报告题目 (Title)：Aharonov-Bohm cages and flat bands in hyperbolic tilings（Aharonov-Bohm笼目与超曲面拼块结构中的平带）
报告人 (Speaker)：Remy Mosseri 教授（法国国家科研中心-索邦大学）
报告时间 (Time)：2024年10月29日(周二) 15:30
报告地点 (Place)：校本部G601
邀请人(Inviter)：钟建新
主办部门：量子科技研究院，理学院物理系
报告摘要：Aharonov-Bohm caging is a localization mechanism stemming from the competition between the geometry and the magnetic field. Originally described for a tight-binding model in the Dice lattice, this destructive interference phenomenon prevents any wavepacket spreading away from a strictly confined region. Accordingly, for the peculiar values of the field responsible for this effect, the energy spectrum consists in a discrete set of highly degenerate flat bands. In the present work, we show that Aharonov-Bohm cages are also found in an infinite set of Dice-like tilings defined on a negatively curved hyperbolic plane.
We detail the construction of these tilings and compute their Hofstadter butterflies by considering periodic boundary conditionson high-genus surfaces.
We also consider the energy spectrum of Kagome-like tilings (which are dual of Dice-like tilings), which displays interesting features, such as highly degenerate states arising for some particular values of the magnetic field. Finally, we also study the triangular Husimi cactus, which is a limiting case in the family of hyperbolic Kagome tilings, and we derive an exact expression for its spectrum versus magnetic flux.
