Superconducting transport in 1d and 2d topological Nanostructures. Nanowires and twisted bilayer graphene

• Autores: Miguel Alvarado Herrero
• Directores de la Tesis: Alfredo Levy-Yeyati (dir. tes.)
• Lectura: En la Universidad Autónoma de Madrid ( España ) en 2023
• Idioma: español
• Número de páginas: 171
• Títulos paralelos:
  • Transporte superconductor en nanoestructuras topológicas 1d y 2d. Nanocables y grafeno bicapa retorcido
• Enlaces
  • Tesis en acceso abierto en: Biblos-e Archivo
• Resumen

  • Hybrid nanostructures have become a suited material basis to engineer exotic phases of mater. One of such non-trivial phases is topological superconductivity, where low energy excitations with non-Abelian statistics would appear (i.e., the Majorana bound states), rising a huge interest due to possible applications in quantum computation. Among the candidates to observe unconventional superconductivity, one-dimensional proximity induced superconducting heterostructures and two-dimensional graphene related superlattices have risen an avid research activity. The former is based on proximitized nanowires with Rashba spin-orbit coupling that may undergo a topological transition by means of an external magnetic field. The latter rely on two-layer graphene stacking, in which a relative twist angle between the slabs induce flat bands and interactions lead to an unconventional phase diagram. The convoluted phenomenology observed on those semiconducting nanostructures, in which correlations and topology play a crucial role, claim for theoretical description of intermediate complexity. First, beyond the over-simplified toy models, that only predict a few phenomenological features (e.g., the low energy excitations) but leaves behind key elements to explain experimental measurements. Second, avoiding over-complicated microscopic calculations which depend on a plethora of microscopic parameters, obscuring the fundamental physics behind experiments. From a mesoscopic point of view, we seek to derive theoretical tools to describe accurate models which account for the relevant physics of such platforms. In this thesis, we explore the incidence of correlations and topology in superconducting transport phenomena in hybrid Josephson junctions involving exotic low-dimensional superconductors. We further compare our precise calculations with the physics derived from toy models. Taking advantage of the Green’s function techniques, we characterize the topological regime by means of local spectral properties (e.g., local density of states) and identify the presence of exotic quasiparticles in the system by associated features in the equilibrium supercurrent. More in particular, for the case of Rashba nanowires, we focus on the phenomena of the “Josephson blockade” which induces vanishing equilibrium supercurrents when both a conventional superconductor, and a topological one are forming a Josephson junction. In order to circumvent this regime, we study conventional and unconventional pairing correlations across the junction, engineering several proposals to obtain finite transport signals in such hybrid configurations. Following with twisted bilayer graphene, we sought to obtain a theoretical description of monolithic Josephson junctions. To do so, we have implemented chiral superconductivity over the flat bands of the material, analyzing the effects of the inherited non-trivial topology from the parent state in the superconducting phase. Finally, we have linked the presence of topological superconductivity in these lowdimensional Josephson junction implementations with the anomalous Josephson effect, where the current phase relation is shifted by a certain value ϕ0 in the biasing superconducting phase. This effect thus reveals the non-trivial nature of the leads and the existence of Majorana bound states in the juncture. Along this thesis, we emphasize the importance of employing “faithful” Hamiltonians to reproduce such exotic transport features