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Flat Bands in Magic-Angle Vibrating Plates

María Rosendo López1, Fernando Peñaranda2, Johan Christensen1, and Pablo San-Jose2,*

  • 1Department of Physics, Universidad Carlos III de Madrid, ES-28916 Leganés, Madrid, Spain
  • 2Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas (ICMM-CSIC), ES-28049 Madrid, Spain

  • *Corresponding author. pablo.sanjose@csic.es
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Phys. Rev. Lett. 125, 214301 – Published 20 November, 2020

DOI: https://doi.org/10.1103/PhysRevLett.125.214301

Abstract

Twisted bilayer graphene develops quasiflat bands at specific “magic” interlayer rotation angles through an unconventional mechanism connected to carrier chirality. Quasiflat bands are responsible for a wealth of exotic, correlated-electron phases in the system. In this Letter, we propose a mechanical analog of twisted bilayer graphene made of two vibrating plates patterned with a honeycomb mesh of masses and coupled across a continuum elastic medium. We show that flexural waves in the device exhibit vanishing group velocity and quasiflat bands at magic angles in close correspondence with electrons in graphene models. The strong similarities of spectral structure and spatial eigenmodes in the two systems demonstrate the chiral nature of the mechanical flat bands. We derive analytical expressions that quantitatively connect the mechanical and electronic models, which allow us to predict the parameters required for an experimental realization of our proposal.

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See Also

Magic-angle bilayer phononic graphene

Yuanchen Deng, Mourad Oudich, Nikhil JRK Gerard, Jun Ji, Minghui Lu, and Yun Jing
Phys. Rev. B 102, 180304(R) (2020)

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Phys. Rev. Lett. 125, 214301– Published 20 November, 2020
  • Received 27 August 2020
  • Accepted 8 October 2020
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