Examining mean-field approximations and Bogoliubov-de Gennes (BdG) equations for topological quantum computing - some considerations on the conceptual basis of Majorana zero modes in p+ip superconductors

Mean-field approximations;Bogoliubov-de Gennes (BdG) equations;Particle number conservation;Majorana zero modes;P+ip superconductors;Topological quantum computing

Lin, Yiruo

关键词: Mean-field approximations;    Bogoliubov-de Gennes (BdG) equations;    Particle number conservation;    Majorana zero modes;    P+ip superconductors;    Topological quantum computing;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/97306/LIN-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The current theoretical framework for studying Majorana zero modes (MZM) in superconductors and its application for topological quantum computing is based on mean-field approximations and is derived from solutions to BdG equations. In this framework, particle number conservation is broken and non-interacting fermion Hamiltonian is used to describe physics of interest. We argue that these features in the current framework may make it insufficient for studying topological properties of MZM pertinent to quantum computing. After reviewing the current theory with an emphasis on its potential problems, we investigate physics beyond the BdG equations in a toy model and find evidence for the non-trivial role of particle number conservation in Berry phase of transporting a bound quasiparticle around a vortex in a s-wave superconductor. We then study the effect of particle number conservation and superconducting condensate on braiding MZM in vortices in chiral p-wave superconductors and find that they may have non-negligible effect on properties of MZM, suggesting the need for further study on the theoretical basis of this intriguing subject.