Bound states and magnetic field-induced valley splitting in gate-tunable graphene quantum dots

The magnetic field dependence of energy levels in gapped single- and bilayer graphene quantum dots (QDs) defined by electrostatic gates is studied analytically in terms of the Dirac equation. Due to the absence of sharp edges in these types of QDs, the valley degree of freedom is a good quantum number. We show that its degeneracy is efficiently and controllably broken by a magnetic field applied perpendicular to the graphene plane. This opens up a feasible route to create well-defined and well controlled spin- and valley-qubits in graphene QDs. We also point out the similarities and differences in the spectrum between single- and bilayer graphene quantum dots. Striking in the case of bilayer graphene is the anomalous bulk Landau level (LL) that crosses the gap which results in crossings of QD states with this bulk LL at large magnetic fields in stark contrast to the single-layer case where this LL is absent. The tunability of the gap in the bilayer case allows us to observe different regimes of level spacings directly related to the formation of a pronounced ``Mexican hat'' in the bulk bandstructure. We discuss the applicability of such QDs to control and measure the valley isospin and their potential use for hosting and controlling spin qubits.Comment: 12 pages, 10 figure

Edge state transport through disordered graphene nanoribbons in the quantum Hall regime

The presence of strong disorder in graphene nanoribbons yields low-mobility diffusive transport at high charge densities, whereas a transport gap occurs at low densities. Here, we investigate the longitudinal and transverse magnetoresistance of a narrow (60 nm) nanoribbon in a six-terminal Hall bar geometry. At B= 11 T, quantum Hall plateaux appear at $\sigma_{xy}=\pm2e^2/h$, $\pm6e^2/h$ and $\pm10e^2/h$, for which the Landau level spacing is larger than the Landau level broadening. Interestingly, the transport gap does not disappear in the quantum Hall regime, when the zero-energy Landau level is present at the charge neutrality point, implying that it cannot originate from a lateral confinement gap. At high charge densities, the longitudinal and Hall resistance exhibit reproducible fluctuations, which are most pronounced at the transition regions between Hall plateaux. Bias-dependent measurements strongly indicate that these fluctuations can be attributed to phase coherent scattering in the disordered ribbon.Comment: experimental paper; 4 pages, 4 figure

Electrostatic confinement of electrons in graphene nano-ribbons

Coulomb blockade is observed in a graphene nanoribbon device with a top gate. When two pn junctions are formed via the back gate and the local top gate, electrons are confined between the pn junctions which act as the barriers. When no pn junctions are induced by the gate voltages, electrons are still confined, as a result of strong disorder, but in a larger area. Measurements on five other devices with different dimensions yield consistent results.Comment: 4 figures, 1 table, 4.4page

Robustness of the optical-conductivity sum rule in Bilayer Graphene

We calculate the optical sum associated with the in-plane conductivity of a graphene bilayer. A bilayer asymmetry gap generated in a field-effect device can split apart valence and conduction bands, which otherwise would meet at two K points in the Brillouin zone. In this way one can go from a compensated semimetal to a semiconductor with a tunable gap. However, the sum rule turns out to be 'protected' against the opening of this semiconducting gap, in contrast to the large variations observed in other systems where the gap is induced by strong correlation effects.Comment: 6 pages, 3 figures. Final versio

Electrical observation of a tunable band gap in bilayer graphene nanoribbons at room temperature

We investigate the transport properties of double-gated bilayer graphene nanoribbons at room temperature. The devices were fabricated using conventional CMOS-compatible processes. By analyzing the dependence of the resistance at the charge neutrality point as a function of the electric field applied perpendicular to the graphene surface, we show that a band gap in the density of states opens, reaching an effective value of ~sim50 meV. This demonstrates the potential of bilayer graphene as FET channel material in a conventional CMOS environment.Comment: 3 pages, 3 figure

Quantum Hall effect in narrow graphene ribbons

The edge states in the integer quantum Hall effect are known to be significantly affected by electrostatic interactions leading to the formation of compressible and incompressible strips at the boundaries of Hall bars. We show here, in a combined experimental and theoretical analysis, that this does not hold for the quantum Hall effect in narrow graphene ribbons. In our graphene Hall bar, which is only 60 nm wide, we observe the quantum Hall effect up to Landau level index k=2 and show within a zero free-parameter model that the spatial extent of the compressible and incompressible strips is of a similar magnitude as the magnetic length. We conclude that in narrow graphene ribbons the single-particle picture is a more appropriate description of the quantum Hall effect and that electrostatic effects are of minor importance.Comment: RevTex, 5 pages, 4 figures (matches published version

Graphene made easy: high quality, large-area samples

We show that by using an original method, bulk graphite can be bonded onto borosilicate glass or potentially any insulating substrate with ionic conductivity and then cleaved off to leave single or few layer graphene on the substrate, identified optically and with Raman spectroscopy. This simple, inexpensive and fast method leads to the preparation of large area graphene and single or few-layer films of layered materials in general. We have prepared mm size few-layer graphene samples and also measured I-V characteristics in a FET. This opens up perspectives both for fundamental research as well as for applications.Comment: 11 pages, 4 figures,Solid State Communications, In pres

The optical conductivity of graphene in the visible region of the spectrum

We compute the optical conductivity of graphene beyond the usual Dirac cone approximation, giving results that are valid in the visible region of the conductivity spectrum. The effect of next nearest neighbor hoping is also discussed. Using the full expression for the optical conductivity, the transmission and reflection coefficients are given. We find that even in the optical regime the corrections to the Dirac cone approximation are surprisingly small (a few percent). Our results help in the interpretation of the experimental results reported by Nair {\it et al.} [Science {\bf 320}, 1308 (2008)].Comment: 8 pages, 6 figure

Accessing the transport properties of graphene and its multi-layers at high carrier density

We present a comparative study of high carrier density transport in mono-, bi-, and trilayer graphene using electric-double-layer transistors to continuously tune the carrier density up to values exceeding 10^{14} cm^{-2}. Whereas in monolayer the conductivity saturates, in bi- and trilayer flling of the higher energy bands is observed to cause a non-monotonic behavior of the conductivity, and a large increase in the quantum capacitance. These systematic trends not only show how the intrinsic high-density transport properties of graphene can be accessed by field-effect, but also demonstrate the robustness of ion-gated graphene, which is crucial for possible future applications.Comment: 4 figures, 4 page

The cultural dimension of uncertainty avoidance impacts police-civilian interaction

This research examines how the cultural dimension of uncertainty avoidance—a person’s (in)tolerance for uncertain or unknown situations—impacts communication alignment in crisis negotiations. We hypothesized that perpetrators high on uncertainty avoidance would respond better to negotiators who use formal language and legitimize their position with reference to law, procedures, and moral codes. Data were transcriptions of 53 negotiations from a Dutch–German police training initiative, where police negotiators interacted with a high (German) and low (Dutch) uncertainty-avoidant mock perpetrator. Consistent with accounts of cross-cultural interaction, negotiators tended to achieve more alignment in within-culture interactions compared to cross-cultural interactions. Moreover, German negotiators, who scored higher on uncertainty avoidance than the Dutch negotiators, were found to use more legitimizing messages and more formal language than their Dutch counterparts. Critically, irrespective of the negotiators cultural background, the use of these behaviors was a significant moderator of the degree to which negotiator and perpetrator aligned their communicative frames: Using legitimizing and formal language helped with German perpetrators but had no effect on Dutch perpetrators. Our findings show the effects of cultural background on communication alignment and demonstrate the benefits of using more formal language and messages that emphasize law and regulations when interacting with perpetrators high on uncertainty avoidanc