Session K15: Transport in Graphene and 1D Structures

Unconventional 1/f noise in Graphene on SrTiO$_{\mathrm{3}}$ substrate

Electrical transport in graphene has been of great interest in both fundamental and applied research. The impact of the substrate is critical to the operation of graphene field effect transistors (FET), which can modify several transport parameters as well as low frequency 1/f noise. Replacing the usual SiO$_{\mathrm{2}}$/Si$^{\mathrm{++\thinspace }}$substrate with SrTiO$_{\mathrm{3\thinspace }}$[STO] having high dielectric constant, has opened up new possibilities, leading to large doping, higher mobility, and also hysteretic transfer characteristics for memory applications. We have studied 1/f noise in dual-gated single layer graphene (SLG) FET sandwiched between STO (substrate) and mechanically exfoliated hexagonal boron-nitride (dielectric for the top gate). The area normalized noise amplitude of SLG on STO followed an unexpected `W'-shape dependence of gate-bias with the central peak at Dirac point in conflict with the usual `V', `M' or `$\Lambda $'-type dependence of SLG noise on SiO$_{\mathrm{2}}$. We discuss possible microscopic mechanisms for such behavior, considering the role of puckering of oxygen atoms introducing inward dipole moments that can form a new source of electrostatically tunable scattering mechanism at the graphene-STO interface.   

1/f Noise in Gated Epitaxial Graphene Nanoribbons

Epitaxial Graphene Nanoribbons (EGNR) grown on sidewall SiC have gained interest as a high-quality interconnect enabling room temperature ballistic transport over micron lengths. To be useful as an interconnect a proper characterization of the noise level in the EGNR needs to be determined. Toward this end, we fabricated EGNR devices with an Aluminum-Oxide top gate and use field effect to tune the fermi energy in the graphene channel. Our studies of the electronic noise and its dependence on the charge density in the ribbon reveal information about the subband structure of the density of states in addition to the ribbon's spectral density at low frequencies. Comparisons to the widely reported 1/f noise in silicon and other forms of graphene provide strong references for analyzing our results.   

\textbf{Observation of insulating behavior and strong localization in suspended monolayer graphene}

Dirac point of graphene is known to be inaccessible due to the electron hole puddles which screen the neutrality point and makes the minimum conductance limited to the order of e$^{2}$/h. However, in extremely clean suspended graphene samples, there is a possibility to observe a diverging resistance approaching the charge neutrality point via yet to be understood localization or Boltzmann transport mechanism. We observe a resistance in excess of $10^{6}$Ohm near the charge neutrality point in a very high quality suspended monolayer graphene in the absence of magnetic field. The sample exhibits negative magnetoresistance indicating a strong localization effect at low charge carrier densities. The possible origins of these observations will be discussed in the context of the transport mechanisms mentioned above.   

Approaching Collimation with a Graphene-based Quantum Point Contact

Quantum point contacts (QPCs) are narrow constrictions on the order of the Fermi wavelength that bridge together two electrically conducting regions. QPCs display sensitive conductance quantization and are a classic playing field to illustrate clean, ballistic transport in low-dimensional materials. However, graphene-based QPCs are challenging to fabricate, in part due to two reasons: edge disorder that suppresses conductance quantization and imperfect gate depletion leading to charge puddles. Using graphene-boron nitride heterostructures, we demonstrate improvements over a simple etch and Au-gating method by introducing a protective alumina dielectric layer. We use this method to create two QPCs in series and explore potential electron-beam collimation at low magnetic field, in the spirit of Molenkamp (1990).   

Realizing 1-D conducting channel between oppositely gated regions in bilayer graphene.

The band gap of bilayer graphene (BLG) can be tuned by applying an external electric field perpendicular to the plane of a BLG sheet. If direction of the electric fields in two adjacent regions in BLG are opposite, one-dimensional (1-D) conducting channel emerges at the boundary between two regions with chiral nature. In this presentation, we introduce a method for fabricating two pairs of split-gates attached to BLG, which is sandwiched between two atomically clean hexagonal boron nitride (h-BN) single crystals and thus allows ballistic transport of carriers at least within the device size. Current-voltage characteristics show a large transport gap, which is comparable to the results obtained from optical measurements and numerical calculations. Opening the band gap in two adjacent regions of the BLG flake by oppositely gated electric fields, we observed metallic behavior in transport characteristics along the boundary between the two regions although the resistance of two gapped regions are a few hundreds of k$\Omega $. These results indicate that a 1-D conducting channel formed between the two regions where the induced band gaps were inverted to each other. The formation of this 1-D conducting channel mimics the topological edge conducting channels emerging at the boundary of a two-dimensional topological insulator and may be utilized for applying BLG to valleytronics   

Orientation-independent conductance step of graphene nanoribbons

Low-energy electronic structure of graphene is characterized by the states from two inequivalent valleys at K and K' points that have opposite chirality. In graphene nanoribbons (GNRs), the K and K' valleys, when projected into one-dimensional (1D) Brillouin zone, can be mixed due to the edge termination. The degree of mixing determines the electronic property of GNRs. However, non-valley mixing properties have been hardly observed so far. In this work, we made effective 1D transport channels by gate-defined carrier guiding. They exhibit a quantum conductance step of 4e2/h, which is the characteristic of non-mixed valleys. To verify these experimental results, we performed both first-principles and tight-binding calculations of GNRs with arbitrary axial orientations. Calculated band structures and quantum conductance of GNRs show zero-energy flat bands and a conductance step of 4e2/h except armchair-edge GNRs. We find that this is a consequence of generic zigzag-type boundary conditions of GNRs with arbitrary axial orientations except armchair-edge cases   

Theoretical Study of All-Electrical Quantum Wire Valley Filters in Bilayer Graphene

Graphene electrons carry valley pseudospin, due to the double valley degeneracy in graphene band structure.[1] In gapped graphene, the pseudospin is coupled to an in-plane electric field, through the mechanism of valley-orbit interaction (VOI),[2] Based on the VOI, a family of electrically-controlled valleytronic devices have been proposed. Here, we report the theoretical study of a recently proposed valley filter consisting of a Q1D channel in bilayer graphene defined and controlled by electrical gates. We discuss two types of calculations -- those of energy subband structure in the channel and electron transmission through a valley valve consisting of two proposed filters. For the former, we have developed a tight binding formulation in the continuum limit. For the latter, we employ the recursive Green's function method. Results from the calculations will be presented. References [1] Rycerz et al., Nat. Phys. 3, 172 (2007); Xiao et al., Phys. Rev. Lett. 99, 236809 (2007). [2] Wu et al., Phys. Rev. B 84, 195463 (2011); ibid B 86, 045456 (2012); ibid B 86, 165411 (2012); ibid B 88, 125422 (2013).   

Transport measurements in quasi-one dimensional graphene wires

ABSTRACT: Recent developments have enabled fabrication of high mobility graphene structures. The elastic mean free path in the 2D bulk of the graphene can be greater than ten microns, whereas the graphene can be patterned to widths of 1 micron or below. Thus, we can make structures for which bulk elastic scattering can be neglected. We experimentally study the role of other length scales, such as electron-electron scattering length, cyclotron length, and the width of the graphene ribbon, on transport properties.   

Near-field study of domain walls in bilayer graphene

Domain wall in bilayer graphene is emerging as a fascinating one-dimensional system due to the presence of structural soliton and electrically valley Hall boundary states. They are expected to process unusual electronic and optical properties because of the modification of atomic structures. We systematically study the bilayer graphene domain walls with different configurations including lines, circles and networks using scanning near-field optical microscopy (SNOM). The SNOM technique provides a convenient way to investigate domain walls in ambient condition. Our results suggest that bilayer graphene domain wall is an interesting and rich system for fundamental research about light-matter interactions.   

Optical signatures of a hypercritical 1D potential in a 2D Dirac metal

Generation of quasi-bound states in graphene near strong charged perturbations is a solid-state analog of atomic collapse of superheavy elements or particle production by hypothetical cosmic strings. We show, for the case of a linelike perturbation, that as the perturbation grows in strength, quasi-bound states are generated sequentially. Each of these critical events is signaled by a sharp change in the local optical conductivity. Tunable linelike perturbations can be realized in experiment using nanowire or nanotube electrostatic gates. We report measurements of local conductivity for such systems obtained through near-field optical microscopy.   

Electronic transport across linear defects in graphene

Graphene is being proposed for a variety of new electronic devices. However, the required high-quality electrical properties are affected by the formation of polycrystalline structures, which are practically unavoidable by the growth methods known so far. As such, the scattering problem of an electron off a grain boundary becomes relevant. We investigate the low-energy electronic transport across grain boundaries in graphene ribbons and in?nite ?akes. Using the recursive Green’s-function method, we compute the electronic transmittance across different types of grain boundaries in graphene ribbons and ?akes. We use the charge and current density spatial distributions to enhance our understanding of their electronic transport properties, and ?nd that electronic transport depends both on the grain boundaries’ microscopic details and on their orientation. We consider extended linear defects of type 585 and 5757, and also a spatial region where the grain boundary is composed by the superposition of two monolayer domains. In addition, we employ the transfer-matrix formalism to analytically study the electronic transport across a class of zigzag grain boundaries with periodicity 3. We ?nd that these grain boundaries give rise to intervalley scattering.   

Theoretical investigation of graphene on STO(111) surface

Graphene, a two-dimensional electronic system which consists of a single layer of graphite, is considered a possible candidate for nano-electronic applications as it has a very high electron mobility. One of the problems in realizing this in practice is the difficulty of doping. Using density functional theory we explore the possibility of field-doing graphene by placing a graphene sheet on a (111)-oriented SrTiO3 (STO) surface that is highly polar. We investigate the electronic structure of the system. Our results suggest that two conduction channels can form near the Fermi level. One is mainly composed of $\pi $-like carbon based orbitals, while the other is localized at the oxide surface.   

Critical Delocalization of Chiral Zero Energy Modes in Graphene

Graphene subjected to chiral-symmetric disorder is believed to host zero energy modes (ZEMs) resilient to localization, as suggested by the renormalization group analysis of the underlying nonlinear sigma model. We report accurate quantum transport calculations in honeycomb lattices with in excess of $\mathop {10}\nolimits^{9} $sites and fine meV resolutions. The Kubo dc conductivity of ZEMs induced by vacancy defects (chiral BDI class) is found to match $\mathop {\mathop {4e}\nolimits^{2} /(\pi h)}\nolimits $ within $1\% $ accuracy, over a parametrically wide window of energy level broadenings and vacancy concentrations. Our results disclose an unprecedentedly robust metallic regime in graphene, providing strong evidence that the early field-theoretical picture for the BDI class is valid well beyond its controlled weak-coupling regime.