F. Cavaliere

Transport properties of quantum dots in the Wigner molecule regime

The transport properties of quantum dots with up to N=7 electrons ranging from a weak to a strong interacting regime are investigated via the projected Hartree–Fock technique. As interactions increase radial order develops in the dot, with the formation of ring and centred-ring structures. Subsequently, angular correlations appear, signalling the formation of a Wigner molecule state.We show striking signatures of the emergence of Wigner molecules, detected in transport. In the linear regime, conductance is exponentially suppressed as the interaction strength grows. A further suppression is observed when centred-ring structures develop, or peculiar spin textures appear. In the nonlinear regime, the formation of molecular states may even lead to a conductance enhancement.

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 is 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 has been proved to be robust both in the thermal electron density and in the linear conductance in the presence of a scanning tunnel microscope tip. The latter probe is not directly proportional to the electron density and may confirm the above phenomena with complementary and additional information.

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 peak 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 the Friedel and Wigner terms are carefully analysed in the whole range of interaction strengths. It is shown that Friedel oscillations, unlike the Wigner ones, are sensitive probes for detecting excited spin states and collective spin density waves involved in the transport.

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 one 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.

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.

Coulomb blockade microscopy of spin-density oscillations and fractional charge in quantum spin Hall dots

We evaluate the spin density oscillations arising in quantum spin Hall quantum dots created via two localized magnetic barriers. The combined presence of magnetic barriers and spin-momentum locking, the hallmark of topological insulators, leads to peculiar phenomena: a half-integer charge is trapped in the dot for antiparallel magnetization of the barriers, and oscillations appear in the in-plane spin density, which are enhanced in the presence of electron interactions. Furthermore, we show that the number of these oscillations is determined by the number of particles inside the dot, so that the presence or the absence of the fractional charge can be deduced from the in-plane spin density. We show that when the dot is coupled with a magnetized tip, the spatial shift induced in the chemical potential allows to probe these peculiar features.

Signatures of Wigner correlations in the conductance of a one-dimensional quantum dot coupled to an AFM tip

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.

Non-monotonic response and light-cone freezing in gapless-to-(partially) gapped quantum quenches of fermionic systems

S. Porta,1, 2 F. M. Gambetta,1, 2 N. Traverso Ziani,3 D. M. Kennes,4 M. Sassetti,1, 2 and F. Cavaliere1, 2 1Dipartimento di Fisica, Università di Genova, 16146 Genova, Italy 2SPIN-CNR, 16146 Genova, Italy 3Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany 4Department of Physics, Columbia University, New York, NY 10027, USA (Dated: January 11, 2018)

Anomalous Friedel oscillations in a quasi-helical quantum dot

The charge and spin patterns of a quantum dot embedded into a spin-orbit coupled quantum wire subject to a magnetic field are investigated. A Luttinger liquid theory is developed, taking into account open boundaries and finite magnetic field. In the quasi-helical regime, when spin-orbit effects dominate over the Zeeman interaction, peculiar states develop at the Fermi surface of the dot. Anomalous Friedel oscillations with twice the expected wavelength develop in the wavefunction of collective excitations of such states, accompanied by peculiar spin patterns in their magnetization. Both effects are analyzed in detail and shown possible to be probed in transport experiments. The stability against electron interactions and magnetic field is investigated. We also discuss how signatures of such states survive in the total charge and spin densities.

Temperature dependence of transport properties in a suspended carbon nanotube

The temperature dependence of the conductance of a suspended carbon nanotube, as probed by means of a scanning tunneling microscope (STM) tip, is analyzed. Employing the theory of coupling between electronic and vibronic degrees of freedom, local linear and nonlinear transport features are studied as a function of temperature. It is shown that the thermal activation of excited vibronic modes leads to a reduction of the STM signal.