| Project/Area Number |
20K14375
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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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| Project Period (FY) |
2020-04-01 – 2025-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2022: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | topological matter / Majorana modes / Hofstadter model / quantum computation / quasiperiodic systems / low dimensional systems / superconductors / トポロジカル量子現象 / トポロジカル超伝導 / 準周期性 / 物質中のマヨラナ粒子 / 超対称性 / ナノワイヤ / 光格子中の冷却原子気体 / Thoulessポンプ / topological states / quasiperiodic structures / majorana fermions / ultracold atomic gases |
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| Outline of Research at the Start |
Topological states of matter are of great interest for their fundamental theoretical aspects and applications in quantum computation, and can lead to a great advance in human society and in physics.
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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
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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| Strategy for Future Research Activity |
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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