Magnetic field-free braiding and nontrivial fusion of Majorana bound states in high-temperature planar Josephson junctions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912467870810112 |
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| author | Sharma, Pankaj Mohanta, Narayan |
| author_facet | Sharma, Pankaj Mohanta, Narayan |
| contents | Demonstration of non-Abelian statistics of Majorana bound states (MBS) is crucial for the realization of fault-tolerant topological quantum computation. Two-dimensional platforms such as planar Josephson junctions require an in-plane magnetic field to generate a pair of MBS at its non-superconducting channel ends; however, the fixed direction of the in-plane magnetic field puts a constraint on the realization of a multi-terminal topological planar junction, and hence its ability to physically move multiple MBS -- which is necessary for performing the fusion and braiding operations. Here we show that in a planar Josephson junction coupled to a skyrmion crystal, which can generate multiple pairs of MBS in the absence of any external magnetic field, the non-trivial fusion and braiding operations can be performed. Our numerical calculations, designed for realistic two-dimensional quantum systems, certify the feasibility of experimental realization of the proposed device schemes. We find that both $s$-wave and $d$-wave superconducting leads can generate the MBS; indicating that the MBS movement operations can be performed at higher temperatures using $d$-wave superconducting leads. Our results establish that the skyrmion crystal-coupled planar Josephson junction is a viable platform for the generation and controlled movement of the MBS. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_04338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magnetic field-free braiding and nontrivial fusion of Majorana bound states in high-temperature planar Josephson junctions Sharma, Pankaj Mohanta, Narayan Superconductivity Mesoscale and Nanoscale Physics Demonstration of non-Abelian statistics of Majorana bound states (MBS) is crucial for the realization of fault-tolerant topological quantum computation. Two-dimensional platforms such as planar Josephson junctions require an in-plane magnetic field to generate a pair of MBS at its non-superconducting channel ends; however, the fixed direction of the in-plane magnetic field puts a constraint on the realization of a multi-terminal topological planar junction, and hence its ability to physically move multiple MBS -- which is necessary for performing the fusion and braiding operations. Here we show that in a planar Josephson junction coupled to a skyrmion crystal, which can generate multiple pairs of MBS in the absence of any external magnetic field, the non-trivial fusion and braiding operations can be performed. Our numerical calculations, designed for realistic two-dimensional quantum systems, certify the feasibility of experimental realization of the proposed device schemes. We find that both $s$-wave and $d$-wave superconducting leads can generate the MBS; indicating that the MBS movement operations can be performed at higher temperatures using $d$-wave superconducting leads. Our results establish that the skyrmion crystal-coupled planar Josephson junction is a viable platform for the generation and controlled movement of the MBS. |
| title | Magnetic field-free braiding and nontrivial fusion of Majorana bound states in high-temperature planar Josephson junctions |
| topic | Superconductivity Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2506.04338 |