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Abstract Periodic band structures are a hallmark phenomenon of condensed matter physics. While often imposed by external potentials, periodicity can also arise through the interplay of couplings that are not necessarily spatially periodic on their own, but this option is generally less explored than the fully-periodic counterpart. Here, we investigate dynamics in a lattice structure that emerges from the simultaneous application of Raman and radio frequency coupling to a dilute-gas Bose-Einstein condensate. We elaborate on the role of Galilean invariance in this system and demonstrate a variety of techniques, including Bloch oscillations and lattice shaking with spin and momentum resolved measurements. This combined coupling scheme allows for tunability and control, enabling future investigations into unconventional band structures such as quasi-flat ground bands and those with semimetal-like band gaps.
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Fine Structure of Flat Bands in a Chiral Model of Magic Angles
Abstract We analyse symmetries of Bloch eigenfunctions at magic angles for the Tarnopolsky–Kruchkov–Vishwanath chiral model of the twisted bilayer graphene (TBG) following the framework introduced by Becker–Embree–Wittsten–Zworski. We show that vanishing of the first Bloch eigenvalue away from the Dirac points implies its vanishing at all momenta, that is, the existence of a flat band. We also show how the multiplicity of the flat band is related to the nodal set of the Bloch eigenfunctions. We conclude with two numerical observations about the structure of flat bands.
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- Award ID(s):
- 1952939
- PAR ID:
- 10548563
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Annales Henri Poincaré
- Volume:
- 26
- Issue:
- 8
- ISSN:
- 1424-0637
- Format(s):
- Medium: X Size: p. 2827-2857
- Size(s):
- p. 2827-2857
- Sponsoring Org:
- National Science Foundation
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