Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913598627905536 |
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| author | Svensson, Viktor Leijnse, Martin |
| author_facet | Svensson, Viktor Leijnse, Martin |
| contents | Realizing Majorana bound states (MBSs) in short, well-controllable chains of coupled quantum dots sidesteps the problem of disorder, but requires fine-tuning and does not give the true topological protection inherent to long chains. Here, we introduce a new quality measure that is applicable also in the presence of strong electron-electron interactions and that quantifies the closeness to topological protection of finetuned MBSs in short quantum-dot chains. We call this measure local distinguishability because it puts a bound to the degree an arbitrary local measurement can distinguish between two states. We study the local distinguishability for quantum-dot chains of different length. The three-dot chain is studied in detail, and we find that it may not always be an improvement over the two-dot case, a fact that can be understood within an effective model derived from perturbation theory. For longer chains, the local distinguishability vanishes exponentially, signalling a transition to a topological phase with two ground states that cannot be distinguished by any local measurement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09211 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length Svensson, Viktor Leijnse, Martin Mesoscale and Nanoscale Physics Quantum Physics Realizing Majorana bound states (MBSs) in short, well-controllable chains of coupled quantum dots sidesteps the problem of disorder, but requires fine-tuning and does not give the true topological protection inherent to long chains. Here, we introduce a new quality measure that is applicable also in the presence of strong electron-electron interactions and that quantifies the closeness to topological protection of finetuned MBSs in short quantum-dot chains. We call this measure local distinguishability because it puts a bound to the degree an arbitrary local measurement can distinguish between two states. We study the local distinguishability for quantum-dot chains of different length. The three-dot chain is studied in detail, and we find that it may not always be an improvement over the two-dot case, a fact that can be understood within an effective model derived from perturbation theory. For longer chains, the local distinguishability vanishes exponentially, signalling a transition to a topological phase with two ground states that cannot be distinguished by any local measurement. |
| title | Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2407.09211 |