Metallic nanowires have several interesting, and sometimes surprising, properties that distinguish them from a macroscopic wire and have been measured in the last ten years: The electrical conductance, instead of following Ohm's law, has a step-like behavior as a function of the cross section area of the wire, the positions of the plateaus showing a statistical preference for integer multiples of the conductance quantum 2e²/h, which is reflected in well-defined peaks in conductance histograms. The shot noise, which represents the time-dependent fluctuations of the electrical current due to the discreteness of the charge of the carriers, is strongly suppressed for contacts with a conductance close to 2e²/h and shows an oscillatory behavior as a function of the conductance of the wire, with minima slightly below integer multiples of the quantum of conductance and an apparent saturation for large conductances. The cohesive force, measured as the resistance of a nanowire to longitudinal deformations, follows a saw-tooth behavior, with jumps, of the order of 2 nano-Newton for gold, that are correlated with conductance steps.

Until recently, the deformation of metallic nanowires was understood in terms of abrupt rearrangements of the atomic structure of the contact, followed by stages of elastic deformation. This interpretation emphasizes on the kinetics of the atomic structure and neglects quantum effects due to the transverse confinement of the electrons in the wire. In this thesis, we take the opposite point of view, neglecting the atomic structure and emphasizing on the electronic effects. To this end we introduce a free-electron model, exoected to be valid for simple s-wave metals, and relate both transport and cohesive properties of the nanowires to a common quantity, the scattering matrix. In this model, conductance channels are seen as elongated metallic bonds whose deformation and breaking is responsible for the observed oscillations of the cohesive force, explaining their correlation with conductance steps.

Using a combination of adiabatic and WKB approximations, we show that this simple model is in quantitative agreement, both in the overall magnitude of the force and in the amplitude of the oscillations, with measurements made with gold nanowires. The force oscillations are predicted to be universal with an amplitude of order E_F / l_F (E_F and l_F being respectively the Fermi energy and Fermi wavelength of the metal). A numerical method, based on a recursive Green's function algorithm, allows the study of the influence of the geometry of the contact on its properties, as well as the inclusion of disorder in the wire. We find that interchannel scattering caused by the geometry of the contact is not able to explain the observed properties even for very short constrictions where these effects are maximal, while backscattering by impurities reproduces most of the observations: Histograms of conductance show well-defined peaks even when individual conductance traces do not show well-defined plateaus. The shifts of the peaks below integer multiples of 2e²/h, as well as the peak heights and widths, are found to be in good agreement with predictions based on random matrix theory, and are similar to those observed experimentally. Results for the shot-noise are found to be in quantitative agreement with measurements made with gold nanowires, while the effects of disorder on cohesion is found to be quite strong and very sensitive to the particular configuration of impurities at the center of the constriction. These results show that abrupt changes in the wire geometry are not necessary for reproducing the observed properties of metallic nanowires, which can be understood as a result of quantum confinement effects.