Non-linear Coulomb blockade microscopy of a correlated one-dimensional quantum dot

We evaluate the chemical potential of a one-dimensional quantum dot, coupled to an atomic force microscope tip. The dot is described within the Luttinger liquid framework and the conductance peaks positions as a function of the tip location are calculated in the linear and non-linear transport regimes for an arbitrary number of particles. The differences between the chemical potential oscillations induced by Friedel and Wigner terms are carefully analyzed in the whole range of interaction strength. It is shown that Friedel oscillations, differently from the Wigner ones, are sensitive probes to detect excited spin states and collective spin density waves involved in the transport.Comment: 4 figure

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

Signatures of fractional Hall quasiparticles in moments of current through an antidot

The statistics of tunneling current in a fractional quantum Hall sample with an antidot is studied in the chiral Luttinger liquid picture of edge states. A comparison between Fano factor and skewness is proposed in order to clearly distinguish the charge of the carriers in both the thermal and the shot limit. In addition, we address effects on current moments of non-universal exponents in single-quasiparticle propagators. Positive correlations, result of propagators behaviour, are obtained in the shot noise limit of the Fano factor, and possible experimental consequences are outlined

Multiple quasiparticle Hall spectroscopy investigated with a resonant detector

We investigate the finite frequency (f.f.) noise properties of edge states in the quantum Hall regime. We consider the measurement scheme of a resonant detector coupled to a quantum point contact in the weak-backscattering limit. A detailed analysis of the difference between the "measured" noise, due to the presence of the resonant detector, and the symmetrized f.f. noise is presented. We discuss both the Laughlin and Jain sequences, studying the tunnelling excitations in these hierarchical models. We argue that the measured noise can better distinguish between the different excitations in the tunnelling process with respect to the symmetrized f.f. counterpart in an experimentally relevant range of parameters. Finally, we illustrate the effect of the detector temperature on the sensibility of this measure.Comment: 24 pages, 8 figure

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

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