Confinement of Dirac electrons in graphene quantum dots

Jolie, Wouter; Craes, Fabian; Petrović, Marin; Atodiresei, Nicolae; Caciuc, Vasile; Blügel, Stefan; Kralj, Marko; Michely, Thomas; Busse, Carsten

doi:10.1103/physrevb.89.155435

Cited by 37 publications

(52 citation statements)

References 36 publications

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“…302 In a recent experiment, the graphene was intercalated by oxygen in order to exclude the influence of surface states of the iridium. 304 Interestingly, one experiment also showed that the modulation of the LDOS did not depend on the type of the edge. 301 …”

Section: Cvd Grown Graphene Islandsmentioning

confidence: 94%

“…[300][301][302][303][304] Besides mapping the topology of the graphene islands, the local density of states (LDOS) was probed as a function of position. [300][301][302][303][304] A modulation of the LDOS with position and dot geometry was found and interpreted as influences from quantum confinement 300,301,303,304 or as the observation of the wave function. 302 In a recent experiment, the graphene was intercalated by oxygen in order to exclude the influence of surface states of the iridium.…”

Section: Cvd Grown Graphene Islandsmentioning

confidence: 99%

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Localized charge carriers in graphene nanodevices

Bischoff

Varlet

Simonet

et al. 2015

Applied Physics Reviews

100

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Graphene—two-dimensional carbon—is a material with unique mechanical, optical, chemical, and electronic properties. Its use in a wide range of applications was therefore suggested. From an electronic point of view, nanostructured graphene is of great interest due to the potential opening of a band gap, applications in quantum devices, and investigations of physical phenomena. Narrow graphene stripes called “nanoribbons” show clearly different electronical transport properties than micron-sized graphene devices. The conductivity is generally reduced and around the charge neutrality point, the conductance is nearly completely suppressed. While various mechanisms can lead to this observed suppression of conductance, disordered edges resulting in localized charge carriers are likely the main cause in a large number of experiments. Localized charge carriers manifest themselves in transport experiments by the appearance of Coulomb blockade diamonds. This review focuses on the mechanisms responsible for this charge localization, on interpreting the transport details, and on discussing the consequences for physics and applications. Effects such as multiple coupled sites of localized charge, cotunneling processes, and excited states are discussed. Also, different geometries of quantum devices are compared. Finally, an outlook is provided, where open questions are addressed.

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Section: Cvd Grown Graphene Islandsmentioning

confidence: 94%

Section: Cvd Grown Graphene Islandsmentioning

confidence: 99%

Localized charge carriers in graphene nanodevices

Bischoff

Varlet

Simonet

et al. 2015

Applied Physics Reviews

100

View full text Add to dashboard Cite

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“…Modifying the properties of Gr/Ir(111) by intercalation of atoms or molecules has been proven to be a straightforward and versatile concept. 7,18 Third, oxygen intercalation, with oxygen strongly bound to the substrate, effectively decouples Gr from its substrate, making its properties very close to those of freestanding Gr. First, oxygen has the potential to strongly interact with Gr under a variety of conditions leading to processes like combustion 16 or graphene oxide formation.…”

Section: Introductionmentioning

confidence: 99%

Oxygen orders differently under graphene: new superstructures on Ir(111)

et al. 2016

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Using scanning tunneling microscopy, the oxygen adsorbate superstructures on bare Ir(111) are identified and compared to the ones formed by intercalation in between graphene and the Ir(111) substrate. For bare Ir(111) we observe O-(2 × 2) and O-(2 × 1) structures, thereby clarifying a persistent uncertainty about the existence of these structures and the role of defects for their stability. For the case of graphene-covered Ir(111), oxygen intercalation superstructures can be imaged through the graphene monolayer by choosing proper tunneling conditions. Depending on the pressure, temperature and duration of O2 exposure as well as on the graphene morphology, O-(2 × 2), O-(√3×√3)-R30°, O-(2 × 1) and O-(2√3 × 2√3)-R30° superstructures with respect to Ir(111) are observed under the graphene cover. Two of these structures, the O-(√3 × √3)-R30° and the (2√3 × 2√3)-R30° structure are only observed when the graphene layer is on top. Phase coexistence and formation conditions of the intercalation structures between graphene and Ir(111) are analyzed. The experimental results are compared to density functional theory calculations including dispersive forces. The existence of these phases under graphene and their absence on bare Ir(111) are discussed in terms of possible changes in the adsorbate-substrate interaction due to the presence of the graphene cover.

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“…To elucidate this, consider a hypothetical graphene electron that is stripped of its spinor structure and instead has a scalar wavefunction. Such a particle would mimic a massless, spinless particle, and thus could be described by the Klein-Gordon equation 9 , which has effectively described finite-sized GQD islands [30][31][32][33] . In similar fashion to our previous Dirac calculations, we solve the Klein-Gordon equation in the presence of a potential step (Supplementary Information) for the GQD in Fig.…”

mentioning

confidence: 99%

“…This is the first reported visualization of quasi-bound Dirac electrons at sharp, step-potential n-p junctions. Previous STM experiments have studied finite-sized patches of chemical vapour deposition (CVD)-grown GQDs on the surface of Ir(111) [30][31][32][33] . We stress that the origin of the quantized states in these prior studies is due to quantum size effects from the finite extent of the graphene flake.…”

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confidence: 99%

Klein tunnelling and electron trapping in nanometre-scale graphene quantum dots

et al. 2016

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Relativistic fermions that are incident on a high potential barrier can pass through unimpeded, a striking phenomenon termed the 'Klein paradox' in quantum electrodynamics. Electrostatic potential barriers in graphene provide a solid-state analogue to realize this phenomenon. Here, we use scanning tunnelling microscopy to directly probe the transmission of electrons through sharp circular potential wells in graphene created by substrate engineering. We find that electrons in this geometry display quasi-bound states where the electron is trapped for a finite time before escaping via Klein tunnelling. We show that the continuum Dirac equation can be successfully used to model the energies and wavefunctions of these quasi-bound states down to atomic dimensions. We demonstrate that by tuning the geometry of the barrier it is possible to trap particular energies and angular momentum states with increased e ciency, showing that atomic-scale electrostatic potentials can be used to engineer quantum transport through graphene.A ccording to the Dirac equation, massless fermions pass unimpeded through arbitrary potential barriers at normal incidence, a phenomenon termed Klein tunnelling 1,2 . The band structure of graphene, a single layer of carbon atoms in a honeycomb lattice, provides a solid-state analogue to this effect 3-9 which is uniquely amenable to direct scanned probe measurements. Klein tunnelling arises from two fundamental properties of graphene. First, the spectrum of states is gapless 10 -regardless of the energy of the incident electron, quantum states always exist across the barrier for the electron to transition into. Second, due to the honeycomb structure of the graphene lattice, the wavefunctions of graphene are two-component spinors with amplitudes on each of the sublattices 10 . Conservation of this sublattice isospin degree of freedom in the tunnelling process is directly responsible for the high transmissibility of electrons at normal incidence 3 . At oblique incidence, however, both reflection and transmission can occur at the barrier, with reflection becoming dominant at large incidence angles 3,4 . The unique nature of Klein tunnelling and the related phenomenon of negative refraction has been proposed as a building block to steer, and even confine, electrons by the use of cleverly designed barriers 5,6,11 . Signatures of these phenomena have been seen in transport 12-14 experiments on graphene devices incorporating electrostatic barriers. However, direct imaging of the wavefunctions at potential boundaries and atomic-scale verification of the predictions of Klein tunnelling has not yet been achieved, and is the subject of this Letter.The basic ideas for Klein tunnelling discussed above can also be applied to the case of a circular quantum well in graphene. In the well-known case of two-dimensional electron gases (2DEG) in semiconductor heterostructures, such quantum wells form bound eigenstates that can be used to completely trap an electron, creating highly tunable quantum dots 15 . For circular...

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Confinement of Dirac electrons in graphene quantum dots

Cited by 37 publications

References 36 publications

Localized charge carriers in graphene nanodevices

Localized charge carriers in graphene nanodevices

Oxygen orders differently under graphene: new superstructures on Ir(111)

Klein tunnelling and electron trapping in nanometre-scale graphene quantum dots

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