Transport measurements on an etched graphene nanoribbon are presented. It is shown that two distinct voltage scales can be experimentally extracted that characterize the parameter region of suppressed conductance at low charge density in the ribbon. One of them is related to the charging energy of localized states, the other to the strength of the disorder potential. The lever arms of gates vary by up to 30% for different localized states which must therefore be spread in position along the ribbon. A single-electron transistor is used to prove the addition of individual electrons to the localized states. In our sample the characteristic charging energy is of the order of 10 meV, the characteristic strength of the disorder potential of the order of 100 meV.PACS numbers: 71.15. Mb, 78.30Na, 81.05.Uw, 63.20.Kr Graphene nanoribbons [1,2,3,4,5] and narrow graphene constrictions [6,7,8] display unique electronic properties based on truly two-dimensional (2D) graphene [9] with potential applications in nanoelectronics [10] and spintronics [11]. Quasi-1D graphene nanoribbons and constrictions are of interest due to the presence of an effective energy gap, overcoming the gap-less band structure of graphene and leading to overall semiconducting behavior, most promising for the fabrication of nanoscale graphene transistors [5], tunnel barriers, and quantum dots [6,7,8]. On the other hand, ideal graphene nanoribbons [12,13] promise interesting quasi-1D physics with strong relations to carbon nanotubes [14]. Zonefolding approximations [13], π-orbital tight-binding models [15,16], and first principle calculations [17,18] predict an energy gap E g scaling as E g = α/W with the nanoribbon width W , where α ranges between 0.2-1.5 eV×nm, depending on the model and the crystallographic orientation of the nanoribbon [4]. However, these theoretical estimates can neither explain the experimentally observed energy gaps of etched nanoribbons of widths beyond 20 nm, which turn out to be larger than predicted, nor do they explain the large number of resonances found inside the gap [1,2,8]. This has led to the suggestion that localized states (and interactions effects) due to edge roughness, bond contractions at the edges [20] and disorder may dominate the transport gap. Several mechanisms have been proposed to describe the observed gap, including re-normalized lateral confinement [2], quasi-1D Anderson localization [21], percolation models [22] and many-body effects (incl. quantum dots) [19], where substantial edge disorder is required. Recently, it has been shown that also moderate amounts of edge roughness can substantially suppress the linear conductance near the charge neutrality point [23], giving rise to localized states relevant for both single particle and many-body descriptions.In this paper we show experimental evidence that the transport gap in an etched graphene nanoribbon (see schematic in Fig. 1a) is primarily formed by local resonances and quantum dots along the ribbon. We employ lateral graphene gates to show that size...
Since the advent of atomic force microscopy [1], mechanical resonators have been used to study a wide variety of phenomena, such as the dynamics of individual electron spins [2], persistent currents in normal metal rings [3], and the Casimir force [4,5].Key to these experiments is the ability to measure weak forces. Here, we report on force sensing experiments with a sensitivity of 12 zN/ √ Hz at a temperature of 1.2 K using a resonator made of a carbon nanotube. An ultra-sensitive method based on cross-correlated electrical noise measurements, in combination with parametric downconversion, is used to detect the low-amplitude vibrations of the nanotube induced by weak forces. The force sensitivity is quantified by applying a known capacitive force. A promising strategy for measuring lower forces is to employ resonators made of a molecular system, such as a carbon nanotube [14][15][16][17][18]. Nanotube resonators are characterized by an ultra-low mass M, which can be up to seven orders of magnitude lower than that of the ultra-soft cantilevers mentioned above [7], whereas their quality factor Q can be high [19] and their spring constant k 0 low. This has a great potential for generating an outstanding force sensitivity, whose classical limit is given byHere k B T is the thermal energy and γ the mechanical resistance [7]. This limit is set To efficiently convert weak forces into sizable displacements, we design nanotube resonators endowed with spring constants as low as ∼ 10 µN/m. This is achieved by fabri-2 cating the longest possible single-wall nanotube resonators. The fabrication process starts with the growth of nanotubes by chemical vapor deposition onto a doped silicon substrate coated with silicon oxide. Using atomic force microscopy (AFM), we select nanotubes that are straight over a distance of several micrometers, so that they do not touch the underlying substrate once they are released [21]. We use electron-beam lithography to pattern a source and a drain electrode that electrically contact and mechanically clamp the nanotube. We suspend the nanotube using hydrofluoric acid and a critical point dryer. Figure 1a shows a nanotube resonator that is 4 µm long. We characterize its resonant frequencies by driving it electrostatically and using a mixing detection method [18,22]. The lowest resonant frequency is 4.2 MHz (Fig. 1c). This gives a spring constant of 7 µN/m using an effective mass of 10 −20 kg, estimated from the size of the nanotube measured by AFM (supplementary information). This spring constant is comparable to that of the softest cantilevers fabricated so far [6]. When changing the gate voltage V DC g applied to the silicon substrate, the resonant frequency splits into two branches (Fig. 1c). These two branches correspond to the two fundamental modes; they vibrate in perpendicular directions (inset to Fig. 1c).We have developed an ultrasensitive detection method based on parametric downconversion, which (i) employs a cross-correlation measurement scheme to reduce the electrical noise ...
We report electronic transport experiments on a graphene single electron transistor. The device consists of a graphene island connected to source and drain electrodes via two narrow graphene constrictions. It is electrostatically tunable by three lateral graphene gates and an additional back gate. The tunneling coupling is a strongly nonmonotonic function of gate voltage indicating the presence of localized states in the barriers. We investigate energy scales for the tunneling gap, the resonances in the constrictions and for the Coulomb blockade resonances. From Coulomb diamond measurements in different device configurations (i.e. barrier configurations) we extract a charging energy of ≈ 3.4 meV and estimate a characteristic energy scale for the constriction resonances of ≈ 10 meV. The recent discovery of graphene [1,2], filling the gap between quasi 1-dimensional (1-D) nanotubes and 3-D graphite makes truly 2-D crystals accessible and links solid state devices to molecular electronics [3]. Graphene, which exhibits unique electronic properties including massless carriers near the Fermi level and potentially weak spin orbit and hyperfine couplings [4,5] has been proposed to be a promising material for spin qubits [6], high mobility electronics [7,8] and it may have the potential to contribute to the downscaling of state-ofthe-art silicon technology [9]. The absence of an energy gap in 2-D graphene and phenomena related to Klein tunneling [10,11] make it hard to confine carriers electrostatically and to control transport on the level of single particles. However, by focusing on graphene nanoribbons, which are known to exhibit an effective transport gap [7,8,12,13] this limitation can be overcome. It has been shown recently that such a transport gap allows to fabricate well tunable graphene nanodevices [14,15,16]. Here we investigate a fully tunable single electron transistor (SET) that consists of a width modulated graphene structure exhibiting spatially separated transport gaps. SETs consist of a conducting island connected by tunneling barriers to two conducting leads. Electronic transport through the device can be blocked by Coulomb interaction for temperatures and bias voltages lower than the characteristic energy required to add an electron to the island [17]. The sample is fabricated based on single-layer graphene flakes obtained from mechanical exfoliation of bulk graphite. These flakes are deposited on a highly doped silicon substrate with a 295 nm silicon oxide layer [1]. Electron beam (e-beam) lithography is used for patterning the isolated graphene flake by subsequent Ar/O 2 reactive ion etching. Finally, an additional e-beam and lift-off step is performed to pattern Ti/Au (2 nm/50 nm) electrodes. For the detailed fabrication process and the * Corresponding author, e-mail: stampfer@phys.ethz.ch single-layer graphene verification we refer to Refs. [14,18,19]. Fig. 1a shows a scanning force micrograph of the investigated device. Both the metal electrodes and the graphene structure are highlighted. In Fig....
We report on Coulomb blockade and Coulomb diamond measurements on an etched, tunable single-layer graphene quantum dot. The device consisting of a graphene island connected via two narrow graphene constrictions is fully tunable by three lateral graphene gates. Coulomb blockade resonances are observed and from Coulomb diamond measurements a charging energy of ≈ 3.5 meV is extracted. For increasing temperatures we detect a peak broadening and a transmission increase of the nanostructured graphene barriers.
Carbon nanotube mechanical resonators have attracted considerable interest because of their small mass, the high quality of their surface, and the pristine electronic states they host [1][2][3][4]. However, their small dimensions result in fragile vibrational states that are difficult to measure. Here we observe quality factors Q as high as 5×10 6 in ultra-clean nanotube resonators at a cryostat temperature of 30 mK, where we define Q as the ratio of the resonant frequency over the linewidth. Measuring such high quality factors requires both employing an ultra-low noise method to detect minuscule vibrations rapidly, and carefully reducing the noise of the electrostatic environment.We observe that the measured quality factors fluctuate because of fluctuations of the resonant frequency. The quality factors we measure are record high; they are comparable to the highest Q reported in mechanical resonators of much larger size [5, 6], a remarkable result considering that reducing the size of resonators is usually concomitant with decreasing quality factors. The combination of ultra-low size and very In recent years, endeavours to boost quality factors in nano and micromechanical resonators have been stimulated by the need to develop innovative approaches to sensing [7], signal processing [8] and quantum physics [9]. Strategies to enhance quality factors have proceeded along three main routes. Firstly, the quality of the host material has been improved. To this end, new materials have been employed, such as high tensile stress silicon nitride membranes [5, 10] and single crystal diamond films [11]. In addition, surface friction has been lowered by optimizing fabrication processes and reducing contamination [12].Secondly, schemes to isolate the resonator from its surrounding environment have been developed, based on new resonator layouts [13,14], and on optical trapping of thin membranes and levitated particles [15,16]. Thirdly, and most straightforwardly, Q-factors have been improved by operating resonators at cryogenic temperatures [17].Schemes to enhance Q-factors in nanotube resonators have focused on reducing contamination by growing ultra-clean nanotubes, and cooling resonators down to millikelvin temperatures [2]. Even though Q-factors, measured from the linewidth of driven resonances, have been improved up to ∼ 1.5 × 10 5 , they are still much lower than values routinely obtained with larger resonators fabricated from bulk materials using top-down techniques [6]. This result is somewhat disappointing, since the high crystallinity of nanotubes and their lack of dangling bonds at the surface are expected to minimize surface friction that limits the Q-factor in some nanomechanical systems [18].Here we find that the actual values of the Q-factors can be significantly higher than hitherto appreciated, but that revealing these values requires to perfect the measurement technique. Namely, the dynamics of the nanotube has to be captured in a regime of vanishingly small displacement in order to minimize nonline...
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