Multiwall Carbon Nanotubes as Quantum Dots

Buitelaar, M. R.; Bachtold, Adrian; Nußbaumer, Thomas; Iqbal, Mahdi; Schönenberger, Christian

doi:10.1103/physrevlett.88.156801

Cited by 188 publications

(206 citation statements)

References 21 publications

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“…The analysis also allows us to deduce the various geometric capacitances of the device [16]. We did not observe any obvious four-fold periodicity in the stability diagrams, an indication that the orbital degeneracy of the nanotubes is broken [17,18].…”

mentioning

confidence: 88%

Measuring the Complex Admittance of a Carbon Nanotube Double Quantum Dot

Chorley¹,

Wabnig²,

Penfold-Fitch³

et al. 2012

Phys. Rev. Lett.

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We investigate radio-frequency (rf) reflectometry in a tunable carbon nanotube double quantum dot coupled to a resonant circuit. By measuring the in-phase and quadrature components of the reflected rf signal, we are able to determine the complex admittance of the double quantum dot as a function of the energies of the single-electron states. The measurements are found to be in good agreement with a theoretical model of the device in the incoherent limit. Besides being of fundamental interest, our results present an important step forward towards non-invasive charge and spin state readout in carbon nanotube quantum dots. PACS numbers: 73.63.Fg, 73.63.Kv, 73.23.Hk, 03.67.Lx An important requirement in any quantum information processing scheme is fast manipulation and readout of the quantum system in which the quantum information is encoded. This requires an understanding of the response of the quantum system at finite frequencies which, in the case of an electronic device, involves an understanding of its complex admittance [1,2]. Of particular interest in the context of quantum information processing are double quantum dots which are widely used to define charge and spin qubits [3]. However, while double quantum dots have been investigated in detail over the last decade, experiments to measure and analyze their complex admittance have not yet been performed and this topic has only recently been addressed theoretically [4]. The admittance of quantum dots at finite frequencies is non-trivial as exemplified by recent experiments on single quantum dots [5,6]. The physics is even richer for double quantum dots as internal charge dynamics, i.e. charge transfer between the quantum dots, has to be taken into account. However, the dependence of the admittance on the internal charge dynamics also provides a route towards charge and spin state readout [7].In this work we present a detailed experimental study of the complex admittance of a carbon nanotube double quantum dot which is measured using rf reflectometry techniques. The measurements are compared with a theoretical model of the device where we use a density matrix approach to calculate the double quantum dot admittance. The good quantitative agreement between the experimental and theoretical results allows us to determine the effective conductance and susceptance of the double dot as a function of the energies of the single-electron states. Our measurements thus present a first quantitative analysis of the complex admittance of a double quantum dot. The demonstrated technique also provides the basis for a simple and fast detection scheme for charge and spin state readout in carbon nanotubes -a material with considerable potential for spin-based quantum information processing [8-13] -without the need for a separate charge detector [14].The device we consider is a carbon nanotube grown by chemical vapour deposition on degenerately doped Si ter- minated by 300 nm SiO 2 , see Fig. 1(a). The nanotube is contacted by Au source and drain electrodes which form the outer ...

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mentioning

confidence: 88%

Measuring the Complex Admittance of a Carbon Nanotube Double Quantum Dot

Chorley¹,

Wabnig²,

Penfold-Fitch³

et al. 2012

Phys. Rev. Lett.

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“…3,4 A continuous improvement in device fabrication and NT quality has enabled the recent observation of twoelectron periodicity in "closed" QDs 5 and four-electron periodicity in "open" single-wall and multiwall NT QDs. 6,7 Theoretically, the low-energy spectrum of single-wall nanotube ͑SWNT͒ QDs has been modeled by Oreg et al 8 Experiments on open NT QDs are compatible with this model, but the presence of the Kondo effect and broadening of the energy levels prevents the observation of the full spectrum. 9 An analysis of the electronic excitations is therefore still lacking.…”

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confidence: 96%

Electronic excitation spectrum of metallic carbon nanotubes

et al. 2005

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We have studied the discrete electronic spectrum of closed metallic nanotube quantum dots. At low temperatures, the stability diagrams show a very regular fourfold pattern that allows for the determination of the electron addition and excitation energies. The measured nanotube spectra are in excellent agreement with the theoretical predictions based on the nanotube band structure. Our results permit the complete identification of the electron quantum states in nanotube quantum dots. DOI: 10.1103/PhysRevB.71.153402 PACS number͑s͒: 73.22.Dj, 73.63.Fg, 73.23.Hk Since their discovery 1 carbon nanotubes ͑NTs͒ have emerged as prototypical one-dimensional conductors. 2 At low temperatures, NT devices form quantum dots ͑QDs͒ where single-electron charging and level quantization effects dominate. 3,4 A continuous improvement in device fabrication and NT quality has enabled the recent observation of twoelectron periodicity in "closed" QDs 5 and four-electron periodicity in "open" single-wall and multiwall NT QDs. 6,7 Theoretically, the low-energy spectrum of single-wall nanotube ͑SWNT͒ QDs has been modeled by Oreg et al. 8 Experiments on open NT QDs are compatible with this model, but the presence of the Kondo effect and broadening of the energy levels prevents the observation of the full spectrum. 9 An analysis of the electronic excitations is therefore still lacking.The twofold degenerate, low-energy band structure of a metallic SWNT is schematically shown in Fig. 1͑a͒. Quantization along the nanotube axis leads to a set of singleparticle states that are equally spaced because of the linear dispersion relation. 10 The combination of the two bands and the spin yields a fourfold periodicity in the electron addition energy. The simplest model to describe QDs is the constant interaction ͑CI͒ model, 11 which assumes that the charging energy is constant and independent of the occupied singleparticle states. To describe NT QDs the CI model has been extended 8 to include five independent parameters: the charging energy E C , the quantum energy-level separation ⌬, the subband mismatch ␦ ͓see Fig. 1͑a͔͒, the exchange energy J, and the excess Coulomb energy dU. Figure 1͑c͒ illustrates the meaning of the last two parameters. An independent verification of the Oreg et al. model 8 requires the observation of the ground-state addition energies and of at least two excited states. To the best of our knowledge, such a study has not been reported.In this paper we investigate the excitation spectrum of closed SWNT QDs. Not only the ground-state, but also the complete excited-state spectrum of these QDs are measured by transport-spectroscopy experiments, enabling us to determine all five parameters independently. With these, the remaining measured excitation energies are well predicted, leading to a complete understanding of the spectrum, without adjustable parameters.High pressure CO conversion 12 ͑HiPco͒-and chemical vapor deposition ͑CVD͒-grown 13 NTs are used for the fabrication of the devices. HiPco tubes are dispersed from a dich...

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“…In the low temperature limit (T T K ), the full width at half-maximum (FWHM) of the Kondo resonance is of the order of k B T K (see figure 3.5(b)). Typical Kondo temperatures are T K ∼ 1 K for semiconductor quantum dots [34], T K ∼ 1-10 K for carbon nanotubes [46,47] and T K ∼ 20-50 K for molecular devices [36][37][38][39]. In the middle of the Coulomb diamond, the height of the Kondo peak as a function of temperature is expected to show the characteristic form [33,34] …”

Section: Intermediate Coupling: Cotunneling and Kondo Effectmentioning

confidence: 99%

Single-molecule transport in three-terminal devices

Osorio

Bjørnholm

Lehn

et al. 2008

J. Phys.: Condens. Matter

103

114

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Transport through single molecules has been studied using different test beds. In this paper we focus on three-terminal devices in which a molecule bridges the gap between two gold electrodes and a third electrode-the gate-is able to modulate the conduction properties of the junction. Depending on the electronic coupling, , between the molecule and the gold electrodes, different transport regimes can be distinguished. We show measurements on junctions incorporating different single-molecule systems which demonstrate the distinction between these regimes, as well as the experimental limitations in controlling the exact value of .

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Multiwall Carbon Nanotubes as Quantum Dots

Cited by 188 publications

References 21 publications

Measuring the Complex Admittance of a Carbon Nanotube Double Quantum Dot

Measuring the Complex Admittance of a Carbon Nanotube Double Quantum Dot

Electronic excitation spectrum of metallic carbon nanotubes

Single-molecule transport in three-terminal devices

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