Tight binding model of a superconducting nanowire

Majorana bound states (MBS) are topologically protected zero energy modes with exciting properties to build a decoherence free quantum computer. MBS appear for the first time in the Kitaev’s toy model, which can be effectively built from elementary interactions. In 2014, an experimental setup was built which consisted of a three layer zig-zag Fe nanowire, which is ferromagnetic (FM), deposited on top of a Pb (110) superconducting (SC) surface where SC and Rashba spin-orbit (SO) interactions are inherited by proximity effects. As expected, the experiment showd clear evidence of MBS localized at the ends of the wire. However, further theoretical analysis is required to understand and control the physical features of the excitations. In this work we develop an analytical tight-binding model of the experimental setup using matrix partitioning techniques. We describe the mobile electrons (π-band) of the nanowire including effectively the σ- band, and the proximity induced SC and SO. The geometrical details of the setup are included within the Slater-Koster formalism, and analytical expressions for the effective interactions are derived. We analyze the interplay between SC and FM and characterize its influence on the topological phase by calculating the spectra and Pfaffian invariant. Finally, we determine optimal experimental conditions for the appearance of MBS.

• Hovedforfatter: Torres Luna, Juan Daniel (author)
• Format: bachelorThesis
• Sprog: eng
• Udgivet: 2020
• Fag: Ferromagnetism; Superconductivity; Spin Orbit; Majorana
• Online adgang: http://repositorio.yachaytech.edu.ec/handle/123456789/202