Probing Wigner correlations in a suspended carbon nanotube

The influence of the electron-vibron coupling on the transport properties of a strongly interacting quantum dot built in a suspended carbon nanotube is analyzed. The latter is probed by a charged AFM tip scanned along the axis of the CNT which induces oscillations of the chemical potential and of the linear conductance. These oscillations are due to the competition between finite-size effects and the formation of a Wigner molecule for strong interactions. Such oscillations are shown to be suppressed by the electron-vibron coupling. The suppression is more pronounced in the regime of weak Coulomb interactions, which ensures that probing Wigner correlations in such a system is in principle possible

Theory of the STM detection of Wigner molecules in spin incoherent CNTs

The linear conductance of a carbon nanotube quantum dot in the Wigner molecule regime, coupled to two scanning tunnel microscope tips is inspected. Considering the high temperature regime, the nanotube quantum dot is described by means of the spin-incoherent Luttinger liquid picture. The linear conductance exhibits spatial oscillations induced by the presence of the correlated, molecular electron state. A power-law scaling of the electron density and of the conductance as a function of the interaction parameter are found. They confirm local transport as a sensitive tool to investigate the Wigner molecule. The double-tip setup allows to explore different transport regimes with different shapes of the spatial modulation, all bringing information about the Wigner molecule

Temperature-induced emergence of Wigner correlations in a STM-probed one-dimensional quantum dot

The temperature-induced emergence of Wigner correlations over finite-size effects in a strongly interacting one-dimensional quantum dot are studied in the framework of the spin coherent Luttinger liquid. We demonstrate that, for temperatures comparable with the zero mode spin excitations, Friedel oscillations are suppressed by the thermal fluctuations of higher spin modes. On the other hand, the Wigner oscillations, sensitive to the charge mode only, are stable and become more visible. This behavior is proved to be robust both in the thermal electron density and in the linear conductance in the presence of an STM tip. This latter probe is not directly proportional to the electron density and may confirm the above phenomena with complementary and additional information

AFM probe for the signatures of Wigner correlations in the conductance of a one-dimensional quantum dot

The transport properties of an interacting one-dimensional quantum dot capacitively coupled to an atomic force microscope probe are investigated. The dot is described within a Luttinger liquid framework which captures both Friedel and Wigner oscillations. In the linear regime, we demonstrate that both the conductance peak position and height oscillate as the tip is scanned along the dot. A pronounced beating pattern in the conductance maximum is observed, connected to the oscillations of the electron density. Signatures of the effects induced by a Wigner molecule are clearly identified and their stability against the strength of Coulomb interactions are analyzed. While the oscillations of the peak position due to Wigner get enhanced at strong interactions, the peak height modulations are suppressed as interactions grow. Oscillations due to Friedel, on the other hand, are robust against interaction.Comment: 9 figure

Fractional Wigner crystal in the helical Luttinger liquid

The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they instead represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we show that the state characterized by such fractional oscillations still bears the signatures of spin momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a non trivial spin texture.Comment: 5 pages, 2 figure

Correlation functions for the detection of Wigner molecules in a one-channel Luttinger liquid quantum dot

In one-channel, finite-size Luttinger one-dimensional quantum dots, both Friedel oscillations and Wigner correlations induce oscillations in the electron density with the same wavelength, pinned at the same position. Therefore, observing such a property does not provide any hint about the formation of a Wigner molecule when electrons interact strongly and other tools must be employed to assess the formation of such correlated states. We compare here the behavior of three different correlation functions and demonstrate that the integrated two point correlation function, which represents the probability density of finding two particles at a given distance, is the only faithful estimator for the formation of a correlated Wigner molecule.Comment: 6 pages, 5 figure

Carbon nanotube sensor for vibrating molecules

The transport properties of a CNT capacitively coupled to a molecule vibrating along one of its librational modes are studied and its transport properties analyzed in the presence of an STM tip. We evaluate the linear charge and thermal conductances of the system and its thermopower. They are dominated by position-dependent Franck-Condon factors, governed by a position-dependent effective coupling constant peaked at the molecule position. Both conductance and thermopower allow to extract some information on the position of the molecule along the CNT. Crucially, however, thermopower sheds also light on the vibrational levelspacing, allowing to obtain a more complete characterization of the molecule even in the linear regime

An electrical probe for mechanical vibrations in suspended carbon nanotubes

The transport properties of a suspended carbon nanotube probed by means of a STM tip are investigated. A microscopic theory of the coupling between electrons and mechanical vibrations is developed. It predicts a position-dependent coupling constant, sizeable only in the region where the vibron is located. This fact has profound consequences on the transport properties, which allow to extract information on the location and size of the vibrating portions of the nanotube.Comment: 11 Pages, 12 color figures, accepted for publication on Physical Review

Oils and fats based biofuels : technological chalendges

Periodically, during petroleum shortage, fatty acids and their derivatives have been used as alternative fuels to those derived from petroleum. Different approaches have been proposed, including the use of neat fats and oils or their derivatives. Indeed, the utilization of biodiesel produced by alcoholysis of triacilglycerides or esterification of fatty acids, or hydrocarbons obtained from cracking of fatty materials were studied and used in several countries. Increasing concerns about energy security and climate changes have lead several countries, including Brazil, to start up biofuels programs. Different technologies are currently being developed in order to produce biofuels with economical feasibility. In this work are discussed alternative fatty raw-materials and processing technologies that are currently being studied in order to produce fuels suitable to sustainable substitute diesel fuel