過去のセミナー

＜4/2024＞
Date
4月4日(木) 10:30-
Speaker
藤本　大仁(東京大学工学研究科物理工学専攻　森本研究室)
Title
Higher vortexability: zero field realization of higher Landau levels

The rise of moir? materials has led to experimental realizations of integer and fractional Chern insulators in small[1] or vanishing magnetic fields[2]. At the same time, a set of minimal conditions sufficient to guarantee an Abelian fractional state in a flat band was identified, namely "ideal" or "vortexable" quantum geometry[3,4]. Such vortexable bands share essential features with the lowest Landau level, while excluding the need for more fine-tuned aspects such as flat Berry curvature. A natural and important generalization is to ask if such conditions can be extended to capture the quantum geometry of higher Landau levels, particularly the first (1LL), where non-Abelian states at ν = 1/2, 2/5 are known to be competitive[5]. The possibility of realizing these states at zero magnetic field, and perhaps even more exotic ones, could become a reality if we could identify the essential structure of the 1LL in Chern bands. In this work[6], we introduce a precise definition of 1LL quantum geometry, along with a figure of merit that measures how closely a given band approaches the 1LL. We apply the definition to identify two models with 1LL structure ? a toy model of double bilayer twisted graphene and a more realistic model of strained Bernal graphene.

[1] Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Khalaf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. Forrester, et al., Fractional Chern insulators in magic-angle twisted bilayer graphene, Nature 600, 439 (2021).

[2] J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, et al., Signatures of fractional quantum anomalous hall states in twisted MoTe2, Nature 622, 63 (2023).

[3] J. Wang, J. Cano, A. J. Millis, Z. Liu, and B. Yang, Exact landau level description of geometry and interaction in a flatband, Physical review letters 127, 246403 (2021).

[4] P. J. Ledwith, A. Vishwanath, and D. E. Parker, Vortexability: A unifying criterion for ideal fractional Chern insulators, Physical Review B 108, 205144 (2023).

[5] G. Moore and N. Read, Nonabelions in the fractional quantum hall effect, Nuclear Physics B 360, 362 (1991).

[6] Manato Fujimoto, Daniel E. Parker, Junkai Dong, Eslam Khalaf, Ashvin Vishwanath, and Patrick Ledwith, Higher vortexability: zero field realization of higher Landau levels, arXiv preprint arXiv:2403.00856 (2024).


＜1/2024＞
Date
1月15日(月) 14:00-
Speaker
戎 弘実(京都大学基礎物理学研究所)
Title
Foliated BF theory and multipole symmetry

分数量子ホール効果、スピン液体などのTopological ordered phase は主に 2 次元系に現れる新奇な相で、これらの相の重要な特徴は分数電荷の励起、すなわち anyon が存在することです。従来のanyonは励起されるとバルクのどこでも動くことができますが、最近になりfracton topological phaseと呼ばれる、この性質を満たさないtopological相が理論的に提案されました。この相では分数電荷の励起の動く範囲に制限がかかり、系の縮退度も局所的な情報によってしまいます。この性質から従来のtopologicalな場の量子論は構築できず、相を記述する新しい理論が必要となっています。この背景のもと、新しい対称性であるmulti-pole symmetry(多極子の保存に対応する対称性)に着目し、そのゲージ理論から新しいtopologicalな場の理論を構築することを議論します。