| 研究課題/領域番号 |
18K03511
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| 研究機関 | 京都大学 |
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研究代表者 |
Peters Robert 京都大学, 理学研究科, 講師 (80734293)
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| 研究期間 (年度) |
2018-04-01 – 2023-03-31
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| キーワード | topological insulator / Kondo insulator / quantum oscillation |
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| 研究実績の概要 |
We have continued our research project on the interplay between strong correlations and topology in topological Kondo insulators.
In the last year, we have mainly focused on understanding quantum oscillations in these systems. Quantum oscillations usually occur in metals that exhibit a Fermi surface. Electrons around the Fermi surface form Landau levels. Furthermore, whenever a Landau level crosses the Fermi energy, a characteristic oscillation can be observed in most physical quantities. However, this conventional theory cannot explain experimentally observed quantum oscillations in Kondo insulators SmB6 and YbB12, which do not have a Fermi surface and thus no electrons at the Fermi energy which could form Landau levels crossing the Fermi energy.
While there have been several unconventional theories trying to explain these quantum oscillations by using neutral Fermions, we took the effort to analyze correlation effects in a three dimensional topological Kondo insulator by using dynamical mean-field theory. It became clear that in strong magnetic fields, the gap in the topological insulator closes, and the insulator becomes a metal. However, we have demonstrated that even before the gap closes, correlated Landau levels periodically approach the Fermi energy. These correlated Landau levels cause oscillations in observable quantities, although the material is still insulating. We believe that this scenario can be relevant for understanding the experiments on topological Kondo insulators SmB6 and YbB12.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
The dynamical mean-field calculations about quantum oscillations in topological Kondo insulators have progressed as expected, and the results have been published. We have shown that quantum oscillations can arise from the insulating bulk of a strongly interacting topological
Kondo insulator. However, during these calculations, it became clear that the metallic surface states will also contribute to the experimentally observed quantum oscillations. We are thus preparing these calculations.
Furthermore, in the last year, it became clear that exceptional points can be observed in equilibrium states of strongly correlated materials. These exceptional points, which are usually connected to non-hermitian systems out-of-equilibrium, emerge particularly easy in systems exhibiting Dirac cones. Because topological materials exhibit Dirac cones at the surface and are strongly correlated, we decided to start calculations about exceptional points in topological Kondo insulators.
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| 今後の研究の推進方策 |
This year, we will analyze the impact of magnetic fields on the surface states of the topological Kondo insulator. While we have demonstrated that it is possible to observe quantum oscillations arising from the bulk in strong magnetic fields, it is clear that the metallic surface states should also contribute to the experiments. It is thus essential to clarify the influence of the surface states on the experiments and to analyze the interplay between strong correlations and magnetic fields at the surface of a topological Kondo insulator.
As a second project, we will analyze the emergence of exceptional points in the band structure of topological Kondo insulators. Exceptional points are points in the Brillouin zone at which the non-hermitian matrix, which describes the single-particle Green's function, cannot be diagonalized. The non-hermiticity arises here due to the self-energy in the strongly correlated system. Exceptional points in the band structure are connected via Fermi arcs, increasing the spectral weight at the energy at which they occur.
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| 次年度使用額が生じた理由 |
Due to urgent tasks, I could not attend international conferences as originally planned.
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