Franck–Condon blockade in suspended carbon nanotube quantum dots

Abstract

Understanding the influence of vibrational motion of the atoms on electronic transitions in molecules constitutes a cornerstone of quantum physics, as epitomized by the Franck-Condon principle 1,2 of spectroscopy. Recent advances in building molecular-electronics devices 3 and nanoelectromechanical systems 4 open a new arena for studying the interaction between mechanical and electronic degrees of freedom in transport at the single-molecule level. The tunneling of electrons through molecules or suspended quantum dots 5,6 has been shown to excite vibrational modes, or vibrons 7-9,6 . Beyond this effect, theory predicts that strong electron-vibron coupling dramatically suppresses the current flow at low biases, a collective behaviour known as Franck-Condon blockade 10 . Here we show measurements on quantum dots formed in suspended single-wall carbon nanotubes revealing a remarkably large electron-vibron coupling and, due to the high quality and unprecedented tunability of our samples, admit a quantitative analysis of vibronmediated electronic transport in the regime of strong electron-vibron coupling. This allows us to unambiguously demonstrate the Franck-Condon blockade in a suspended nanostructure. The large observed electron-vibron coupling could ultimately be a key ingredient for the detection of quantized mechanical motion 11,12 . It also emphasizes the unique potential for nanoelectromechanical device applications based on suspended graphene sheets and carbon nanotubes. In a polar semiconductor, a conduction electron deforms the surrounding lattice to form a polaron state 13 . The formation of this quasi-particle, by combining an electron and a cloud of lattice vibrations, or phonons, strongly influences the transport properties. The possibility for localization of strongly coupled polarons was suggested by Landau more than 70 years ago 13 . Recently, Koch et al. predicted that a related trapping of heavy polarons can occur in a quantum dot (QD) formed in a mechanically suspended nanostructure 10 . In such a nanoelectromechanical system (NEMS), the vibrational modes of the nanostructure can be strongly affected by the presence of electrons in the QD, as they deform the embedding medium. For strong electron-phonon coupling, the deformation effectively blocks electronic transport, termed Franck-Condon (FC) blockade. By analysing electronic transport through a suspended carbon nanotube (CNT) quantum dot over a wide range of electronic states, we are able to highlight generic features of vibron-assisted electronic transport, and unambiguously confirm the FC blockade scenario.Scanning electron microscope images and a scheme of our suspended CNT quantum dot device are shown in Figs. 1a, 1b and 1c. The CNT is electrically and mechanically connected to both source (S) and drain (D) contacts, while the central electrode acts as a suspended top-gate (TG). A quantum dot in the CNT is formed between defects 14 , which are presumably created during the release process and act as local barriers. The double top-and back-gat...

Spin-orbit effects in carbon-nanotube double quantum dots

“…[10][11][12][13][14] This band gap allows for electrostatic confinement of electrons and creation of few-electron QDs, otherwise not possible due to the Klein paradox. 15 Recent experiments have shown that it is indeed possible to confine electrons in single [16][17][18][19] and double QDs ͑DQDs͒ in a CNT by means of electrostatic gates in cleanly grown small band-gap nanotubes. 5,15,20 The present study is motivated by these experimental results.…”

Lifting the Franck-Condon blockade in driven quantum dots

“…Electronic transport through the system requires the electron number to change and hence the polarons to be broken up, which is energetically disfavored if the electron-vibron coupling that holds them together is strong. This effect has been observed in single-molecule junctions 19 as well as in CNT systems, 12 adding to the variety of ways in which material structure can influence conductance. In addition, it has also been shown that the coupling between the mechanical and electronic degrees of freedom can be tailored to some extent.…”

“…Such a quantum dot may be realized on a suspended CNT using electronic back gates to confine an electron in a specific section of the nanotube. 6,[9][10][11][12][15][16][17]20 The vibrations of the CNT can be strongly coupled to the charge degree of freedom of the electron and thus have a great influence on its conductive properties. 12,20,21 Additionally, a back gate can be used to apply an ac voltage, thus modulating the dot energy level.…”

“…6 CNTs are superb mechanical oscillators due to (i) their high Q-factors and stiffness, 9,10 (ii) high vibrational frequencies in the GHz range, 11 and (iii) large electron-phonon coupling. 12 Besides these mechanical properties, the electronic and transport properties of CNTs can also be tuned depending on the setup. For instance, electronic back gates allow for a controlled shaping of the nanotube's electrostatic potential which can be used to confine single electrons on the CNT, thus creating a quantum dot on the nanotube.…”

“…13,14 Nanoelectromechanics is a growing field of research with various experiments investigating the interplay between the mechanical and the quantized electronic degree of freedom in suspended CNTs. 12,[15][16][17] A general feature of interacting systems composed of electrons and quantized mechanical vibrations ("vibrons") is the suppression of conductance, in certain parameter regimes, for strong coupling between the two degrees of freedom. This effect, commonly referred to as Franck-Condon blockade, 18 results from the atomic constituents of the system accommodating for the presence of a number of electrons by means of displacement, thus forming composite electron-vibron particles termed polarons.…”