of nanoscale graphene devices. We consider nanostructures composed of overlapping graphene nanoribbons with ferromagnetic contacts in different magnetic configurations. Our results show that the charge Seebeck effect is greatly enhanced when the magnetic leads are in an antiparallel configuration, due to the enlargement of the transport gap. However, for the optimization of the charge figure of merit ZT it is better to choose a parallel alignment of the magnetization in the leads, because …
We report on a magneto-Raman scattering study of graphene flakes located on the surface of a bulk graphite substrate. By spatially mapping the Raman scattering response of the surface of bulk graphite with an applied magnetic field, we pinpoint specific locations which show the electronic excitation spectrum of graphene. We present the characteristic Raman scattering signatures of these specific locations. We show that such flakes can be superimposed with another flake and still exhibit a graphene-like excitation spectrum. Two different excitation laser energies (514.5 and 720 nm) are used to …
Linear conductance of junctions formed by graphene flakes with order of nanometer-thick electrodes attached at the corners of the flakes is studied. The explored structures have sizes up to 20000 atoms and the conductance is studied as a function of applied gate voltage varied around the Fermi level. The finding, obtained computationally, is that junctions formed by armchair-edge flakes with the electrodes connected at the acute-angle corners block the electron transport while only junctions with such electrodes at the obtuse-angle corners tend to provide the high electrical conductance typica…
We study fully hexagonal boron nitride (hBN)-encapsulated graphene spin valve devices at room temperature. The device consists of a graphene channel encapsulated between two crystalline hBN flakes; thick-hBN flake as a bottom gate dielectric substrate which masks the charge impurities from SiO2/Si substrate and single-layer thin-hBN flake as a tunnel barrier. Full encapsulation prevents the graphene from coming in contact with any polymer/chemical during the lithography and thus gives homogeneous charge and spin transport properties across different regions of the encapsulated graphene. Furthe…
Manipulation of intrinsic magnetic and electronic structures of graphene nanoflakes is of technological importance. Here we carry out systematic study of the magnetic and electronic phases, and its manipulation in graphene nanoflakes employing first-principles calculation. We illustrate the intricate shape and size dependence on the magnetic and electronic properties, and further investigate the effects of carrier doping, which could be tuned by gate voltage. A transition from nonmagnetic to magnetic phase is observed at a critical flake size for the flakes without sublattice imbalance, which …
We propose a novel conceptual design for a graphene-based quantum engine, driven by a superposition of mechanical strain and an external magnetic field. Engineering of strain in a nanoscale graphene flake creates a gauge field with an associated uniform pseudo-magnetic field. The strain-induced pseudo-magnetic field can be combined with a real magnetic field, leading to the emergence of discrete relativistic Landau levels within the single-particle picture. The inter-level distance and hence their statistical population can be modulated by quasi-statically tuning the magnetic field along a seq…
In this paper, the form of the indirect interaction between local impurities in flakes and in graphene ring is analytically investigated. We calculate this characteristic in the framework of the tight-binding model for a finite nanocarbon system with periodic boundary conditions. A pronounced dependence of the bond value on the impurity position inside the graphene sample is found, which is due to quantum size effects. The influence of the flake size on the value of the indirect interaction constant is also studied.
We investigate the spin-dependent thermoelectric effect of graphene flakes with magnetic edges in the ballistic regime. Employing static, respectively, dynamic mean-field theory we first show that magnetism appears at the zigzag edges for a window of Coulomb interactions that increases significantly with increasing flake size. We then use the Landauer formalism in the framework of the non-equilibrium Green's function method to calculate the spin and charge currents in magnetic hexagonal graphene flakes by varying the temperature of the junction for different flake sizes. While in non-magnetic …
Electrons in clean macroscopic samples of graphene exhibit an astonishing variety of quantum phases when strong perpendicular magnetic field is applied. These include integer and fractional quantum Hall states as well as symmetry broken phases and quantum Hall ferromagnetism. Here we show that mesoscopic graphene flakes in the regime of strong disorder and magnetic field can exhibit another remarkable quantum phase described by holographic duality to an extremal black hole in two dimensional anti-de Sitter space. This phase of matter can be characterized as a maximally chaotic non-Fermi liquid…
We investigate the formation of edge states in graphene ribbons and flakes with proximity induced valley-Zeeman and Rashba spin-orbit couplings in the presence of a perpendicular magnetic field $B$. Two types of edges states appear in the spin-orbit gap at the Fermi level at zero field: strongly localized pseudohelical (intervalley) states and weakly localized intravalley states. We show that if the magnetic field is stronger than a crossover field $B_c$, which is a few mT for realistic systems such as graphene/WSe$_2$, only the pseudohelical edge states remain in zigzag graphene ribbons; the …
