Robustness of Chiral and Bound Majorana Fermions in the superconductor and 3D topological insulator bilayer without and with antidot vortex

Superconductor (SC) and Topological insulator (TI) interfaces are an important platform for realizing Majorana modes in materials [1]. Using an effective model for the surface state (SSs) of a 3D TI [2] with the paring potential, the stability of Majorana zero modes trapped by an antidot was recently investigated [3]. Here, we consider a bilayer system consisting of the TI SS and a SC explicitly to model the SC proximity effect induced by the interlayer tunneling (t_p), and explore the interplay between t_p, SC gap (△) and the system size in the formation of Majorana modes. We observe Majorana modes for realistic parameter regimes, weak t_p (<< △) to intermediate t_p (~ △), consistent with [1,3], but such Majorana modes disappear at strong t_p (>> △). Our work, hence, helps to understand the conditions and limitations to realize Majorana states in the SC-TI hybrid systems. We also discuss the details of phase transitions of the current model and its applicability to describe real systems.

[1] L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008)

[2] D. J. J. Marchand and M. Franz, Phys. Rev. B 86, 155146 (2012).

[3] R. Rechciński, A. Khindanov, D. I. Pikulin, J. Liao, L. P. Rokhinson, Y. P. Chen, R. M. Lutchyn, and J. I. Väyrynen, Phys. Rev. B 110, 075433 (2024)