When an electronic wave packet is propagating in rhombohedral three-layer graphene, it hops between the layers (shown by different colors) in an aperiodic fashion in certain energies. The hopping dynamics of this quantum mechanical system is similar to a simple classical system, three coupled pendulums. Such aperiodic behavior is typical of a 3-body system . This massive wave packet dynamical calculation, including many thousands of atoms, was made possible by our new Carbon pseudopotential.

Wave packet dynamics makes us possible to calculate the transport of electrons in nanosystems containing several thousands of atoms. Figure (a) shows the atomic structure of a bilayer graphene nanoribbon, where the two layers are connected along the cicumference of a hole. Figure (b) and (c) show two electrode configarations used in our calculations. We found that the hole is a kind of energy filter, by changing the voltage applied across the electrodes, it is possible to control the transmission, delay, and reflection of the wave packet.

Understanding the causal links between the genotype of an organism, the environmental factors, and its phenotype is a hot topic in current biology. We investigated in detail, how an environmental factor (prolonged cooling of the pupae) influence the wing structure of the adult butterflies. This graph shows, that a relatively short cooling (up to 2 weeks) does not influence the eclosed fraction, but somewhat increases the number of wing defets. A prolonged cooling (more that 10 weeks), however, decreases the eclosed fraction to zero. Good illumination during pupation is also an essential factor (see the point marked "low light").

The image shows a real space lattice of four translation periodic layers with lateral periodicity d and layer distance a. The arrows show the possible light scattering processes -- green is the incoming light, red is the outgoing light. The first- and second order processes (left and right, respectively) give spectral peaks at different locations. In this work we showed that for butterfly wings the visible part of the spectum is generally well reproduced by taking into account first order scattering only, but the second order contribution is important at the UV range.

We investigated the vapour sensing properties of different graphene-gold hybrid nanostructures. We observed the shifts in the optical spectra near the local surface plasmon resonance of the gold nanoparticles by changing the concentration and nature of the analytes (ethanol, 2-propanol, and toluene). The smaller, dome-like gold nanoparticles proved to be more sensitive to these vapours compared to slightly larger, flat nanoparticles. We investigated how the optical response of the gold nanoparticles can be tuned with a corrugated graphene overlayer. We showed that the presence of rippled graphene increased the sensitivity to ethanol and 2-propanol, while it decreased it towards toluene exposure (at concentrations higher than 30%). The slope changes observed on the optical response curves were well described by capillary condensation. These results can have potential impact on the development of sensors based on graphene gold nanohybrids.

This image shows the three states of a graphene transistor made of a graphene nanoribbon. According to our theoretical calculations, this transistor has three separate magnetic states, tunable merely with a back gate electrode, without the need of ferromagnetic contacts. This device can serve as a basic building block of hybrid electronic and spintronic graphene data processing systems.

During the past decade, the color patterns of insects have emerged as model systems for studying the interplay between development and evolution. The complex patterns encountered on butterfly wings are more often generated by various pigments than by structural colors, but composite patterns, having both pigmentary and structural origins, also occur. The structural colors of butterflies, generated by sophisticated nanoarchitectures that are able to manipulate light propagation, are frequently used in sexual communication and may be an indicator of mate quality. While numerous papers have investigated the effects of thermal stress on the pigmentary colors of butterfly wings, such studies regarding structural colors are mostly lacking, despite the important role they play in sexual communication. To gain insight into the possible differences between the responses of the two kinds of coloration, we investigated the effects of prolonged cold stress (cooling at 5 C for up to 62 days) on the pupae of Polyommatus icarus butterflies. The wing surfaces colored by photonic crystal-type nanoarchitectures (dorsal) and by pigments (ventral) showed markedly different behaviors.

The AFM image shows a graphene/metal nanoparticle hybrid material fabricated by transferring graphene onto closely spaced gold nanoparticles produced on a silica wafer. Graphene is highly rippled and suspended between nanoparticles. This study shows that the graphene Raman peaks are enhanced by a factor which depends on the excitation wavelength, in accordance with the surface plasmon resonance of the gold nanoparticles, and also on the graphene nanoparticle distance which is tuned by annealing at moderate temperatures. Scanning tunneling microscopy and spectroscopy (STM/STS) measurements show that the local density of electronic states in graphene is modulated by the underlying gold nanoparticles.

Large scale ab-initio calculations of our Russian partners within the framework of the Faemcar EU Project showed that if we make a hole in bilayered graphene, the edges of the two layers bend and stitch together. If we create many hexagonal holes in a periodic arrangement, the resulting structure is similar to a hexagonal array of nanotubes. Our wave packet dynamical transport calculations proved that this superstructure can be metallic or semiconductor, depending on the size and distance of the holes.

This image shows the elasticity of graphene in nano scale. We covered an array of 25 nm diamener SiO₂ nanoparticles with a graphene sheet. The membrane parts bridging the nanoparticles are suspended. Then we scanned this suspended part with an AFM tip and found that a larger force causes a larger indentation. Revealing the details of the elastic behavior of graphene on the nanoscale is very important for creating nanomechanical devices.

These images show the increasing disorder in a graphene grain boundary (GB). (a) periodic; (b) "serpentine"; (c) disordered structure. We found that the "serpentine" GB (b), though it does not have 1D periodicity and it is not rectilinear, has similar transport properties than the perfect periodic GB (a), while the resistivity of the disordered GB (c) is much higher. Our calculations show that the increased resistivity is due to the many vacancies and 4-coordinated rings, i.e. the discontinuity of the sp² network.

This pair of STM images was recorded on the same 195x195 nm area of graphene, but with different voltage. Note that the ripples, which are seen on both images are sharper on the 0.5 V image than on the 0.1 V image. This means that the shape of the graphene membrane can be controlled by the electric field of the STM tip.

This animation (click here for a larger version) shows the simulated formation process of a disordered graphene grain boundary. Such grain boundaries (GBs) are predominant in CVD prepared graphene and considerably alter the transport properties of the samples. We identified two main factors governing the electronic transport through GBs: the misorientation angle of the two adjacent graphene grains and the atomic structure of the GB. Results show a reduced transport for the disordered GBs, primarily attributed to electronic localized states caused by C atoms with only two covalent bonds.

Left pane of this animation shows that an electronic wave packet constructed from Bloch waves travels unhindered on a graphene surface. The right pane shows that a structural defect causes scattering to the wave packet. Note that the scatteing pattern is not circular, but hexagonal. Such calculations help us understand the Scanning Tunneling Microscopy images of 2D materials containing structural defects.

This figure shows the generations and photos (male and female) of two different populations of the same butterfly species, Polyommatus dorylas (Turquoise blue). The lowland population (Dorylas, upper row) has two generations each year, but the mountainous population (Magna, lower row) has only one generation (note the winter hybernation of the larvae). As you can see on the photos, Magna exemplars are larger, than Dorylas I and Dorylas II examplars. Our detailed studies showed that the size of the wing scales correlate with the body size, but the dimensions of the photonic nanostructures generating the conspicious blue color remain constant. Hence the optical spectrum is the same for the two populations. This proves that the dimensions of the photonic nanostructure are genetically determined, because the structural color is an important species-specific trait.

Web-Schrödinger is a program for the interactive solution of the time dependent and stationary two dimensional (2D) Schrödinger equation. The program itself runs on our server and can be used through the Internet with a simple Web browser.

The new 3.2 version makes it possible to use piecewise linear and quadratic potentials, as demonstrated on this simple model of a diatomic molecule.

The chemical inertness of the defect-free basal plane confers environmental stability to MoS₂ single layers, but it also limits their chemical versatility and catalytic activity. The stability of pristine MoS₂ basal plane against oxidation under ambient conditions is a widely accepted assumption however, L. Tapaszto et. al. recently reported in Nature Chemistry single-atom-level structural investigations that reveal that oxygen atoms spontaneously incorporate into the basal plane of MoS₂ single layers during ambient exposure. The use of scanning tunnelling microscopy reveals a slow oxygen-substitution reaction, during which individual sulfur atoms are replaced one by one by oxygen, giving rise to solid-solution-type 2D MoS_2-xO_x crystals. Oxygen substitution sites present all over the basal plane act as single-atom reaction centres, substantially increasing the catalytic activity of the entire MoS₂ basal plane for the electrochemical H₂ evolution reaction.

This computer simulated image shows a snapshot from the time development of an electronic wave packet injected into the surface of a molybdenum disulfide (MoS2) sheet from the apex of a Scanning Tunneling Microscope tip. Studying the evolution of a packet of electrons having their momentum distributed around a given value gives information on the transport properties of the material. This approach has been used for graphene and MoS2. Due to its complex band structure MoS2 presents an interesting dynamics for electrons.

These two butterfly specimens, Polyommatus icarus (A, Common Blue) and Plebejus argus (B, Silver-studded Blue) collected in Hungary (scale bar 10 mm) have similar color to the human eye, but their near UV spectra are different. Despite living in the same type of habitat, these two species display differences in prezygotic mating strategy: the males of P. icarus are patrolling, while P. argus males have sedentary behavior. Therefore, the species-specific photonic nanoarchitecture, which is the source of the structural coloration, may have been subjected to different evolutionary effects. The structural coloration of the four wings of 25 male individuals (100 samples for each species) was measured. Significant differences were found in the near UV wavelength region that are perceptible by these polyommatine butterflies but are invisible to human observers.

This graph shows the Reflection, Transmission, and Absorption of a 30 um thick nanocarbon-PLA (poly lactic acid) composite as the function of nanocarbon content for 30 GHz microwave radiation. The electromagnetic shielding efficiency increases with increasing amount of nanocarbon in the layer. 3D printing combined with hot pressing is a low cost method to create light-weight and enviromentally friendly electromagnetic shielding layers active in a broad frequency range.

We constructed a new type of light-weight material by 3D printing of nano-carbon doped plastic layers and pure plastic layers -- see the cross sectional optical microscopy image above. Sandwich structures containing only two nanocarbon layers already become not transparent to the microwaves. By such combination of conductive and dielectric materials we can easily realize photonic crystal like structures active in the microwave (GHz) and THz range. These studies serve as a basis for design and realization of optimal geometries of meta-surface type, in order to reach a high level of electromagnetic interference shielding performance for EM cloaking and EM ecology applications.

This image shows the color change of the butterfly scale in our vapor sensing experiments in the 3D chromaticity diagram using 7 vapors at 10 concentrations. We proved that a modification of the surface may offer a possibility to sensitize / desensitize the sensors for certain volatiles and to produce sensor arrays. Interestingly we found that the evaluation of color changes induced by the different vapors in the 3D visual space of the butterflies ( The role of structural colours as optical signals in species recognition of butterflies) and by Principal Component Analyis (PCA) results in alsmost perfectly coincident trajectories. It is remarkable that a color generating biologic nanoarchitecture, evolved in the scales, and its receptor: the butterfly eye, and a purely matehmatical algorithm yielded the very same result.

These images show the different response of butterfly wings upon cooling, depending on whether the color is given by a photonic nanostructure containing open nanovoids or a pigment. The effect is caused by water vapor condensation.

This pair of Scanning Tunneling Microscope (STM) images shows an ordered and a disordered grain boundary (GB) in graphene. (Ordered: J.Cervenka et al, disordered: our measurement). Such disordered GBs are often seen in graphene samples prepared by CVD, hence we studied their properties by experimental and theoretical methods. This is important for nanoelectronic applications of graphene.

Due to its high electron mobility and long coherence length, graphene is a promising material for next generation electronic devices. Patterning graphene with well controlled crystallographic orientation and atomically precise edges is very important for such applications. Formerly, we developed a method for producing graphene edges with zigzag orientation, and our new procedure makes it now possible to etch edges with armchair orientation.

L. Tapaszto and coworkers realized subnanometre-wavelength periodic ripples of suspended graphene membranes. The observed nanorippling mode violates the predictions of the continuum model. Nevertheless, microscopic simulations based on a quantum mechanical description of the chemical binding accurately describe the observed rippling mode. The ability of graphene to ripple down to subnanometre wavelengths can be exploited in strain-engineering graphene-based nanoelectronic and nanoelectromechanical devices beyond the boundaries set by continuum mechanics.

This image shows the number of graphene related publications for the years 1990-2011 in logarithmic scale. The fast evolution of research made possible the preparation of samples with arbitrary sizes. Available sample production techniques, combined with the right patterning tools, can be used to tailor the graphene sheet into functional nanostructures, even whole electronic circuits. Our review paper gives a survey of existing graphene patterning techniques and potential applications of related lithographic methods.

This animation (click to enlarge) shows the time evolution of an electron wave packet on the graphene surface. The wave packet is inserted from a simulated Scanning Tunneling Microscope tip (see the left image, a vertical cross section). The right image (horizontal cross section) shows a peculiar anisotropic dynamics, which may have important applications in future graphene nanodevices.

Theory has predicted rich and very distinct physics for graphene nanodevices with boundaries that follow either the armchair or the zigzag crystallographic directions. We have demonstrated that hexagonal holes obtained by anisotropic etching of graphene are bounded predominantly by zigzag edges which do not contribute to the D peak in Raman spectroscopy.