We investigate the electronic transport properties of a bilayer graphene flake contacted by two monolayer nanoribbons. Such a finite-size bilayer flake can be built by overlapping two semiinfinite ribbons or by depositing a monolayer flake onto an infinite nanoribbon. These two structures have a complementary behavior, that we study and analyze by means of a tight-binding method and a continuum Dirac model. We have found that for certain energy ranges and geometries, the conductance of these systems oscillates markedly between zero and the maximum value of the conductance, allowing for the design of electromechanical switches. Our understanding of the electronic transmission through bilayer flakes may provide a way to measure the interlayer hopping in bilayer graphene.
We investigate quantum transport properties of triangular graphene flakes with zigzag edges by using first principles calculations. Triangular graphene flakes have large magnetic moments which vary with the number of hydrogen atoms terminating its edge atoms and scale with its size. Electronic transmission and current-voltage characteristics of these flakes, when contacted with metallic electrodes, reveal spin valve and remarkable rectification features. The transition from ferromagnetic to antiferromagnetic state under bias voltage can, however, terminate the spin polarizing effects for speci…
Based on a tight-binding model and a recursive Green's function technique, spin-depentent ballistic transport through tinny graphene sheets (flakes) is studied. The main interest is focussed on: electrical conductivity, giant magnetoresistance (GMR) and shot noise. It is shown that when graphene flakes are sandwiched between two ferromagnetic electrodes, the resulting GMR coefficient may be quite significant. This statement holds true both for zigzag and armchair chiralities, as well as for different aspect (width/length) ratios. Remarkably, in absolute values the GMR of the armchair-edge grap…
The electronic conductance of graphene-based bilayer flake systems reveal different quantum interference effects, such as Fabry-Pérot resonances and sharp Fano antiresonances on account of competing electronic paths through the device. These properties may be exploited to obtain spin-polarized currents when the same nanostructure is deposited above a ferromagnetic insulator. Here we study how the spin-dependent conductance is affected when a time-dependent gate potential is applied to the bilayer flake. Following a Tien-Gordon formalism we explore how to modulate the transport properties of su…
In this paper, we study the thermal rectification in asymmetric U-shaped graphene flakes by using nonequilibrium molecular dynamics simulations. The graphene flakes are composed by a beam and two arms. It is found that the heat flux runs preferentially from the wide arm to the narrow arm which indicates a strong rectification effect. The dependence of the rectification ratio upon the heat flux, the length and the width of the beam, the length and width of the two arms are studied. The result suggests a possible route to manage heat dissipation in U-shaped graphene based nanoelectronic devices.
Nano-indentation of circular graphene flakes are studied by using Molecular Dynamics simulation. We show that the theory of continuum elasticity based on nonlinear Föpple-Hencky equations is applicable on a circular suspended graphene flake. Our simulation results are plenty compatible to those results calculated by the nonlinear elasticity theory. We find the force-displacement curves in good agreement with the recent experimental measurements and conclude they are temperature independent. In addition, we find the vibration frequency for such a system and monitor that it behaves as a sinusoid…
The authors proposed a simple model for the lattice thermal conductivity of graphene in the framework of Klemens approximation. The Gruneisen parameters were introduced separately for the longitudinal and transverse phonon branches through averaging over phonon modes obtained from the first-principles. The calculations show that Umklapp-limited thermal conductivity of graphene grows with the increasing linear dimensions of graphene flakes and can exceed that of the basal planes of bulk graphite when the flake size is on the order of few micrometers. The obtained results are in agreement with e…
We present the first experimental investigation of nonlinear optical properties of graphene flakes. We find that at near infrared frequencies a graphene monolayer exhibits a remarkably high third-order optical nonlinearity which is practically independent of the wavelengths of incident light. The nonlinear optical response can be utilized for imaging purposes, with image contrasts of graphene which are orders of magnitude higher than those obtained using linear microscopy.
The electronic shell structure of triangular, hexagonal and round graphene quantum dots (flakes) near the Fermi level has been studied using a tight-binding method. The results show that close to the Fermi level the shell structure of a triangular flake is that of free massless particles, and that triangles with an armchair edge show an additional sequence of levels ("ghost states"). These levels result from the graphene band structure and the plane wave solution of the wave equation, and they are absent for triangles with an zigzag edge. All zigzag triangles exhibit a prominent edge state at …
We study the transport properties of a twisted bilayer graphene flake contacted by two monolayer nanoribbons which act as leads. We analyze the conductance in terms of the spectra of the bilayer nanoribbon and the monolayer contacts. The low-energy transport properties are governed by the edge states with AB stacking. Remarkably, the electronic conductance in this energy region does not depend much on the relative position of the leads, in contrast with that of bilayer flakes with more symmetric stackings. We attribute this feature to the localization of these low-energy states in the AB edge …
We report the observation and characterization of field emission current from individual single- and few-layer graphene flakes laid on a flat SiO2/Si substrate. Measurements were performed in a scanning electron microscope chamber equipped with nanoprobes, used as electrodes to realize local measurements of the field emission current. We achieved field emission currents up to 1 μA from the flat part of graphene flakes at applied fields of few hundred V/μm. We found that emission process is stable over a period of several hours and that it is well described by a Fowler-Nordheim model for curren…
We present a fabrication method producing large and flat graphene flakes that have a few layers down to a single layer based on substrate bonding of a thick sample of highly oriented pyrolytic graphite (HOPG), followed by its controlled exfoliation down to the few to single graphene atomic layers. As the graphite underlayer is intimately bonded to the substrate during the exfoliation process, the obtained graphene flakes are remarkably large and flat and present very few folds and pleats. The high occurrence of single layered graphene sheets having tens of micron wide in lateral dimensions is …
Using nonequilibrium molecular dynamics simulations, we study the heat conduction in graphene flakes composed by two regions. One region is mass-loaded and the other one is intact. It is found that the mass interface between the two regions greatly decreases the thermal conductivity, but it would not bring thermal rectification effect. The dependence of thermal conductivity upon the heat flux and the mass difference ratio are studied to confirm the generality of the result. The interfacial scattering of solitons is studied to explain the absence of rectification effect.
We present a calculation of the free energy, the surface free energy and the elastic constants ("Lam'e parameters" i.e, Poisson ratio, Young's modulus) of graphene flakes on the level of the density functional theory employing different standard functionals. We observe that the Lam'e parameters in small flakes can differ from the bulk values by 30% for hydrogenated zig-zag edges. The change results from the edge of the flake that compresses the interior. When including the vibrational zero point motion, we detect a decrease in the bending rigidity by ~26%. This correction is depending on the f…
Transformation of graphene flakes to fullerenes assisted by Ni clusters is investigated using molecular dynamics simulations. The bond-order potential for Ni-C systems is developed. The potential reproduces the experimental and first-principles data on the physical properties of pure Ni as well as on relative energies of carbon species on Ni surfaces and in Ni bulk. The potential is applied for molecular dynamics simulations of the transformation of graphene flakes consisting of 50 - 400 atoms with and without Ni clusters attached. Free fullerenes, fullerenes with Ni clusters attached from out…
We show that a bilayer graphene flake deposited above a ferromagnetic insulator can behave as a spin-filtering device. The ferromagnetic material induces exchange splitting in the graphene flake, and due to the Fano antiresonances occurring in the transmission of the graphene flake as a function of flake length and energy, it is possible to obtain a net spin current. This happens when an antiresonance for one spin channel coincides with a maximum transmission for the opposite spin. We propose these structures as a means to obtain spin-polarized currents and spin filters in graphene-based syste…
We show that the manifestation of quantum interference in graphene is very different from that in conventional two-dimensional systems. Due to the chiral nature of charge carriers, it is sensitive not only to inelastic, phase-breaking scattering, but also to a number of elastic scattering processes. We study weak localization in different samples and at different carrier densities, including the Dirac region, and find the characteristic rates that determine it. We show how the shape and quality of graphene flakes affect the values of the elastic and inelastic rates and discuss their physical o…
We show that it is possible to deposit, by mechanical exfoliation on SiO2/Si wafers, atomically thin mica flakes down to a single monolayer thickness. The optical contrast of these mica flakes on top of a SiO2/Si substrate, which depends on their thickness, the illumination wavelength and the SiO2 substrate thickness, can be quantitatively accounted for by a Fresnel law based model. The preparation of atomically thin insulating crystalline sheets will enable the fabrication of ultrathin defect-free insulating substrates, dielectric barriers or planar electron tunneling junctions. Additionally,…
In this letter we study thermal conduction in mass-graded graphene flakes by nonequilibrium molecular dynamics simulations. It is found that mass-graded graphene flakes reveal no thermal rectification effect in thermal conduction process. The dependence of thermal conductivity upon the heat flux and the mass gradient are studied to confirm the generality of the result.The mechanism leading to the absence of thermal rectification effect is also discussed.
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 …
A clear gate voltage tunable weak antilocalization and a giant magnetoresistance of 400 percent are observed at 1.9 K in single layer graphene with an out-of-plane field. A large magnetoresistance value of 275 percent is obtained even at room temperature implying potential applications of graphene in magnetic sensors. Both the weak antilocalization and giant magnetoresistance persists far away from the charge neutrality point in contrast to previous reports, and both effects are originated from charged impurities. Interestingly, the signatures of Shubnikov-de Haas oscillations and the quantum …
The self-retracting motion of a graphene flake on a stack of graphene flakes is studied using molecular dynamics simulations. It is shown that in the case when the extended flake is initially rotated to an incommensurate state, there is no barrier to the self-retracting motion of the flake and the flake retracts as fast as possible. If the extended flake is initially commensurate with the other flakes, the self-retracting motion is hindered by potential energy barriers. However, in this case, the rotation of the flake to incommensurate states is often observed. Such a rotation is found to be i…
Graphene nano-flakes (GNFs) are predicted to host spin-polarized metallic edge states, which are envisioned for exploration of spintronics at the nanometer scale. To date, experimental realization of GNFs is only in its infancy because of the limitation of precise cutting or synthesizing methods at the nanometer scale. Here, we use low temperature scanning tunneling microscope (STM) to manipulate coronene molecules on a Cu(111) surface to build artificial triangular and hexagonal GNFs with either zigzag or armchair type of edges. We observe that the metallic edge states only exist in the GNFs …
We report large-yield production of graphene flakes on glass by anodic bonding. Under optimum conditions, we counted several tens of flakes with lateral size around 20-30 μm and few tens of flakes with larger size. 60-70% of the flakes have negligible D peak. We show that it is possible to easily transfer the flakes by wedging technique. The transfer on silicon does not damage graphene and lowers the doping. The charge mobility of the transferred flakes on silicon is of the order of 6000 cm^2/V s (at carrier concentration of 10^12 cm^-2), which is typical for devices prepared on this substrate…
The sliding energy landscape of the heterogeneous graphene/h-BN interface is studied by means of the registry index. For a graphene flake sliding on top of h-BN the anisotropy of the sliding energy corrugation with respect to the misfit angle between the two naturally mismatched lattices is found to reduce with the flake size. For sufficiently large flakes the sliding energy corrugation is expected to be at least an order of magnitude lower than that obtained for matching lattices regardless of the relative interlayer orientation thus resulting in a stable low-friction state. This is in contra…
Orbital magnetism is studied for graphene flakes with various shapes and edge configurations using the tight-binding approximation. In the low-temperature regime where the thermal energy is much smaller than to the energy level spacing, the susceptibility rapidly changes between diamagnetism and paramagnetism as a function of Fermi energy, in accordance with the energy level structure. The susceptibility at charge neutral point is generally larger in armchair flake than in zigzag flake, and larger in hexagonal flake than in triangular flake. As the temperature increases, the discrete structure…
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…
Diffusion of a graphene flake on a graphene layer is analyzed and a new diffusion mechanism is proposed for the system under consideration. According to this mechanism, rotational transition of the flake from commensurate to incommensurate states takes place with subsequent simultaneous rotation and translational motion until the commensurate state is reached again, and so on. The molecular dynamics simulations and analytic estimates based on ab initio and semi-empirical calculations demonstrate that the proposed diffusion mechanism is dominant at temperatures T ~ Tcom, where Tcom corresponds …
The mechanical behaviour of graphene flakes under both tension and compression is examined using a cantilever-beam arrangement. Two different sets of samples were employed involving flakes just supported on a plastic bar but also embedded within the plastic substrate. By monitoring the shift of the 2D Raman line with strain, information on the stress transfer efficiency as a function of stress sign and monolayer support were obtained. In tension, the embedded flake seems to sustain strains up to 1.3%, whereas in compression there is an indication of flake buckling at about 0.7% strain. The ret…
Diffusion and drift of a graphene flake on a graphite surface are analyzed. A potential energy relief of the graphene flake is computed using ab initio and empirical calculations. Based on the analysis of this relief, different mechanisms of diffusion and drift of the graphene flake on the graphite surface are considered. A new mechanism of diffusion and drift of the flake is proposed. According to the proposed mechanism, rotational transition of the flake from commensurate to incommensurate state takes place with subsequent simultaneous rotation and translational motion until a commensurate s…
The electronic shell and supershell structure of triangular graphene quantum dots has been studied using density functional and tight-binding methods. The density functional calculations demonstrate that the electronic structure close to the Fermi energy is correctly described with a simple tight-binding model where only the p_z orbitals perpendicular to the graphene layer are included. The results show that (i) both at the bottom and at the top of the p_z band a supershell structure similar to that of free electrons confined in a triangular cavity is seen, (ii) close to the Fermi level the sh…
Using a tight-binding atomistic simulation, we simulate the recent atomic-force microscopy experiments probing the slipperiness of graphene flakes made slide against a graphite surface. Compared to previous theoretical models, where the flake was assumed to be geometrically perfect and rigid, while the substrate is represented by a static periodic potential, our fully-atomistic model includes quantum mechanics with the chemistry of bond breaking and bond formation, and the flexibility of the flake. These realistic features, include in particular the crucial role of the flake rotation in determ…
We have investigated thermal conductivity of graphene laminate films deposited on polyethylene terephthalate substrates. Two types of graphene laminate were studied - as deposited and compressed - in order to determine the physical parameters affecting the heat conduction the most. The measurements were performed using the optothermal Raman technique and a set of suspended samples with the graphene laminate thickness from 9 to 44 micrometers. The thermal conductivity of graphene laminate was found to be in the range from 40 W/mK to 90 W/mK at room temperature. It was found unexpectedly that th…
Combining the tight-binding approximation and linear elasticity theory for a planar membrane, we investigate stretching of a graphene flake assuming that two opposite edges of the sample are clamped by the contacts. We show that, depending on the aspect ratio of the flake and its orientation, gapped states may form in the membrane in the vicinity of the contacts. This gap in the pre-contact region should be biggest for the armchair orientation of the flake and width to length ratio of around 1.
We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as 1/6 of the band width of clean graphene. We clarify that, in order for this Anderson-type localisation to be manifested, graphene flakes of size of approximately 200 x 200 nm^2 or larger are needed. For smaller samples, due to the surprisingly large extent of the electronic wave functions, a regime of apparently extended (or even critical) states is identified. Our results complement earlier studies of macroscopically large s…
We study quantum dots defined by external potentials within finite flakes of bilayer graphene using the tight-binding approach. We find that in the limit of large flakes containing zigzag edges the dot-localized energy levels appear within the energy continuum formed by extended states. As a consequence no ionization threshold for the carriers contained within the dot exists. For smaller flakes with zigzag boundaries the dot-localized energy levels appear interlaced with the energy levels outside the flake, so in a charging experiment the electrons will be added alternately to the dot area and…
We have measured the mechanical properties of few-layer graphene and graphite flakes that are suspended over circular holes. The spatial profile of the flake's spring constant is measured with an atomic force microscope. The bending rigidity of and the tension in the membranes are extracted by fitting a continuum model to the data. For flakes down to eight graphene layers, both parameters show a strong thickness-dependence. We predict fundamental resonance frequencies of these nanodrums in the GHz range based on the measured bending rigidity and tension.
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…
We study the localization properties of the wavefunctions in graphene flakes with short range disorder, via the numerical calculation of the Inverse Participation Ratio($IPR$) and it scaling which provides the fractal dimension $D_{2}$. We show that the edge states which exist at the Dirac point of ballistic graphene (no disorder) with zig-zag edges survive in the presence of weak disorder with wavefunctions localized at the boundaries of the flakes. We argue, that there is a strong interplay between the underlying destructive interference mechanism of the honeycomb lattice of graphene leading…
Using the recently developed technique of microsoldering, we perform a systematic transport study of the influence of PMMA on graphene flakes revealing a doping effect of up to 3.8x10^12 1/cm^2, but a negligible influence on mobility and gate voltage induced hysteresis. Moreover, we show that the microsoldered graphene is free of contamination and exhibits a very similar intrinsic rippling as has been found for lithographically contacted flakes. Finally, we demonstrate a current induced closing of the previously found phonon gap appearing in scanning tunneling spectroscopy experiments, strongl…
We present transport measurements on quantum dots of sizes 45, 60 and 80 nm etched with an Ar/O2-plasma into a single graphene sheet, allowing a size comparison avoiding effects from different graphene flakes. The transport gaps and addition energies increase with decreasing dot size, as expected, and display a strong correlation, suggesting the same physical origin for both, i.e. disorder-induced localization in presence of a small confinement gap. Gate capacitance measurements indicate that the dot charges are located in the narrow device region as intended. A dominant role of disorder is fu…
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 demonstrate the local oxidation nanopatterning of graphene films by an atomic force microscope. The technique provides a method to form insulating trenches in graphene flakes and to fabricate nanodevices with sub-nm precision. We demonstrate fabrication of a 25-nm-wide nanoribbon and sub-micron size nanoring from a graphene flake. We also found that we can write either trenches or bumps on the graphene surface depending on the lithography conditions. We attribute the bumps to partial oxidation of the surface and incorporation of oxygen into the graphene lattice.
We study rectangular graphene flakes using mean field states as the basis for a configuration interaction calculation, which allows us to analyze the low lying electronic excited states including electron correlations beyond the mean field level. We find that the lowest energy transition is polarized along the long axis of the flake, but the charge distributions involved in these transitions are invariably localized on the zigzag edges. We also investigate the impact of both short and long range impurity potentials on the optical properties of these systems. We predict that even a weak impurit…
We use anhydrous ferric chloride (FeCl3) to intercalate graphite flakes consisting of 2 to 4 graphene layers and to dope graphene monolayers. The intercalant, staging, stability and doping of the resulting intercalation compounds (ICs) are characterized by Raman scattering. The G peak of monolayer graphene heavily-doped by FeCl3 upshifts to~1627cm-1. 2-4 layer ICs have similar upshifts, and a Lorentzian lineshape for the 2D band, indicating that each layer behaves as a decoupled heavily doped monolayer. By performing Raman measurement at different excitation energies we show that, for a given …
The electronic properties of a triaxially strained hexagonal graphene flake with either armchair or zig-zag edges are investigated using molecular dynamics simulations and tight-binding calculations. We found that: i) the pseudo-magnetic field in the strained graphene flakes is not uniform neither in the center nor at the edge of zig-zag terminated flakes, ii) the pseudo-magnetic field is almost zero in the center of armchair terminated flakes but increases dramatically near the edges, iii) the pseudo-magnetic field increases linearly with strain, for strains lower than 15$%$ while growing non…
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.
Among the most common few-layers transition metal dichalcogenides (TMDs), WSe2 is the most challenging material from the lattice dynamics point of view. Indeed, for a long time the main two phonon modes (A1g and E12g) have been wrongly assigned. In the last few years, these two modes have been properly interpreted, and their quasi-degeneracy in the monolayer has been used for its identification. In this work, we show that this approach has a limited validity and we propose an alternative, more general approach, based on multi-phonon bands. Moreover, we show and interpret all the peaks (about 4…
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…
We model the optical visibility of monolayer and bilayer graphene deposited on a silicon/silicon oxide substrate or thermally annealed on the surface of silicon carbide. We consider reflection and transmission setups, and find that visibility is strongest in reflection reaching the optimum conditions when the bare substrate transmits light resonantly. In the optical range of frequencies a bilayer is approximately twice as visible as a monolayer thereby making the two types of graphene distinguishable from each other.
The growth of single and multilayer graphene nano-flakes on MgO and ZrO2 at low temperatures is shown through transmission electron microscopy. The graphene nano-flakes are ubiquitously anchored at step edges on MgO (100) surfaces. Density functional theory investigations on MgO (100) indicate C2H2 decomposition and carbon adsorption at step-edges. Hence, both the experimental and theoretical data highlight the importance of step sites for graphene growth on MgO.
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…
A method is described for levitating micron-sized few layer graphene flakes in a quadrupole ion trap. Starting from a liquid suspension containing graphene, charged flakes are injected into the trap using the electrospray ionization technique and are probed optically. At micro-torr pressures, torques from circularly polarized light cause the levitated particles to rotate at frequencies >1 MHz, which can be inferred from modulation of light scattering off the rotating flake when an electric field resonant with the rotation rate is applied. Possible applications of these techniques will be prese…
We have explored the electronic properties of stacked graphene flakes with the help of the quantum chemistry methods. We found that the behavior of a bilayer system is governed by the strength of the repulsive interactions that arise between the layers as a result of the orthogonality of their $π$ orbitals. The decoupling effect, seen experimentally in AA stacked layers is a result of the repulsion being dominant over the orbital interactions and the observed layer misorientation of 2$^{\circ}-5^{\circ}$ is an attempt by the system to suppress that repulsion and stabilize itself. For misorient…
We study the Brownian motion (BM) of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics, measure force and torque constants and derive a full electromagnetic theory of optical trapping. The understanding of two dimensional BM paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules.
The valley of transition metal dichalcogenides provides an additional platform to manipulate spin due to its unique selection rule. Normally, intralayer optical transitions in magnetic field show a Zeeman splitting with g factor of about $-4$. Here we report remarkable valley Zeeman effect exhibited by splitting of excitonic emission in a bilayer WS$_{2}$, with a value of g factor as large as $-16.5$. The observed large g factor results from the interlayer recombination, as the conduction band and valence band are modified in opposite directions by magnetic field in different layers. The inter…
The effect of strain in graphene is usually modeled by a pseudo-magnetic vector potential which is, however, derived in the limit of small strain. In realistic cases deviations are expected in view of graphene's very high strain tolerance, which can be up to 25%. Here we investigate the pseudo-magnetic field generated by a Gaussian bump and we show that it exhibits significant differences with numerical tight-binding results. Furthermore, we calculate the electronic states in the strained region for a hexagon shaped flake with armchair edges. We find that the six-fold symmetry of the wave func…
We study the conductance of a biased bilayer graphene flake with monolayer nanoribbon contacts. We find that the transmission through the bilayer ribbon strongly depends on the applied bias between the two layers and on the relative position of the monolayer contacts. Besides the opening of an energy gap on the bilayer, the bias allows to tune the electronic density on the bilayer flake, making possible the control of the electronic transmission by an external parameter.
