2018 Fiscal Year Research-status Report
Novel Quantum States in Topological Kondo insulators
| Project/Area Number |
18K03511
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| Research Institution | Kyoto University |
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Principal Investigator |
Peters Robert 京都大学, 理学研究科, 講師 (80734293)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | Kondo insulator / strong correlations / topolgy |
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| Outline of Annual Research Achievements |
In the last year, I focused on the study of magnetic phases in topological Kondo insulators. It is known that SmB6, a candidate for a topological Kondo insulator, becomes magnetic under pressure. At this point, interesting questions arise such as what kind of magnetic order is realized, can surface states still be observed and are those still protected? Furthermore, if surface states still exist, it is important to study the impact of the magnetic order on those.
Using real-space dynamical mean field theory, I have analyzed a three-dimensional model of a topological Kondo insulator. The application of pressure has been simulated by changing the strength of the hybridization between c- and f-electrons. As in the experiments, I find that for decreasing hybridization strength (corresponding to increasing pressure), magnetic order appears. Depending on the c-electron filling, I find an A-type antiferromagnetic phase and a ferromagnetic phase. Although the time-reversal symmetry, which protects surface states in the nonmagnetic system, is broken, I find that surface states can still exist, but only on surfaces with in-plane magnetization. These surface states are protected by the reflection symmetry of the crystal. The emergence or absence of surface states depending on the magnetization direction could thereby yield interesting technological applications. Switching the magnetization direction by an external magnetic field would generate or destroy the surface states spanning the gap.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
As originally planned, I am currently studying quantum oscillations in topological Kondo insulators such as SmB6 and YbB12, which have been experimentally observed but contradict our conventional theories.
Using real-space dynamical mean field theory, I have succeeded in performing numerical calculations for two-dimensional topological Kondo insulators with an applied magnetic field. Due to the presence of a magnetic field, I have to include Peierls phases into the model. These complex phases make it necessary to perform calculations on very large clusters, which make the use of supercomputers such as at the ISSP necessary. Although the calculations are heavy and take time, I am progressing as planned.
As has been found in previous works for noninteracting continuum models, the gap closes in strong magnetic fields. Interestingly, in my calculations, quantum oscillations in several quantities are observable due to interacting Landau levels coming very close to the Fermi energy already before the gap closes. Remarkably, interactions seem to enhance the amplitude of these oscillations.
To further understand these quantum oscillations, I am currently analyzing the impact of interaction strength and temperature on these quantum oscillations. Because new and interesting phenomena have been found during the calculations, finalizing these calculations will take more time. However, all the results look very promising.
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| Strategy for Future Research Activity |
While the calculations for analyzing quantum oscillations in topological Kondo insulators are progressing, there are still several open questions. It has been proposed that quantum oscillations could be observed due to exceptional points, where the matrix describing the single-particle spectral function is non-diagonalizable. While I have shown that exceptional points are not necessary to observe quantum oscillations, we have also shown in another work that exceptional points can occur in strongly correlated f-electron materials. Thus, naturally, the question arises whether and how exceptional points influence quantum oscillations in these materials.
Another important question concerns the dimensionality. My calculations until now are mainly done for two-dimensional models. However, the materials are three-dimensional. Although I have confirmed that the gap-closing and quantum oscillations in a magnetic field can be observed also in simulations for three-dimensional models, the impact of the dimensionality on the quantum oscillations is still obscure.
Furthermore, I am currently preparing to study quantum oscillations using a model based on a realistic band structure, which has been obtained using first principles. Such a realistic three-dimensional model could even be used to compare calculated oscillation frequencies with experiments.
Thus, there are several interesting questions, which will be studied in the near future.
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| Causes of Carryover |
Originally I had planned to attend the interactional conference for strongly correlated electron systems (SCES 2018) held together with the international conference on magnetism (ICM 2018) in San Francisco. Unfortunately, due to other urgent tasks, I had to cancel these plans.
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