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Register a new userAsymmetric Franck-Condon factors in suspended carbon nanotube quantum dots
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Electronic states and vibrons in carbon nanotube quantum dots have in general different location and size. As a consequence, the conventional Anderson-Holstein model, coupling vibrons to the dot total charge only, may no longer be appropriated in general. Here we explicitly address the role of the spatial fluctuations of the electronic density, yielding space-dependent Franck-Condon factors. We discuss the consequent marked effects on transport which are compatible with recent measurements. This picture can be relevant for tunneling experiments in generic nano-electromechanical systems.
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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 of spectroscopy. Recent advances in building molecular-electronics devices and nanoelectromechanical systems 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 has been shown to excite vibrational modes, or vibrons. 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. 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 vibron-mediated 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. It also emphasizes the unique potential for nanoelectromechanical device applications based on suspended graphene sheets and carbon nanotubes.
A low energy theory of suspended carbon nanotube quantum dots in weak tunnelling coupling with metallic leads is presented. The focus is put on the dependence of the spectrum and the Franck-Condon factors on the geometry of the junction including several vibronic modes. The relative size and the relative position of the dot and its associated vibrons strongly influence the electromechanical properties of the system. A detailed analysis of the complete parameters space reveals different regimes: in the short vibron regime the tunnelling of an electron into the nanotube generates a plasmon-vibron excitation while in the long vibron regime polaron excitations dominate the scenario. The small, position dependent Franck-Condon couplings of the small vibron regime convert into uniform, large couplings in the long vibron regime. Selection rules for the excitations of the different plasmon-vibron modes via electronic tunnelling events are also derived.
We investigate charge pumping in carbon nanotube quantum dots driven by the electric field of a surface acoustic wave. We find that at small driving amplitudes, the pumped current reverses polarity as the conductance is tuned through a Coulomb blockade peak using a gate electrode. We study the behavior as a function of wave amplitude, frequency and direction and develop a model in which our results can be understood as resulting from adiabatic charge redistribution between the leads and quantum dots on the nanotube.
We present a simple technique which uses a self-aligned oxide etch to suspend individual single-wall carbon nanotubes between metallic electrodes. This enables one to compare the properties of a particular nanotube before and after suspension, as well as to study transport in suspended tubes. As an example of the utility of the technique, we study quantum dots in suspended tubes, finding that their capacitances are reduced owing to the removal of the dielectric substrate.
Excited-state relaxations in molecules are responsible for a red shift of the absorption peak with respect to the emission peak (Franck-Condon shift). The magnitude of this shift in semiconductor quantum dots is still unknown. Here we report first-principle calculations of excited-state relaxations in small (diameter < 2.2 nm) Si nanocrystals, showing that the Franck-Condon shift is surprisingly large (~60 meV for a 2.2 nm-diameter nanocrystal). The physical mechanism of the excited-state relaxations changes abruptly around 1 nanoeter in size, providing a clear demarcation between ``molecules and ``nanocrystals.
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