Topological transition due to quantum confinement in thin superconductor films

May 12, 2023
10:00 AM - 11:00 AM
Prof. Dr. Alessio Zaccone
University of Milan, Department of Physics
Main Topic
Ines Firlle
The quantum states of particles in materials and devices are the solutions of the Schrӧdinger equation in a “box” of a certain shape, in the space dimensionality of interest. There is always the question of what to do with the boundary conditions at the walls: These must be irrelevant for a large system, but they may be important for mesoscopic systems at the nano-scale. I will start from the basic principle that shrinking a 3D material along one of the three space dimensions puts a restriction on the propagation of quantum waves inside the material [1,2]. This leads to a number of states in momentum space that remain unoccupied. For the simple example of bosons (e.g. phonons) the problem admits an analytical solution valid for thin films, from which we can compute fundamentally new laws, and surprising effects for the phonon density of states of thin films at low energy [3], the elasticity of thin films [1], as well as Bose-Einstein condensation in thin films [4]. The same principle can be applied to the distribution of quantum states of electrons in confined metallic systems such as superconducting thin films. In particular, the Fermi sphere develops two spherical cavities of unoccupied states that grow upon shrinking the film thickness. By implementing this model within the BCS theory of superconductivity, the critical superconducting temperature can be calculated as a function of film thickness in good agreement with experiments on Pb thin films, with a strong enhancement of the Tc upon decreasing the thickness followed by a maximum and a decrease to zero upon approaching the 2D limit (in accord with the Mermin-Wagner theorem) [5]. Intriguingly, as the two spherical cavities keep growing, a new topological transition in the Fermi surface of metallic thin films is predicted [5], which is different from any previously known topological transitions of the Fermi surface (e.g. the Lifshitz transition). Interestingly, previous numerical models based on hard-wall boundary conditions (e.g. Thompson-Blatt) predict large fluctuations of the Tc as a function of film thickness, which are not visible in the experimental data, as the latter are instead very well matched by the new theory. [1] A. Zaccone & K. Trachenko, PNAS 117 (33) 19653-19655 (2020) [2] A. E. Phillips et al., Phys. Rev. Materials 5, 035602 (2021) [3] Y. Yu et al., Nature Communications 13, 3649 (2022) [4] R. Travaglino and A. Zaccone, J. Phys. B: At. Mol. Opt. Phys. 55 055301 (2022) [5] R. Travaglino and A. Zaccone, J. Appl. Phys. 133, 033901 (2023)

Last modified: May 12, 2023, 7:37:40 AM


Leibniz Institut für Festkörper- und Werkstoffforschung Dresden (A1E.10, Hörsaal, IFW Dresden)Helmholtzstraße2001069Dresden


Leibniz Institut für Festkörper- und Werkstoffforschung DresdenHelmholtzstraße2001069Dresden
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