| 研究課題/領域番号 |
16F16027
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| 研究機関 | 国立研究開発法人理化学研究所 |
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研究代表者 |
NORI FRANCO 国立研究開発法人理化学研究所, 創発物性科学研究センター, グループディレクター (50415262)
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| 研究分担者 |
LI ZHOU 国立研究開発法人理化学研究所, 創発物性科学研究センター, 外国人特別研究員
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| 研究期間 (年度) |
2016-10-07 – 2019-03-31
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| キーワード | topological |
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| 研究実績の概要 |
The platform to study longitudianl and Hall conductivity of a topological thin film has been build in the Terahertz region without and with an external magnetic field. The results have been extended to the low frequency DC limit. Take the input of the spectral function (Green’s function) measured from ARPES, one can determine the conductivity from this platform. The linear conductivity from the Kubo’s formula has been generalized to study the nonlinear second harmonic conductivity, first in the Terahertz region with the hope to be extended to the DC limit as well.
In study of the magneto-optical physics of topological materials (considering Dirac fermions continuum states quantized in disrete Landau levels in a magnetic field), similarities was noticed with Jaynes-Cummings model and the more complicated Rabi model. A general review (or a book) on these topics was planned by studying the deep connections, primarily focused on the Yukawa-like interaction of electron-phonon coupling in condensed matter and spin-boson coupling in quantum optics.
A numerical method to determine the ground state energy of a spin boson model have been developed, the accuracy can be very high, up to the machine accuracy (16 digits for double variable). To understand the multiple-mode nature in the spin boson model can help in the understanding of the quantum nature of acoustic phonons, which remains a difficulty for example in the mysterious Su-Schrieffer-Heeger model where only semiclassical solutions are available.
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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
This project proposes to study the optical and magneto-optical properties of topological materials, the theory of which has been awarded the 2016 Nobel Prize in Physics, partly because this theory successful explains the quantum (quantized) Hall effect. The quantized Hall plateau is very accurate, at least up to 8 digits accuracy and has been smartly incorporated into the Watt balance to redefine the Kilogram. My research on the nonlinear extension of the Kubo formula to study the magneto-optical and DC limit of the nonlinear optical conductivities is in good progress. At the time of making the proposal, my work was focused on the linear optical conductivity only and I never thought about the nonlinear effects. The new direction was motived by the experiments done at RIKEN and Sendai recently in 2015 and 2016. So it is a progress I made after interacting with experimental physicists working in Japan.
Also I spend a lot of time reading literature in understanding the deeper connection in the spin boson model, Holstein model, Jaynes-Cummings model and the Rabi model. At the same time I spend some time in writing code to develop numerical accurate simulations of these models. Primary numerical results has been obtained for the spin boson model. I believe all these progress are in good accordance with the plan.
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| 今後の研究の推進方策 |
1. Plan to finish the paper on "Second harmonic generation in topological insulators” and work further towards the nonlinear physics.
2. Plan to work on highly accurate numerical methods in polaron and spin boson models.
3. Plan to have business trips to communicate research results and build collaborations.
We plan to carry out a study of the ground state (imaginary time evolution) of Rabimodel on a tight binding lattice, the goal is to develop an accurate numerical method to study coupled superconducting qubits. Also, we plan to study Berry curvature and quantum Hall effect in photonic systems. This is quite different from electronic system and may be very challenging.
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