Electronic Structure Engineering of Graphene Using Patterned Dielectric Superlattices*

The ability to manipulate electrons with external electric fields provides a route to design electronic structures beyond the constraints of naturally occurring atomic crystals. We reported a new approach to fabricate high mobility superlattice devices by integrating dielectric patterning with atomically thin van der Waals materials [1].
In this talk, we theoretically investigate the band structures of graphene on dielectric superlattices [1]. The effects of different superlattice symmetries (square or triangular) and interaction strengths on the band structures will be emphasized. The fundamental difference between the different superlattice symmetries becomes more evident when external magnetic fields are applied to the superlattices. The theoretically predicted fractal evolution of electronic gap structures, aka Hofstadter’s butterfly [2], reveals the intrinsic electron-hole asymmetry in the triangular superlattices. And the non-monotonic sequence of the quantized Hall conductivity is consistent with experimental data.
[1] C. Forsythe et al., arXiv:1710.01365 (2017).
[2] D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).