Session X25: Focus Session: Graphene XVII: p-n Junctions, Nanoribbons, and Quantum Dots

Theoretical investigations of deformed graphene nanoribbons

Graphene nanoribbons (GNRs) have attracted considerable attention in the last two years. Recent experimental work [Science, 319, 1229 (2008)] has reported semiconducting GNRs with width of a few nanometers and suitable band gap widths for electronic applications. One desirable aim in the investigation of GNRs is to control their electronic properties. It has been proposed, for instance, that chemical edge modifications or external strain can modify their electronic properties. In this work, we report density functional calculations for GNRs with structural and topological deformations. In particular, we investigate modifications of the electronic structure as a function of those defornations. Finally, we study the effect of a transverse electric field in those ribbons.   

Quantum Dot Behavior in Graphene Nanoconstrictions

Graphene nanoribbons have been proposed as novel high-frequency transistors due to their high mobility and transport gap that scales inversely with width. In order to understand the origin of the transport gap in long nanoribbons, we measure transport through short side-gated nanoconstrictions. Unlike in long ($\geq$250 nm) nanoribbons, where we observe transport through multiple quantum dots in series, shorter ($\leq$60 nm) constrictions display behavior characteristic of single and double quantum dots. We find that dot size scales with constriction width. In the narrowest short constrictions, high on/off ratios are achievable, while in wider ($\geq$35 nm) constrictions we observe quantum dot behavior overlaid on a highly conducting background. We hypothesize that the metal side gates in close proximity to our short constrictions suppress the importance of edge disorder, and compare constrictions fabricated with and without metal side gates. We propose a model where transport occurs through quantum dots nucleated by disordered background potential in the presence of a confinement gap.   

Interaction effects in graphene p-n junctions

We review our recent analytical and numerical studies of a new class of graphene devices: lateral p-n junctions. Such structures are realized experimentally by modulating the electron density in graphene samples with external gates. Our theory describes the charge density distribution, the electric field profile, and the resistance of such p-n junctions. The proper treatment of the electrostatic screening beyond the linear order is crucial for obtaining correct results for all these quantities. In particular, the electric field at the interface of the electron and hole regions is strongly enhanced due to limited screening capacity of Dirac vacuum. This nonlinear screening effect can significantly reduce the junction resistance. It is necessary to include it in order to obtain a good agreement with the experiments. More subtle interaction effects such as the Bragg reflection of quasiparticles on Friedel oscillations near the p-n interface are also discussed.   

Effect of Shape on Electronic and Magnetic Properties of Graphene Nanoribbons (GNRs)

We have studied electronic and magnetic properties of grapheme nano-structures with different shapes. In particular, we have studied both zigzag and armchair graphene nanoribbons (GNR) of triangular shape using density functional method. We find electronic and magnetic properties of triangular structures are drastically different from their rectangular counterparts and our results suggest that, in addition to size effect, shape of the structure has a large impact on the underlying intrinsic electronic properties of GNRs. We will compare our results with available experiments.   

Probing the transport gap in edge disordered graphene nanoribbons

We present experimental studies on the detailed nature of the transport gap observed in etched graphene nanoribbons. Temperature dependent measurements of electronic transport in the ``gapped'' region of suppressed conductance suggest transport via localized states or charge islands, giving rise to separate energy scales for hopping conductance and the transport gap. Distinct temperature regimes with different exponential temperature dependences are observed, with a crossover temperature dependent on ribbon width. A transition to ``bulk'' graphene electronic behavior is observed for wider ribbons, and the size of the transport gap shows a length dependence consistent with conduction due to hopping.   

Role of edge states in graphene nano-ribbons: - DFT studies

We present first principle calculations to study the effect of edge states in graphene nano-ribbons. Spin restricted calculations for graphene nano-ribbons were performed using ground state density functional theory. The plot of electron localization function corresponding to the edge dangling bonds has revealed highly reactive edge states in graphene nano-ribbons. The reactivity of the nano-ribbons with respect to the edge structure is discussed. This study has been supplemented by band structure studies in armchair and zigzag edged graphene nano-ribbon systems. This work is supported in part by NSF DMR-0512196.   

Electronic properties of Graphene quantum dots

We study electronic properties of Graphene quantum dots in magnetic fields. Graphene quantum dots are atomically thick nanometer-scale islands constructed by connecting benzene molecules. Quantum dots with triangular and hexagonal shape have shown to have different edge properties [1,2], and triangular zig-zag structures have recently attracted attention due to their half-filled zero-energy edge states. In this work, we investigate electronic and magnetic properties of triangular and hexagonal shaped islands. We study the effect of first and second nearest neighbour interactions, magnetic field and the number of atoms on the single-particle properties using a tight-binding model. We then use configuration interaction method to study the effect of electron-electron interactions on the ground state properties including magnetization, excitation spectra, and their effect on Coulomb blockade and tunneling through graphene islands. [1] J. Fernandez-Rossier and J.J. Palacios, Phys.Rev.Lett. {\bf 99}, 177204 (2007), [2] M. Ezawa, Phys.Rev.B, {\bf 77}, 155411 (2008).   

Charge transport in ballistic multiprobe bilayer graphene dots.

We present a numerical analysis of the transport properties of the bilayer graphene quantum dots attached to multiple leads. In the framework of the tight binding model and using the nonequilibrium Green's function technique, we study numerically effects due to: magnetic fields, bias voltage between the layers, geometrical shape, and the arrangement of the attachments of the leads to the device. The results are compared to those obtained for similar quantum dot structures made from a graphene monolayer.   

Graphene Josephson Qubit

We propose to combine the advantages of graphene, such as easy tunability and long coherence times, with Josephson physics to manufacture qubits. These qubits can either be built around a 0 and $\pi$ junction and controlled by external flux or a d- wave Josephson junction can itself be tuned via a gate voltage to create superpositions between macroscopically degenerate states. We show that ferromagnets are not required for realizing $\pi$ junction in graphene, thus considerably simplifying its physical implementation. We demonstrate that one qubit gates, such as arbitrary phase rotations and the exchange gate, can be implemented easily.   

Quantum Transport in Graphene pnp Junctions with Contactless Top Gates

Graphene offers the unique opportunity to explore relativistic physics in a condensed matter system. One such example is the phenomenon of klein tunneling in graphene pnp junctions. By using a contactless top gate, we are able to fabricate very high quality pnp junctions, and perform electrical transport spectroscopy measurements in zero and finite magnetic fields. We observe oscillations in conductance of the pnp junction and changes in magnetoresisitance. Latest experimental progress and comparison with theoretical predictions will be discussed.   

Systematic study of the transport gap and localization in graphene nanoribbons of varying lengths

Recent studies of very short graphene nanoconstrictions\footnote{Ponomarenko, L. A.; Schedin, F.; Katsnelson, M. I.; Yang, R.; Hill, E. W.; Novoselov, K. S.; Geim, A. K. Science \textbf{2008}, 320, 356-358.} have found that short constrictions lack the large transport gap displayed by longer nanoribbons, implying that localization behavior plays a critical role in the transport gap. We present transport measurements on graphene nanoribbons of constant width and varying length and report on gap characteristics and Coulomb blockade behavior. We discuss the relevant theoretical models and compare their predictions to our data.   

Signatures of classical chaos in gate-defined graphene quantum dots

A generic, non-integrable, gate-potential can not confine electrons in graphene. Integrable gate-defined quantum dots, in contrast, do have well defined bound states. This difference between integrable and non-integrable graphene quantum dots is revealed in e.g. the two terminal conductance, whose dependence on the gate potential strength is starkly different for the two cases.   

Quantum Hall Effect in Two-Terminal Graphene Devices.

We report on transport measurements in the quantum Hall regime of two-terminal single and bilayer graphene devices. The mixture of the longitudinal and transverse conductivities in the two-terminal geometry results in departures from the expected conductance values on the Hall plateaus and are found to be device-geometry dependent. The experimental results are compared to theory and discrepancies are discussed. Research supported in part by INDEX, an NRI Center, and by the Harvard NSEC.   

New Computational Approach to Electron Transport in Irregular Graphene Nanostructures

For novel graphene devices of nanoscale-to-macroscopic scale, many aspects of their transport properties are not easily understood due to difficulties in fabricating devices with regular edges. Here we develop a framework to efficiently calculate and potentially screen electronic transport properties of arbitrary nanoscale graphene device structures. A generalization of the established recursive Green's function method is presented, providing access to arbitrary device and lead geometries with substantial computer-time savings. Using single-orbital nearest-neighbor tight-binding models and the Green's function-Landauer scattering formalism, we will explore the transmission function of irregular two-dimensional graphene-based nanostructures with arbitrary lead orientation. Prepared by LBNL under contract DE-AC02-05CH11231 and supported by the U.S. Dept. of Energy Computer Science Graduate Fellowship under grant DE-FG02-97ER25308.