Flat Bands in Magic-Angle Vibrating Plates
Lopez, MR; Penaranda, F; Christensen, J; San-Jose, P
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.
Band structure of vibrating plates. Dirac cones in the normalized band structure Ω(k) of a single patterned plate (a), two decoupled (κ=0) but rotated (m=5, θ≈6°) plates (b), and two coupled (κ=20) and rotated plates (c). Red and blue denote eigenvalues mostly concentrated on the top and bottom layers, whose respective Dirac points are located at K±. The anticrossing at the M point forms a van Hove singularity. In green is the normalized band structure of the equivalent graphene counterparts.