First-principle investigation of Kohn anomalies and Peierls instabilities in metallic nanowires

In this thesis, a theoretical analysis of the causes and effects of charge density waves (CDW) in metals is presented, focusing on 1D systems. CDWs are the periodic spatial modulation of the charge density that occurs in some metals at T = 0 K. The origin of CDWs varies depending on the dimensionality of the metal itself. In 1D, it is mainly due to the Fermi surface nesting, while in 2D and 3D, the origin ought to be found in the electron-phonon coupling, which anyway plays a role in 1D systems as well. Furthermore, CDWs induce instabilities in the lattice too. As mentioned, the ions might redistribute following different processes. Firstly, a Peierls transition may take place: the unit cell dimension doubles, the number of atoms in it doubles as well, and a metal-insulator transition occurs. The transition is energetically favored when the reduction in energy due to the opening of the gap overcomes the energy needed for the lattice relaxation. Secondly, a Kohn instability might appear: a phonon mode softens due to the lack of screening ability of the electron gas for a certain wave vector. A lower temperature enhances the depth of the dip. When the phonon frequency becomes negative, the mode is unstable and a structural relaxation takes place. A metal-insulator transition is not guaranteed by this latter structural relaxation. Afterwards, a first-principle analysis is performed using the ABINIT software. The analysis is organized as follows: the electron band structure is computed as well as the phonon dispersion relation. Comparing the two, the occurrences of Kohn anomalies and their relation with the Fermi surface nesting is portrayed. Afterwards, electron-phonon coupling matrix elements are calculated and related to the properties of the Kohn anomalies.