Inhomogeneous stripe phase and tunable Majorana zero modes in Rashba <i>s</i>-wave superconducting systems in the presence of in-plane Zeeman field

Based on the extended Bogoliubov–de Gennes theory, the inhomogeneous stripe order and Majorana bound states are demonstrated in s-wave superconducting systems with Rashba spin–orbit interaction when the in-plane Zeeman field is applied. For a fully open square sample, topological phase transitions can be driven by the Zeeman field, and the stripe phase with spatially oscillating order parameter shows up across a critical field strength. The topological channels arise in this phase, which can be utilized to create and manipulate Majorana zero modes. Interestingly, (quasi-)one-dimensional channels with diminished pairing amplitude can be formed in narrow arms of a square loop, accompanied by the reconstruction of energy spectra of the condensate and the realization of robust Majorana zero-energy states at the ends of channels. The associated evolution of topological phases and the location of Majorana zero modes are highly sensitive to the field direction. Moreover, the effects of the rectangular aspect-ratio and the off-centered hole as well as the surface defects on Majorana end modes are explored in Rashba asymmetric loops. In comparison, the field-dependent evolution processes of low-energy levels behave more complicated because the emergence of confined topological channels can be effectively tuned by the length and width of loop arms as well as the size and position of an introduced small indentation at the outer edge. Rich patterns of Majorana corner-like states are generated for such asymmetric systems. Our theoretical predictions may shed new light on the tunability of Majorana zero modes and provide useful guidance for future experiments and applications.