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Transport through a strongly coupled graphene quantum dot in perpendicular magnetic field.

Güttinger J, Stampfer C, Frey T, Ihn T, Ensslin K - Nanoscale Res Lett (2011)

Bottom Line: Lateral graphene gates are used to electrostatically tune the device.We show the evolution of Coulomb resonances as a function of perpendicular magnetic field, which provides indications of the formation of the graphene specific 0th Landau level.Finally, we demonstrate that the complex pattern superimposing the quantum dot energy spectra is due to the formation of additional localized states with increasing magnetic field.

View Article: PubMed Central - HTML - PubMed

Affiliation: Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland. guettinj@phys.ethz.ch.

ABSTRACT
We present transport measurements on a strongly coupled graphene quantum dot in a perpendicular magnetic field. The device consists of an etched single-layer graphene flake with two narrow constrictions separating a 140 nm diameter island from source and drain graphene contacts. Lateral graphene gates are used to electrostatically tune the device. Measurements of Coulomb resonances, including constriction resonances and Coulomb diamonds prove the functionality of the graphene quantum dot with a charging energy of approximately 4.5 meV. We show the evolution of Coulomb resonances as a function of perpendicular magnetic field, which provides indications of the formation of the graphene specific 0th Landau level. Finally, we demonstrate that the complex pattern superimposing the quantum dot energy spectra is due to the formation of additional localized states with increasing magnetic field.

No MeSH data available.


Related in: MedlinePlus

Evolution of Coulomb peaks under the influence of a magnetic field in different gate voltage regimes (Vb = 200 μV). (a) More on the hole side. (b) More on the electron side. In contrast to (a) Vrg = -2.15 V is applied to the right gate in (b). The effect of the right gate to the dot is taken into account in the back gate scale to allow comparison with Figure 1b. (c, d) Reproducibility of the measurement for different magnetic field sweep directions (0-7 T in (c), 7-0 T in (d)). The right side gate is changed according to Vrg = -0.57·Vbg - 1.59 V (see Figure 2), with an applied bias of Vb = 200 μV.
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Figure 3: Evolution of Coulomb peaks under the influence of a magnetic field in different gate voltage regimes (Vb = 200 μV). (a) More on the hole side. (b) More on the electron side. In contrast to (a) Vrg = -2.15 V is applied to the right gate in (b). The effect of the right gate to the dot is taken into account in the back gate scale to allow comparison with Figure 1b. (c, d) Reproducibility of the measurement for different magnetic field sweep directions (0-7 T in (c), 7-0 T in (d)). The right side gate is changed according to Vrg = -0.57·Vbg - 1.59 V (see Figure 2), with an applied bias of Vb = 200 μV.

Mentions: In Figure 3 we show a large number of Coulomb resonances as function of a magnetic field perpendicular to the graphene sample plane. The measurement shown in Figure 3a has been taken in the back gate voltage range from Vbg = -5 to -3.5 V, at Vrg = 0 V (highlighted by the horizontal line (A) in Figure 1b). Thus we are in a regime where transport is dominated by holes (i.e. we are at the left hand side of the charge neutrality point in Figure 1b), which is also confirmed by the evolution of the Coulomb resonances in the perpendicular magnetic field as shown in Figure 3a. There is a common trend of the resonances to bend towards higher energies (higher Vbg) for increasing magnetic field, in good agreement with Refs. [27,28,32-34]. The finite magnetic field introduces an additional length scale which competes with the diameter d of the dot. Therefore, the ratio d/ℓB is a relevant parameter for the observation of Landau levels in graphene quantum dot devices. Here, the comparatively large size (d ≈ 140 nm) of the dot promises an increased spectroscopy window for studying the onset and the formation of Landau levels in graphene quantum dots in contrast to earlier work [27,28] (where d ≈ 50 nm). Moreover, we expect that in larger graphene quantum dots, where the surface-to-boundary ratio increases edge effects should be less relevant. In Figure 3a, c, d we indeed observe some characteristics of the Fock-Darwin-like spectrum [32-34] of hole states in a graphene quantum dot in the near vicinity of the charge neutrality point: (i) the levels stay more or less at constant energy (gate voltage) up to a certain B-field, where (ii) the levels feature a kink, whose B-field onset increases for increasing number of particles, and (iii) we observe that the levels convergence towards higher energies (see white dashed lines in Figure 3a). The pronounced kink feature (see arrows in Figure 3c, d) indicate filling factor ν = 2 in the quantum dot. However, this overall pattern is heavily disturbed by additional resonances caused by localized states, regions of multi-dot behavior, strong amplitude modulations due to constriction resonances and a large number of additional crossings, which are not yet fully understood. This becomes even worse when investigating the electron regime (see horizontal line (B) in Figure 1b), as shown in Figure 3b. Individual Coulomb resonances can (only) be identified for low magnetic fields B < 2 T and a slight tendency for their bending towards lower energies might be identified (please see white dashed lines in Figure 3b). For magnetic fields larger than 3 T it becomes very hard to identify individual Coulomb resonances in the complex and reproducible conductance pattern.


Transport through a strongly coupled graphene quantum dot in perpendicular magnetic field.

Güttinger J, Stampfer C, Frey T, Ihn T, Ensslin K - Nanoscale Res Lett (2011)

Evolution of Coulomb peaks under the influence of a magnetic field in different gate voltage regimes (Vb = 200 μV). (a) More on the hole side. (b) More on the electron side. In contrast to (a) Vrg = -2.15 V is applied to the right gate in (b). The effect of the right gate to the dot is taken into account in the back gate scale to allow comparison with Figure 1b. (c, d) Reproducibility of the measurement for different magnetic field sweep directions (0-7 T in (c), 7-0 T in (d)). The right side gate is changed according to Vrg = -0.57·Vbg - 1.59 V (see Figure 2), with an applied bias of Vb = 200 μV.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3211315&req=5

Figure 3: Evolution of Coulomb peaks under the influence of a magnetic field in different gate voltage regimes (Vb = 200 μV). (a) More on the hole side. (b) More on the electron side. In contrast to (a) Vrg = -2.15 V is applied to the right gate in (b). The effect of the right gate to the dot is taken into account in the back gate scale to allow comparison with Figure 1b. (c, d) Reproducibility of the measurement for different magnetic field sweep directions (0-7 T in (c), 7-0 T in (d)). The right side gate is changed according to Vrg = -0.57·Vbg - 1.59 V (see Figure 2), with an applied bias of Vb = 200 μV.
Mentions: In Figure 3 we show a large number of Coulomb resonances as function of a magnetic field perpendicular to the graphene sample plane. The measurement shown in Figure 3a has been taken in the back gate voltage range from Vbg = -5 to -3.5 V, at Vrg = 0 V (highlighted by the horizontal line (A) in Figure 1b). Thus we are in a regime where transport is dominated by holes (i.e. we are at the left hand side of the charge neutrality point in Figure 1b), which is also confirmed by the evolution of the Coulomb resonances in the perpendicular magnetic field as shown in Figure 3a. There is a common trend of the resonances to bend towards higher energies (higher Vbg) for increasing magnetic field, in good agreement with Refs. [27,28,32-34]. The finite magnetic field introduces an additional length scale which competes with the diameter d of the dot. Therefore, the ratio d/ℓB is a relevant parameter for the observation of Landau levels in graphene quantum dot devices. Here, the comparatively large size (d ≈ 140 nm) of the dot promises an increased spectroscopy window for studying the onset and the formation of Landau levels in graphene quantum dots in contrast to earlier work [27,28] (where d ≈ 50 nm). Moreover, we expect that in larger graphene quantum dots, where the surface-to-boundary ratio increases edge effects should be less relevant. In Figure 3a, c, d we indeed observe some characteristics of the Fock-Darwin-like spectrum [32-34] of hole states in a graphene quantum dot in the near vicinity of the charge neutrality point: (i) the levels stay more or less at constant energy (gate voltage) up to a certain B-field, where (ii) the levels feature a kink, whose B-field onset increases for increasing number of particles, and (iii) we observe that the levels convergence towards higher energies (see white dashed lines in Figure 3a). The pronounced kink feature (see arrows in Figure 3c, d) indicate filling factor ν = 2 in the quantum dot. However, this overall pattern is heavily disturbed by additional resonances caused by localized states, regions of multi-dot behavior, strong amplitude modulations due to constriction resonances and a large number of additional crossings, which are not yet fully understood. This becomes even worse when investigating the electron regime (see horizontal line (B) in Figure 1b), as shown in Figure 3b. Individual Coulomb resonances can (only) be identified for low magnetic fields B < 2 T and a slight tendency for their bending towards lower energies might be identified (please see white dashed lines in Figure 3b). For magnetic fields larger than 3 T it becomes very hard to identify individual Coulomb resonances in the complex and reproducible conductance pattern.

Bottom Line: Lateral graphene gates are used to electrostatically tune the device.We show the evolution of Coulomb resonances as a function of perpendicular magnetic field, which provides indications of the formation of the graphene specific 0th Landau level.Finally, we demonstrate that the complex pattern superimposing the quantum dot energy spectra is due to the formation of additional localized states with increasing magnetic field.

View Article: PubMed Central - HTML - PubMed

Affiliation: Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland. guettinj@phys.ethz.ch.

ABSTRACT
We present transport measurements on a strongly coupled graphene quantum dot in a perpendicular magnetic field. The device consists of an etched single-layer graphene flake with two narrow constrictions separating a 140 nm diameter island from source and drain graphene contacts. Lateral graphene gates are used to electrostatically tune the device. Measurements of Coulomb resonances, including constriction resonances and Coulomb diamonds prove the functionality of the graphene quantum dot with a charging energy of approximately 4.5 meV. We show the evolution of Coulomb resonances as a function of perpendicular magnetic field, which provides indications of the formation of the graphene specific 0th Landau level. Finally, we demonstrate that the complex pattern superimposing the quantum dot energy spectra is due to the formation of additional localized states with increasing magnetic field.

No MeSH data available.


Related in: MedlinePlus