Coexistence and Interconversion of Multiple-Order Majorana Modes in Topological Superconductor Films with Varying Thickness
Abstract
We theoretically investigate the thickness-dependent evolution of Majorana modes in C2h-symmetric topological superconductor films (such as the recently discovered 2M-WS2) proximity coupled with magnetic insulators. For sufficiently thick films, two Majorana bound states coexist as end modes at the surface and interface along a vortex line, with the interfacial mode evolving into a chiral Majorana edge mode upon increasing the proximity-induced exchange field. The intrinsic C2h crystalline symmetry selects two chiral Majorana modes circulating along the hinges on two of the four side surfaces of the film. When the penetration depth of the exchange field is sufficiently shallow, the two circulating modes are localized near the interface, but with qualitatively different subsequent evolutions. One of them further collapses to form two Majorana corner modes, while the other merges with the chiral Majorana mode circulating around the interface. Importantly, the corner modes are well decoupled from the interfacial chiral mode, thereby enabling an unprecedented coexistence of first-, second-, and third-order Majorana modes within a single material platform. We further show that such coexistence persists even in the ultrathin-film limit, where the electric-field-controlled two-dimensional Z2 topology offers an extra advantage to readily interconvert the multiple-order Majorana modes. These findings highlight the pivotal role of the proper crystalline symmetry in enabling emergence, manipulation, and potential braiding of Majorana modes for demonstrating non-Abelian statistics and fault-tolerant quantum computation.
Related
- Dissipation-induced nonlocal phase-coherent transport in a topological superconductor
- Topological Superconducting Phases in a Strained Altermagnet-Superconductor Heterostructure
- Direct transition from a fractional Chern insulator to a topological superconductor
- Topological superconductivity in an altermagnet-superconductor heterostructure
- Geometrical approach and topological electron density in the p x + ip y superconductor
BibTeX
@misc{ding2026coexistence,
title = {{Coexistence and Interconversion of Multiple-Order Majorana Modes in Topological Superconductor Films with Varying Thickness}},
author = {Zhizhong Ding and Chuanbao Zhang and Shunhong Zhang and Xiaoyu Zhu and Wei Qin and Ping Cui and Zhenyu Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24311},
eprint = {2609.24311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24311},
}
RIS
TY - UNPB
TI - Coexistence and Interconversion of Multiple-Order Majorana Modes in Topological Superconductor Films with Varying Thickness
AU - Zhizhong Ding
AU - Chuanbao Zhang
AU - Shunhong Zhang
AU - Xiaoyu Zhu
AU - Wei Qin
AU - Ping Cui
AU - Zhenyu Zhang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24311
UR - https://arxiv.org/abs/2609.24311
AB - We theoretically investigate the thickness-dependent evolution of Majorana modes in C_2h-symmetric topological superconductor films (such as the recently discovered 2M-WS_2) proximity coupled with magnetic insulators. For sufficiently thick films, two Majorana bound states coexist as end modes at the surface and interface along a vortex line, with the interfacial mode evolving into a chiral Majorana edge mode upon increasing the proximity-induced exchange field. The intrinsic C_2h crystalline symmetry selects two chiral Majorana modes circulating along the hinges on two of the four side surfaces of the film. When the penetration depth of the exchange field is sufficiently shallow, the two circulating modes are localized near the interface, but with qualitatively different subsequent evolutions. One of them further collapses to form two Majorana corner modes, while the other merges with the chiral Majorana mode circulating around the interface. Importantly, the corner modes are well decoupled from the interfacial chiral mode, thereby enabling an unprecedented coexistence of first-, second-, and third-order Majorana modes within a single material platform. We further show that such coexistence persists even in the ultrathin-film limit, where the electric-field-controlled two-dimensional Z_2 topology offers an extra advantage to readily interconvert the multiple-order Majorana modes. These findings highlight the pivotal role of the proper crystalline symmetry in enabling emergence, manipulation, and potential braiding of Majorana modes for demonstrating non-Abelian statistics and fault-tolerant quantum computation.
ER -