Transport through a strongly coupled graphene quantum dot in perpendicular magnetic field
 Johannes Güttinger^{1}Email author,
 Christoph Stampfer^{1, 2},
 Tobias Frey^{1},
 Thomas Ihn^{1} and
 Klaus Ensslin^{1}
DOI: 10.1186/1556276X6253
© Güttinger et al; licensee Springer. 2011
Received: 2 September 2010
Accepted: 24 March 2011
Published: 24 March 2011
Abstract
We present transport measurements on a strongly coupled graphene quantum dot in a perpendicular magnetic field. The device consists of an etched singlelayer 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.
Introduction
Graphene [1, 2], a twodimensional solid consisting of carbon atoms arranged in a honeycomb lattice has a number of unique electronic properties [3], such as the gapless linear dispersion, and the unique Landau level (LL) spectrum [4, 5]. The low atomic weight of carbon and the low nuclear spin concentration, arising from the ≈99% natural abundance of ^{12}C, promises weak spin orbit and hyperfine coupling. This makes graphene a promising material for spintronic devices [6, 7] and spinqubit based quantum computation [8–11]. Additionaly, the strong suppression of electron backscattering [4, 5] makes it interesting for future high mobility nanoelectronic applications in general [12, 13]. Advances in fabricating graphene nanostructures have helped to overcome intrinsic difficulties in (i) creating tunneling barriers and (ii) confining electrons in bulk graphene, where transport is dominated by Klein tunnelingrelated phenomena [14, 15]. Along this route, graphene nanoribbons [16–22] and quantum dots [23–30] have been fabricated. Coulomb blockade [23–25], quantum confinement effects [26–28] and charge detection [29] have been reported. Moreover, graphene nanostructures may allow to investigate phenomena related to massless Dirac Fermions in confined dimensions [24, 31–36]. In general, the investigation of signatures of graphenespecific properties in quantum dots is of interest to understand the addition spectra, the spin states and dynamics of confined graphene quasiparticles.
Here, we report on tunneling spectroscopy (i.e. transport) measurements on a 140nm graphene quantum dot with open barriers, which can be tuned by a number of lateral graphene gates [37]. In contrast to the measurements reported in Ref. [27] the more open dot in the present investigation enables us to observe Coulomb peaks with higher conductance and the larger dot size reduces the magnetic field required to see graphene specific signatures in the spectra. We characterize the graphene quantum dot device focusing on the quantum dot Coulomb resonances which can be distinguished from additional resonances present in the graphene tunneling barriers. We discuss the evolution of a number of Coulomb resonances in the vicinity of the charge neutrality point in a perpendicular magnetic field from the lowfield regime to the regime where Landau levels are expected to form. In particular, we investigate the device characteristics at elevated perpendicular magnetic fields, where we observe the formation of multipledots giving rise to (highly reproducible) complex patterns in the addition spectra.
Device fabrication
The fabrication process of the presented graphene nanodevice is based on the mechanical exfoliation of (natural) graphite by adhesive tapes [24, 25, 28]. The substrate material consists of highly doped silicon (Si^{++}) bulk material covered with 295 nm of silicon oxide (SiO_{2}), where thickness (and roughness) of the SiO_{2} top layer is crucial for the Raman [38] and scanning force microscope based identification of singlelayer graphene flakes. Standard photolithography followed by metallization and liftoff is used to pattern arrays of reference alignment markers on the substrate which are later used to reidentify the locations of individual graphene flakes on the chip and to align further processing patterns. The graphene flakes are structured to submicron dimensions by electron beam lithography (EBL) and reactive ion etching based techniques to fulfill the nanodevice design requirement. After etching and removing the residual resist, the graphene nanostructures are contacted by an additional EBL step, followed by metallization and liftoff.
Measurements
All measurements have been performed at a base temperature of T = 1.8 K in a variable temperature cryostat. We have measured the twoterminal conductance through the graphene quantum dot device by applying a symmetric DC bias voltage V _{b} while measuring the sourcedrain current through the quantum dot with a noise level below 10 fA. For differential conductance measurements a small AC bias, V _{b,ac} = 100 μ V has been superimposed on V _{b} and the differential conductance has been measured with lockin techniques at a frequency of 76 Hz.
In Figure 1b we show the conductance G _{qd} as a function of back gate voltage at low bias (V _{b} = 200 μ V) highlighting the strong suppression of the conductance around the charge neutrality point (5 < V _{bg} < 3 V) due to the socalled transport gap [19–22]. Here we tune transport from the hole to the electron regime, as illustrated by the left and the right inset in Figure 1b. The large number of resonances with amplitudes in the range of up to 0.1 e ^{2}/h inside the gap region may be due to both, (i) resonances in the graphene constrictions acting as tunneling barriers [4] (and thus being mainly responsible for the large extension of this transport gap) and (ii) Coulomb resonances of the quantum dot itself (see also examples of Coulomb diamonds in Figure 1c). At room temperature these resonances disappear and a conductance value of 0.76 e ^{2}/h is measured at V _{bg} = 0 V.
Coulomb blockade measurements at B= 0 T
Corresponding Coulomb diamond measurements [39], that is, measurements of the differential conductance as a function of bias voltage V _{b} and V _{bg} (i.e. V _{rg} = 0.57·V _{bg}  1.59 V) have been performed along the (diagonal) solid gray line in Figure 2 and are shown in Figure 1c. From the extent of these diamonds in bias direction we estimate the average charging energy of the graphene quantum dot to be E _{c} = 4.5 meV, which is in reasonable agreement with the size of the graphene quantum dot [23, 25, 26]. Moreover, we observe faint strongly broadened lines outside the diamonds running parallel to their edges, as indicated by arrows in Figure 1c. The extracted energy difference of roughly 1 meV is reasonable for electronic excited states in this system [26].
Coulomb resonances as a function of a perpendicular magnetic field
In order to demonstrate the reproducibility of these complex patterns we show an up (Figure 3c) and a down (Figure 3d) sweep of the very same B  V _{bg} parameter space. These two measurements, have different resolution and thus different sweep rates in both the B and V _{bg} direction. However, all the individual features are highly reproducible (but hard to understand) despite the fact that we find some small hysteresis in magnetic field for B < 3 T (see white arrows in Figure 3c, d). The origin of the complex patterns shown in Figure 3 can be understood when having a closer look at charge stability diagrams (such as Figure 2) for different magnetic fields.
We interpret the magnetic field dependence in the following way. At low but increasing magnetic field we see in almost all measurements an increase of the conductance through the dot (see, e.g. Figure 3). Assuming diffusive boundary scattering such a conductance onset in magnetic field occurs due to reduced backscattering [41] and has been observed in other measurements on graphene nanoribbons [42, 43]. The maximum conductance is reached around B ≈ 1.5 T corresponding to a magnetic length nm in rough agreement with the size of the constrictions. As the magnetic field is further increased the complex pattern with many crossings starts to emerge, attributed to the formation of additional quantum dots around the right constriction with strong coupling to the original dot. The formation of such localized puddles is understood as a consequence of the increased magnetic confinement where ℓ_{B} is getting smaller than the extension of potential valleys induced by disorder.
Conclusion
In summary, we have presented detailed studies of transport through an open and larger graphene quantum dot (compared to Ref. [27]) in the vicinity of the charge neutrality point as a function of perpendicular magnetic field. The evolution of Coulomb resonances in a magnetic field showed the signatures of Landau level formation in the quantum dot. Indications for the crossing of filling factor ν = 2 are obtained by the observation of kinks in spectral lines before bending towards the charge neutrality point. However, the observation is disturbed by the formation of a pronounced additional localized state at high magnetic fields in the vicinity of the right constriction. Although the use of open constrictions enhances the visibility of the Coulomb peaks and reduces the transportgap region, emerging pronounced parasitic localized states make the analysis very difficult. For a further indepth analysis of the addition spectra around the electronhole crossover, it is hence beneficial to minimize the amount of disorder and to use clearly defined constrictions. These should be thin compared to the dot diameter to get different energy scales for quantum dot resonances and constriction resonances, which are easy to distinguish. However, the constrictions need to be wide enough to enable conductance measurements around the electronhole crossover without a charge detector.
Abbreviations
 BG:

back gate
 EBL:

electron beam lithography
 LL:

Landau level
 LG:

left side gate
 PG:

plunger gate
 RG:

right side gate
 SiO_{2} :

silicon dioxide.
Declarations
Acknowledgements
The authors wish to thank F. Libisch, P. Studerus, C. Barengo, F. Molitor and S. Schnez for help and discussions. Support by the ETH FIRST Lab, the Swiss National Science Foundation and NCCR nanoscience are gratefully acknowledged.
Authors’ Affiliations
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