2022 Fiscal Year Research-status Report
Topological states of matter induced by spatially-modulated fields
| Project/Area Number |
20K14375
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
Marra Pasquale 東京大学, 大学院数理科学研究科, 特任研究員 (20799861)
|
|---|
| Project Period (FY) |
2020-04-01 – 2024-03-31
|
| Keywords | 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 |
|---|
| Outline of Annual Research Achievements |
In this last fiscal year, my research resulted in 3 publications, one accepted paper, 6 oral contributions to conferences, and 4 invited seminars in research institutions. Scientifically, the main achievements were:
We demonstrated the possibility to braid Majorana modes via spatially-modulated fields, employing Majorana modes localized in discrete 1D arrays.
We proposed a novel way to manipulate Majorana modes in 2D superconductors via inhomogeneous superconducting order.
We developed a novel framework to describe nontrivial Majorana modes and other kinds of trivial modes in 1D superconductors.
I wrote an extended review on Majorana modes in topological superconductors, which summarizes the main achievements in the field and will hopefully serve as inspiration for future research.
|
| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
At the end of this fiscal year, the main research goals of my proposal have led to major publications, pushing the research in the field of topological states of matter in mesoscopic systems and in cold atomic gases, shedding new light on physical phenomena such as supersymmetry, Majorana modes, Thouless pumps, and quasiperiodicity. However, part of the research has been slowed down due to the lack of scientific discussions during the pandemic. As a result of this situation, some of the research achievements have not been published, but they will soon be submitted to review.
|
| Strategy for Future Research Activity |
In the near future, I am planning to:
1) develop a proposal to employ spatially-modulated long-range orders, such as magnetic orders or superconducting inhomogeneous phases, in order to manipulate and braid topologically nontrivial anyons, such as Majorana modes in topological superconductors.
2) develop a more general framework to describe topologically protected edge modes in the presence of smoothly modulated fields, and to understand possible crossovers between different regimes.
3) develop a deeper understanding of the connections between quantum geometry and quasiperiodicity induced by spatially-modulated fields.
4) extend some of my previous findings obtained in one-dimensional models to two or higher dimensions.
|
| Causes of Carryover |
Many conferences and academic visits were postponed due to the pandemic. As a consequence, I did not spend all the amount of funds planned. I will use the remaining funds for academic visits and conferences in the next fiscal year.
|
