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Grant amount：\14820000 （ Direct Cost: \11400000 、 Indirect Cost：\3420000 ）

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Grant amount：\2600000 （ Direct Cost: \2000000 、 Indirect Cost：\600000 ）

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Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）

本研究は、キタエフ模型におけるマヨラナ粒子に着目し、それを活用したスピン流制御を理論的に解明・探索することを目的としている。電荷の自由度が凍結した量子スピン系において、量子スピン液体が注目を集めている。この量子スピン液体はキタエフ模型において実現し、そこではスピンの分数化によりマヨラナ粒子とフラックスが生じることが知られている。この系においては、マヨラナ粒子を媒介としたスピン振動を伴わないスピン輸送現象が起こる。この現象はマヨラナ粒子の非可換性を必要としないため、量子計算素子などへの応用が期待される。本研究では、キタエフ模型のマヨラナ粒子のスピン流を量子計算機上で実行することを目的とし、量子計算アルゴリズムを開発した。

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Grant amount：\15210000 （ Direct Cost: \11700000 、 Indirect Cost：\3510000 ）

The objective of this research project is to propose theoretical devices with relatively simple controllability that take advantage of the novel physical properties predicted in the Kitaev model. Two types of the Kitaev model are known: a quantum spin type and a one-dimensional p-wave superconductor type. With regard to the quantum spin type model, a new switching mechanism has been proposed that controls the transport of magnetic excitations by Majorana quasiparticles. Furthermore, we predicted the emergence of rotationally symmetry-breaking superconducting states in carrier-doped systems, along with the proposal of a superconducting switch utilizing this mechanism. With regard to the 1D p-wave model, various Josephson current-phase relationships and also the superconducting diode effect have been predicted when the models are arranged in parallel pairs.

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Grant amount：\156780000 （ Direct Cost: \120600000 、 Indirect Cost：\36180000 ）

Hypermaterials such as quasicrystals and approximants are characterized by their high dimensionality and have a “complementary space”, which is orthogonal to the real space and has structural degrees of freedom. We have studied the physical properties of hypermaterials for the purpose of elucidating the order, dynamics, and laws hidden in the complementary space. Major results include: (1) discovery of new superconducting quasicrystals and approximants, (2) magnetism and quantum critical phenomena: important clues to the relationship between high dimensionality and physical properties, (3) specific heat anomalies at high temperature and phason, (4) visualization of quasiperiodic order with complementary space mapping, (5) hyperuniformity and multifractals, and (6) Applications of hypermaterials.

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