Session D11: Focus Session: Graphene Structure, Stacking, Interactions: Mesoscopics

Electronic localization in rotated graphene multi-layer

Rotated graphene bilayers show an interesting electronic structure with a tendency to layer decoupling at large rotation angles and a stronger electronic mixing at small angles, associated with a strong decrease of the velocity ([1] and Refs. therein). These inter-layer mixed states allow us [2] to address the long lasting problem of the origin of the Moir\'{e} pattern observed on STM images. For large and intermediate rotation angles, we present analytical and numerical studies of the local density of states in the Moir\'{e} that compare well to STM spectra. For very small angles, the inter-layer mixed states ultimately lead to electronic confinement in AA stacking regions in an energy range close to the Dirac point. In graphene multi-layer (up to 10 layers) containing twisted intercalated layers [3], we found both bands with a strong velocity reduction, and bands without velocity reduction. This could explain [2] why velocity renormalization is not observed experimentally in rotated multi-layers on SiC [3,4]. \\[4pt] [1] G. Trambly de Laissardi\`{e}re et al., Nano Lett. 10, 804 (2010). \\[0pt] [2] G. Trambly de Laissardi\`{e}re et al., in preparation. \\[0pt] [3] M. Sprinkle et al., J. Phys. D: Appl. Phys. 43, 374006 (2010). \\[0pt] [4] M. Sprinkle et al., Phys. Rev. Lett. 103, 226803 (2009).   

Interferences and Fabry-Perot Oscillations in ABA Trilayer Graphene

ABA trilayer graphene (TLG) is a 2D system with multiple sub-bands which can be divided into one monolayer graphene-like sub-band and one bilayer graphene-like sub-band, therefore comprising a system wherein massive and massless bands coexist. Here, we study electronic transmission in the ballistic regime through a 70nm-wide tunable electrostatic potential barrier on exfoliated ABA trilayer graphene encapsulated by hexagonal Boron Nitride. We report Fabry-Perot oscillations of the conductance caused by multiple reflections of the charges in the potential barrier, and we also present a study of their magneto dependence.   

Quantum Pumping in Graphene Nanoribbons

The interest in the development of devices at the nanoscale has intensified the search for mechanisms that provide control of transport properties while reducing effects of heat dissipation and contact resistance. Charge pumping, in which dc currents are generated in open-quantum systems by applying local de-phased time-dependent potentials, may achieve these goals. We analyze the properties of non-equilibrium zero-bias currents through nano-ribbons using a tight-binding Hamiltonian and the Keldysh formalism beyond the adiabatic and perturbative regimes. Using a numerical implementation with two local single-harmonic time-dependent potentials, we first contrast results for 1d and 2d metallic systems (square lattice). Next, we focus on quasi-1d systems and graphene ribbons, and discuss the role of reservoirs. We analyze the dependence of the dc pumped current as a function of different parameters such as chemical potential, pumping amplitude, and frequency. We observe a considerable increase of pumped current with the dimensionality of the system. Furthermore, we show that lattice mismatch with reservoirs favors the pumping mechanism for graphene ribbons.   

Conductance fluctuations in graphene as a probe of broken-symmetry and fractional quantum Hall states

The observation in macroscopic transport studies of the interaction induced broken symmetry and fractional quantum Hall states in graphene normally requires very clean samples and/or strong magnetic fields. Here we report that even when these fragile states are not developed well enough to produce any of the quantum Hall signatures, they are strongly visible in differential conductance fluctuations that appear as a result of charge carrier localization when the system breaks up into compressible islands with incompressible areas in between when the corresponding integer or fractional filling factor is approached. The conductance fluctuations give access to local information even though a macroscopic measurement is performed. The existence of a landscape of compressible islands is unambiguously proved in Coulomb blockade phenomena in the quantum Hall insulating regime where all other conduction channels are switched off. This work has been carried in collaboration with D.S. Lee, V. Skakalova, R.T. Weitz, K. von Klitzing.   

Interference of electronic states between the two misoriented crossed graphene nanoribbons

In a twisted bilayer graphene, where one layer is rotated with respect to the other one, for rotation angles more than 20 degrees each layer remains electronically decoupled even though they are vertically separated by only a fraction of a nanometer. A relative rotation between two graphene nanoribbons (GNRs), with one place on top of the other, creates a crossed GNR (xGNR) with an overlap region that is neither AA nor AB stacking. The geometry of the overlap region of the xGNR is that of a twisted bilayer graphene. Calculations, based on the extended Huckel theory and the non-equilibrium Green's function formalism, show that the electronic states of the individual GNRs of an unbiased xGNR are decoupled from each other similar to the decoupling that occurs in a twisted bilayer graphene. The decoupling occurs due to the quantum mechanical interference between the electronic states of the individual GNRs. This results in a strong suppression of inter-GNR transmission over a large energy of window. The transmission is, however, a strong function of the potential difference between the GNRs and the atomistic geometry of the overlap region which depends on relative translation and rotation angle between the GNRs. Thus, a bias can be used to control the inter-GNR current.   

Gap opening in graphene by 1D and 2D periodic corrugations

Using first-principles methods and symmetry arguments, we show that a graphene monolayer, which is periodically corrugated in one or two direction(s), can be either semimetal or semiconductor, depending on how strong corrugation is or how the initial symmetry is broken. In the case of 1D periodic ripples, a gap at the Dirac points opens up only due to (i) breaking of the inversion symmetry or equivalence between A and B sublattices and/or (ii) merging of two inequivalent Dirac points, \textbf{D} and -\textbf{D}. Since breaking the inversion symmetry has only relatively modest effect, a tangible gap can be mainly induced by mutual annihilation of the Dirac points, which requires large corrugations, close to mechanical breaking point. In contrast to 1D, the 2D ripples can additionally induce a semiconducting gap via mixing of electronic states belonging to two different $\textbf{K}$, \textbf{K}$'$ valleys. In this case, a gap on the order of 0.5 eV can be opened up at strains safely lower than the graphene failure strain [1]. \\[4pt] [1] I.I. Naumov, A.M. Bratkovsky, arXiv:1104.0314v1.   

Electronic structure and energetics of graphene antidot lattice

We have made a systematic study of the electronic structure and the energetics of graphene with periodic array of vacancy clusters (graphene antidot lattice) in the framework of the density-functional theory (DFT). We find that the electronic property of the system is well controlled by its lattice periodicity. More specifically, this system can be either metallic or semiconducting, depending on its lattice geometry. Interestingly, some of them are predicted to be direct-gap semiconductors. For example, graphene sheet with high-symmetry arrangements of periodic circle-shape vacancies always has a direct fundamental gap [1]. The DFT total-energy calculations indicate that the geometry of hole edges plays an important role in determining its stability. [1] ``Electronic properties of graphene and boron-nitride based nanostructured materials'' M. Sakurai, Y. Sakai, and S. Saito, J. Phys.: Conf. Ser. 302 (2011) 012018.   

Localization and Conductivity of Graphene with Adsorbates

We compute the conductivity of graphene for two models of resonant and non resonant adsorbates. Away from the Dirac point the conductivity is well given by the semi-classical Drude formula and localization lengths are exponentially large. For some energies, near the Dirac point, the conductivity is well represented by $\sigma \simeq $4e$^{2}$/$\pi $h-$\alpha $Log(Li/Le) as a function of the inelastic scattering length Li and the elastic mean free path Le $<$ Li. This implies a magneto-conductivity that varies also linearly with Log(B) where B is the magnetic field. Our results suggest that the divergence of the localization length which is expected close to the Dirac point affects only a narrow energy region.   

Effects of disorder on recombination and relaxation processes via acoustic phonons in graphene

Recombination and relaxation processes via acoustic phonons are allowed in a disordered graphene because of violation of the energy-momentum conservation requirements. These processes are analyzed taking into account the interference of electron-phonon and electron-impurity scattering mechanisms. The recombination and relaxation rates are calculated for the cases of intrinsic and heavily-doped graphene. The transient evolution of nonequilibrium carriers is described by the exponential fit dependent on doping conditions and disorder level. The obtained electron recombination and relaxation rates are compared with available experimental data. [1] F. Vasko et al., Phys. Rev. B 84, 155445 (2011).   

Phase coherent states in graphene heterostructure with chiral asymmetry

The chiral nature of the fermionic excitations in graphene, bilayer graphene, and topological insulators, induces unique electronic properties in these materials. In bilayer heterostructures the interlayer interaction can induce the formation of an interlayer phase coherent state. An interesting class of heterostructures is constituted by bilayers in which the electrons in the two layers have different chirality. An example of such a system that can be realized experimentally is the heterostructure formed by single layer graphene and bilayer graphene. In this talk I will discuss the conditions for the realization of an interlayer phase-coherent state in chiral-asymmetric heterostructures. In particular I will show how the voltage difference between the two layers affects the conditions for the realization of the phase coherent state, and its properties. I will then discuss the relevance for experiments of our results.   

Visualizing Electronic Chirality and Berry's Phases in Graphene Systems Using Photoemission with Circularly Polarized Light

Electronic chirality near the Dirac point is a key property of graphene systems, which is revealed by the spectral intensity patterns as measured by angle-resolved photoemission spectroscopy under various polarization conditions. Specifically, the strongly modulated circular patterns for monolayer (bilayer) graphene rotate by +-90 degrees (+-45 degrees) in changing from linearly to circularly polarized light; these angles are directly related to the phases of the wave functions and thus visually confirm the Berry's phase of pi (2pi) around the Dirac point. The details are verified by calculations.   

Electronic Properties of Curved Graphene-Ring Structures

Recently, deformed graphene in the form of bubbles have been produced on different substrates in a variety of controllable shapes [1]. These findings raise the possibility of changing the electronic properties of these structures allowing for band-structure engineering. We have undertaken a study of the electronic properties of graphene-ring systems with circularly symmetric Gaussian curvature in the Dirac approximation. We obtain energy spectra and wave functions using perturbation theory on the gauge field amplitude describing the curvature. We further analyze the competition between curvature-induced magnetic field and real external fields and the resulting persistent currents generated in their presence. As expected, the results depend on the boundary conditions describing the confined ring edges. In addition, we discuss the effects of the angular asymmetry in the probability density due to the curvature [2] on single rings and more complex confined annular geometries.\\[4pt] [1] T. Georgiou et al., APL 99\\[0pt] [2] Wakker et al., PRB 84.