Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length

• URL: http://arxiv.org/abs/2407.09211v1
• Date: Fri, 12 Jul 2024 12:17:36 GMT
• Title: Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length
• Authors: Viktor Svensson, Martin Leijnse,
• Abstract summary: Majorana bound states (MBSs) in short, well-controllable chains of coupled quantum dots sidesteps the problem of disorder. We introduce a new quality measure that quantifies the closeness to topological protection of finetuned MBSs in short chains. We study the local distinguishability for quantum-dot chains of different length.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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