GRAPHENE the first 2D crystal lattice

GRAPHENE the first 2D crystal lattice

dimensionality of carbon diamond, graphite GRAPHENE realized in 2004 (Novoselov, Science 306, 2004) carbon nanotubes fullerenes, buckyballs

what s so special about graphene? crystal honeycomb symmetry with two sublattices A and B - two atoms per unit cell - two conical points per Brillouin zone - band crossing at K and K -linear low-energy dispersion E = hv F k fermi velocity v F = 10 6 m -1 s -1

relativistic, massless Dirac fermions linear dispersion at the Dirac-point effective mass m* = 0 description rather with Dirac instead of Schrödinger equation: this is a spinor wavefunction in QED where the pseudospin σ indicates the sublattices A and B the projection of the pseudospin on the k-direction gives rise to a new internal degree of freedom: chirality many features of graphene are understood as conservation of chirality and pseudospin σ

graphene on Si/SiO 2 substrate etched into a Hall-bar structure charge transport in graphene resistance conductance universal quantum conductance minimum?

half-integer QHE graphene: half-integer QHE no plateau at zero energy Landau levels in the density of states bilayer graphene: integer QHE but N=0 plateau missing!

Klein paradox tunneling of relativistic particels through potential barriers with T =1 -barrier repulsive for electrons -but attractive for positrons magic angles for single and bilayer graphene therefore electrostatic definition of devices with metal gates is not possible!

mechanical cleavage peeling off layers of graphite with a sticky tape transfer onto substrate optical microscope image of resulting flakes

further steps - localisation of appropriate flakes with optical microscope - contacting with metal electrodes by e-beam lithographie -writing an etch-mask with e-beam lithographie - reactive ion etching with Ar/O 2 plasma - wire-bonding to contact pins and testing the device - further etching, if necessary to narrow the graphene structures

submicron device conductance measurements of a 250 nm graphene quantum dot @ T = 4K; typical V-shape with fluctuations inset: - CB oscillations in the low-conductance region - Coulomb diamonds E c = 3 mev periodic CB resonances of the same dot @ T= 0.3K V g = 16 mev

intermediate quantum dot CB peaks and Coulomb diamonds of a 40 nm graphene dot @ T = 4K; irregular spacing and height excited states are hardly visible at V b =10 mev δe = 10meV E = E c +δe large V g variation indicates the confinement energy beeing larger than E c due to δe = α/d for massless quasiparticels α =0.2-1.5 ev nm

chaotic Dirac billiards peak spacing histograms for different D: random position for D < 100 nm Dirac fermions confined to a ideal disk Poisson distribution of E observed: Gaussian unitary ensemble quantum chaos in Dirac billiards δe ~ 1/D 2 at relatively large diameters

quantum confinement dot D < 30 nm quantum confinement dominating levelspacing up to 50 mev excited states visible due to extremely narrow constrictions defining the quantum dots

room temperature graphene FET transistor action of ~ 1nm constriction device at room temperature level spacing: ~ 0.5 ev

large gaps for narrow constrictions quantum point contacts mesoscopic fluctuations in conductance QPC transparencies limit the CB region of the quantum dots

CONCLUSION graphene is a great material there s a lot of work to be done Thank You!