Ganesh C. Paul

Very recently few theoretical proposals have been put forward to simulate twisted bilayers using cold atoms in state-dependent optical lattices, which can be used as an alternative platform to investigate twisted bilayers in solid-state experiments. We study the band structure of both square and hexagonal geometries in an optical lattice set-up, where the band structure can be tuned to be almost flat by proper implementation of interlayer Gaussian-type coupling. We examine the evolution of a particle in the twisted bilayer square-like potential, and find that the particle follows specific paths forming channels when the interlayer hopping is much stronger than the intralayer hopping strength. Due to the flexibility of controlling the inter- and intralayer coupling in optical lattices, our proposals should be easy to be realised in a cold atom set-up.