»ã±¨±êÌâ (Title)£ºAharonov-Bohm cages and flat bands in hyperbolic tilings£¨Aharonov-BohmÁýÄ¿Ó볬ÇúÃæÆ´¿é½á¹¹ÖеÄƽ´ø£©

»ã±¨ÈË (Speaker)£ºRemy Mosseri ½ÌÊÚ£¨·¨¹ú¹ú¶È¿ÆÑÐÖÐÐÄ-Ë÷¹ú´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê10ÔÂ29ÈÕ(Öܶþ) 15:30

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿G601

Ô¼ÇëÈË(Inviter)£ºÖÓ½¨ÐÂ

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»ã±¨ÌáÒª£ºAharonov-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.