Topological phase transitions and impurity-modulated Majorana zero modes in spin–orbit coupled superconducting nanoloops

By considering two-dimensional s-wave superconducting square nanoloops with Rashba spin–orbit (SO) coupling, we systematically investigate the transitions between topologically trivial and nontrivial superconducting phases under the in-plane Zeeman field in the framework of the microscopic Bogoliubov–de Gennes theory. The Zeeman-induced topological channel with weak pairing amplitude, which has been proposed to host Majorana bound states, is highly sensitive to the Rashba SO-coupling strength and the arm width of the loop. The topological phase transitions can also be driven by the admixed Dresselhaus SO interaction and may be detected through the evolution characteristics of persistent supercurrents when a vertical magnetic flux is applied. Moreover, the influences of nonmagnetic and magnetic impurities on energy spectra and Majorana zero modes are mainly analyzed in the Rashba square-loop sample. The occurrence of Majorana zero-energy states can be effectively tuned by the impurity types and locations. For the case of a single nonmagnetic impurity, no impurity bound states arise inside the pairing gap, while the Zeeman-field ranges of nontrivial topological phases depend on scattering strengths of the impurity potential resulting from enhanced or suppressed superconducting order parameters at the impurity site. By contrast, a single magnetic impurity with some appropriate strength can induce subgap quasiparticle states, which in turn strongly impact the evolution processes of low-energy levels and the patterns of Majorana bound states. Additionally, rich Majorana features can be realized by embedding a (non)magnetic impurity bilayer into the loop arm to model a tunneling junction.