| 研究課題/領域番号 |
20K14375
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| 研究機関 | 東京大学 |
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研究代表者 |
Marra Pasquale 東京大学, 大学院数理科学研究科, 特任研究員 (20799861)
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| 研究期間 (年度) |
2020-04-01 – 2025-03-31
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| キーワード | topological matter / Majorana modes / Hofstadter model / quantum computation / quasiperiodic systems / low dimensional systems / superconductors |
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| 研究実績の概要 |
In the last fiscal year, my research resulted in 1 publication and 2 papers submitted, currently under review.
The main scientific results are: 1) We established a scaling law for the lowest energy state in systems composed of arrays of several Majorana modes. This result is relevant for the realization of scalable quantum computers. 2) We proposed a novel platform for realizing Majorana modes in 2D topological superconductors with inhomogeneous order parameters. This may open new avenues for realizing Majorana-based quantum computers. 3) We derived an exact formula to parametrize the energy spectrum of the Hofstadter model. This result can be applied both to quasiperiodic systems in cold atomic gases trapped in optical lattices, and spatially periodic 2D systems in strong magnetic fields.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
The research outcome was more than originally planned:
1) Our work describing a new platform to realize Majorana modes in 2D topological superconductors with inhomogeneous order parameters was not originally planned. This platform, where Majorana modes localize at the ond of topologically nontrivial stripes, may be a versatile and realistic implementation of the Sachdev-Ye-Kitaev model (which can be regarded as a toy model to study the chaotic behavior of black holes). This model was not considered in the original research plan. 2) Our work on the Hofstadter model also has implications for the Toda lattice model studied in high-energy physics. This connection was not expected in the original research plan.
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| 今後の研究の推進方策 |
In the near future, I am planning to:
1) Generalize our novel platform to realize Majorana in 2D topological superconductors with inhomogeneous order parameters to similar systems with inhomogeneous fields.
2) Develop a framework to describe the adiabatic braiding of Majorana modes in these systems.
3) Study in more detail the connection between the Hofstadter model and the Toda lattice model.
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| 次年度使用額が生じた理由 |
I will use the remaining grant (149,214円) to travel to conferences, and pay article publications fees.
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