Topological invariant for finite systems in the presence of disorder
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913996376899584 |
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| author | Eissele, Robert Roy, Binayyak B. Tewari, Sumanta Stanescu, Tudor D. |
| author_facet | Eissele, Robert Roy, Binayyak B. Tewari, Sumanta Stanescu, Tudor D. |
| contents | Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as semiconductor-superconductor (SM-SC) hybrid nanowires hosting Majorana zero modes, the interplay between strong disorder and finite-size effects renders these indicators (e.g., the so-called topological visibility) biased and ill-defined, significantly limiting their usefulness. In this paper, we propose the topological invariant rigorously defined for an infinite system constructed by periodically repeating the original finite disordered system, as a topological indicator. Using the one-dimensional SM-SC hybrid nanowire as an example, we show that this general and transparent approach yields faithful topological indicators free from the biases affecting commonly used finite-size indicators, capturing the nature (topological or trivial) of the phase at generic points in parameter space, and providing a reliable tool for interpreting experimental results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological invariant for finite systems in the presence of disorder Eissele, Robert Roy, Binayyak B. Tewari, Sumanta Stanescu, Tudor D. Mesoscale and Nanoscale Physics Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as semiconductor-superconductor (SM-SC) hybrid nanowires hosting Majorana zero modes, the interplay between strong disorder and finite-size effects renders these indicators (e.g., the so-called topological visibility) biased and ill-defined, significantly limiting their usefulness. In this paper, we propose the topological invariant rigorously defined for an infinite system constructed by periodically repeating the original finite disordered system, as a topological indicator. Using the one-dimensional SM-SC hybrid nanowire as an example, we show that this general and transparent approach yields faithful topological indicators free from the biases affecting commonly used finite-size indicators, capturing the nature (topological or trivial) of the phase at generic points in parameter space, and providing a reliable tool for interpreting experimental results. |
| title | Topological invariant for finite systems in the presence of disorder |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2508.13146 |