Session Y3: Novel Physics and Quantum Interference in Weakly Disordered Graphene Devices

Theoretical studies of quantum interference effects in graphene

We review the recently-developed theory of weak localization in monolayer and bilayer graphene [Phys. Rev. Lett. 97, 146805 (2006); Phys. Rev. Lett. 98, 176806 (2007)]. Owing to the chiral nature of electrons in a monolayer of graphite (graphene) one can expect weak antilocalization and a positive weak-field magnetoresistance in it. For high-density monolayer graphene and for any-density bilayers, the dominant factor affecting weak localization properties is trigonal warping of graphene bands, which reflects asymmetry of the carrier dispersion with respect to the center of the corresponding valley. The suppression of weak antilocalization by trigonal warping is accompanied by a similar effect caused by random- bond disorder (due to bending of a graphene sheet) and by dislocation/antidislocation pairs. As a result, weak localization in graphene can be observed only in samples with sufficiently strong inter-valley scattering due to atomically sharp scatterers or by edges in a narrow wire, reflected by a characteristic form of conventional negative magnetoresistance. We show this by evaluating the dependence of the magnetoresistance of graphene on relaxation rates associated with various possible ways of breaking a ``hidden'' valley symmetry of the system.   

Quantum interference in Epitaxial Graphene: Evidence for Chiral Electrons

The extraordinary transport properties of graphene originate from its unique band structure. Electrons in the band have chirality, which correlates the directions of the momentum and the psuedospin. This chirality prevents electrons from being back-scattered, hence causing a particular quantum phase coherent phenomenon, called weak-antilocalization. Recent theoretical work suggested that multilayer epitaxial graphene (EG) grown on SiC possesses essentially same band structure as single layer graphene because of the rotational stacking order between layers. We have investigated the magnetoresistance of EG. We found that weak anti-localization manifests itself as a broad cusp-like depression in the longitudinal resistance for magnetic fields 10 mT $B$ 5 T. An extremely sharp weak-localization resistance peak at $B=0$ is also observed. These features quantitatively agree with graphene weak-(anti)localization theory implying the chiral electronic character of the samples. Scattering contributions from the trapped char ges in the substrate and from trigonal warping due to the graphite layer on top are tentatively identified. The phase coherence length was found about 1 $\mu$m at 4.2 K and the main phase-breaking mechanism was $e-e$ scattering.   

Quantum Interference in Single and Bilayer Graphene

It is known that interference of charge carriers scattered by impurities results in a quantum correction to the conductivity of a two-dimensional (2D) system. This phenomenon of weak localisation (WL) is usually seen as magnetoconductivity, as magnetic field changes the phase of interfering waves. Here we show that quantum interference in graphene -- a single layer of carbon atoms [1] -- is very different from that in conventional 2D systems. Due to the \textit{chiral} nature of carriers, it becomes sensitive to different \textit{elastic} scattering mechanisms. By changing the geometry and quality of samples we show that quantum interference in graphene can take a variety of forms, and that WL is a sensitive tool to detect defects in graphene crystals [2]. We perform a comparative study of WL in single-layers and bilayers. Although the two systems are different in their spectrum (massless and massive fermions, respectively), the carriers in both are chiral. As a result WL in a bilayer is also affected by elastic scattering [3]. Analysis of the magnetoresistance using theories [4] allows us to determine the phase-breaking time as well as times of inter- and intra-valley scattering, which together control WL. They are found at different carrier densities, including the electro-neutrality point where the nominal carrier density is zero. We show that in all cases WL is not suppressed, and that the reason for this is strong inter-valley scattering. The study of WL is complemented by AFM imaging of the surface which provides information about the nature of the defects responsible for the different manifestations of WL in graphene systems. In addition to the studies of WL, we perform analysis of universal conductance fluctuations (UCF) in both systems. They have the same physical origin as WL -- quantum interference -- and are controlled by the same characteristic times. We compare the times found from analysis of WL and UCF. \newline [1] K.S. Novoselov \textit{et al}., Science \textbf{306}, 666 (2004) \newline [2] F.V.Tikhonenko \textit{et al.}, arXiv: 0708.1700 (to be published in Phys. Rev. Lett.) \newline [3] R.V. Gorbachev \textit{et al.}, Phys. Rev. Lett. \textbf{98}, 176805 (2007). \newline [4] E. McCann et al., Phys. Rev. Lett. \textbf{97}, 146805 (2006); K. Kechedzhi \textit{et al}., Phys. Rev. Lett. \textbf{98}, 176806 (2007).   

Experimental studies of conductance fluctuation and tunneling spectroscopy of weakly disordered graphene devices

We measured the conductance fluctuation and tunneling spectra of single-, bi- and trilayer graphene prepared by mechanical exfoliation. Reproducible fluctuations in conductance as a function of applied gate voltage or magnetic field were found in the electric transport measurements. As the Fermi energy was tuned to near the charge neutral point, the amplitude of the conductance fluctuation was suppressed quickly from a value consistent with universal conductance fluctuations, even though the devices were still well within the weakly disordered regime. The physical origin of the observed suppression may be related to the presence of edge states, or puddles of electrons or holes in graphene devices. The tunneling spectra of planar tunnel junctions of micron size were found to exhibit interesting features that evolve with the backgate voltage, temperature, and applied magnetic field. The implications of these observations will be discussed. This work is done in collaboration with Neal Staley, Conor Puls, and Haohua Wang.   

Excitations from Filled Landau Levels in Graphene

Recent experimental progress has allowed the fabrication of graphene, a two-dimensional honeycomb lattice of carbon atoms that forms the basic planar structure in graphite. Graphene exhibits a host of interesting properties that can be understood in terms of a non-interacting system whose single-particle excitations are described by the Dirac equation. What, then, is the role of the Coulomb interactions between electrons in graphene? In this talk, I will present a study of the collective excitations of graphene in the quantum Hall regime. These excitations open a window into the nature of Coulomb interaction effects and may be observable by optical spectroscopy. Such excitations are well-understood in the case of the standard two-dimensional electron gas (2DEG), in which the low-lying collective mode spectrum may be interpreted in terms of a single particle-hole pair bound into a stable exciton by Coulomb forces. Using a similar analysis for graphene, we find that, in spite of the linear electronic dispersion near the Dirac points, the exciton spectrum is qualitatively quite similar to that of the 2DEG. On the other hand, the additional pseudospin degree of freedom strongly enhances many-body corrections relative to the 2DEG case. We also find that the presence or absence of certain branches of the exciton spectrum is sensitive to the number of filled spin and pseudospin sublevels. Finally, I will discuss these results in relation to infrared spectroscopy measurements and comment on the screening of the Coulomb interaction in graphene.