**Transport properties and molecular electron states of mesoscopic systems.**

Planar quantum dot defined by metallic gates on a semiconducting heterostructure. Image by the Nano-Electronics group of Christian Schönenberger in Basel.

[Close]

,
quantum rings
[Close]

Four-terminal quantum ring defined in a two-dimensional electron gas by means of the local anodic oxidation technique. Image submitted for the SPMage Prize by Dr Andreas Fuhrer, ETH Zürich.

[Close]

and more in general one-dimensional systems such as carbon nanotubes.
[Close]

Carbon nanotube (red) connected to four metallic gates (yellow). Image by the Nano-Electronics group of Christian Schönenberger in Basel.

[Close]

We have investigated the occurrence of negative differential conductance (NDC) as induced by electron interactions
in quantum dots embedded into one-dimensional electron channels. In collaboration with Maximiliam Rogge and Rolf Haug of the nanostructures group at the University of Hannover, we have investigated also peculiar patterns of NDC repeating with striking regularity in planar dots created by the local anodic oxidation technique. I have also studied the out-of-equilibrium (shot) noise of one-dimensional quantum rings and interpreted the occurrence of super-Poissonian fluctuations as due to the competition of different time scales related to the transport dynamics of the system.[Close]

I also considered the study of quantum states of strongly correlated systems such as few-electron quantum dots. For such an investigation, phenomenological models are clearly unadvisable and one has to resort to numerical methods. We have developed a fully projected Hartree-Fock technique, capable to produce correlated wavefunctions for quantum dots with a higher precision than the Hartree-Fock method, but with a payload much smaller than exact diagonalization. Recently, we have applied this technique to investigate the signatures of the transition towards the Wigner molecule

Two-body correlation function for a quantum dot with 6 electrons in the strong correlations regime, where Wigner molecular states develop in the dot. The centered pentagon structure with one electron in the core and five (4 blobs + correlation hole) electrons in a ring is clearly visible. [Close]

on the transport properties of quantum dots. All the above works have been developed within an ongoing collaboration with Bernhard Kramer at the Jacobs University Bremen.
**NanoElectroMechanical Systems (NEMS).**

Colorized SEM image of a ultra-high frequency NEMS cantilever. Image by the Roukes group of Nanoscale Systems. [Close]

to
suspended carbon nanotubes.
SEM image of a suspended nanotube (tiny rope) attached to two large gold electrodes. Image by B. Lassagne et al., Nano Letters 8, 3735 (2008).

[Close]

We have focused our investigation on two complementary aspects. In collaboration with Rosario Fazio at SNS Pisa we have studied the shot noise of a NEMS connected to a dissipative environment which damps the motion of the oscillator. Interestingly, we have found that the electronic noise can be minimized by tuning the damping strength. Successively, we have studied the influence of the current on the vibrational properties of the system. In this context, we have found that peculiar sub-Poissonian phonon populations can be achieved in selected transport regimes. This work has been developed together with Elisabetta Paladino at the DMFCI of Catania University.[Close]

**Non-adiabatic pumping in interacting quantum dots**.

Electron pump fabricated from a surface-gated Gallium Arsenide wire. Pumping action is created by modulating the surrounding gates. See the work by D. Blumenthal et al, Nature Physycs 3, 343 (2007).

[Close]

Pumping is realized by periodically modulating some of the system parameters. For weakly interacting systems which can be essentially treated within the mean field approach, a very general theory based on the Floquet scattering matrix has been developed by M. Moskalets and M. Büttiker, allowing to treat cases from the adiabatic one (period of the modulation larger than the average charge dwell time) all the way up to the non-adiabatic regime. For strongly interacting systems on the other hand, theoretical studies have usually considered either the limit of very small or the regime of very large frequencies. In collaboration with Michele Governale and Jürgen König, we have recently developed a theory to evaluate the pumped current through interacting quantum dots for frequencies beyond the adiabatic regime up to the tunneling rate. Restricting to the case of sequential tunneling regime, we have shown that strong deviations from the adiabatic regime are observed. Firstly, in-phase two-parameter pumping is possible. Even more importantly, by tuning the driving frequency, pure spin pumping with no net charge flow can be achieved. All these effects are genuine manifestations of non-adiabatic dynamics.
[Close]

Fabio Cavaliere © 2009