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Register a new userPhonon-assisted tunneling in interacting suspended single wall carbon nanotubes
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Transport in suspended metallic single wall carbon nanotubes in the presence of strong electron-electron interaction is investigated. We consider a tube of finite length and discuss the effects of the coupling of the electrons to the deformation potential associated to the acoustic stretching and breathing modes. Treating the interacting electrons within the framework of the Luttinger liquid model, the low-energy spectrum of the coupled electron-phonon system is evaluated. The discreteness of the spectrum is reflected in the differential conductance which, as a function of the applied bias voltage, exhibits three distinct families of peaks. The height of the phonon-assisted peaks is very sensitive to the parameters. The phonon peaks are best observed when the system is close to the Wentzel-Bardeen singularity.
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Current-voltage characteristics of suspended single-wall carbon nanotube quantum dots show a series of steps equally spaced in voltage. The energy scale of this harmonic, low-energy excitation spectrum is consistent with that of the longitudinal low-k phonon mode (stretching mode) in the nanotube. Agreement is found with a Franck-Condon-based model in which the phonon-assisted tunneling process is modeled as a coupling of electronic levels to underdamped quantum harmonic oscillators. Comparison with this model indicates a rather strong electron-phonon coupling factor of order unity.
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.
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 propose a framework for inducing strong optomechanical effects in a suspended carbon nanotube based on deformation potential exciton-phonon coupling. The excitons are confined using an inhomogeneous axial electric field which generates optically active quantum dots with a level spacing in the milli-electronvolt range and a characteristic size in the 10-nanometer range. A transverse field induces a tunable parametric coupling between the quantum dot and the flexural modes of the nanotube mediated by electron-phonon interactions. We derive the corresponding excitonic deformation potentials and show that this interaction enables efficient optical ground-state cooling of the fundamental mode and could allow us to realise the strong and ultra-strong coupling regimes of the Jaynes-Cummings and Rabi models.
We have performed low-temperature scanning tunneling spectroscopy measurements on suspended single-wall carbon nanotubes with a gate electrode allowing three-terminal spectroscopy measurements. These measurements show well-defined Coulomb diamonds as well as side peaks from phonon-assisted tunneling. The side peaks have the same gate voltage dependence as the main Coulomb peaks, directly proving that they are excitations of these states.
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