Pilkyung Moon1 Carlos Forsythe2 Xiaodong Zhou3 Takashi Taniguchi4 Kenji Watanabe4 Abhay Pasupathy2 Mikito Koshino5 Philip Kim6 Cory Dean2

1, New York University Shanghai, Shanghai, , China
2, Columbia University, New York, New York, United States
3, Fudan University, Shanghai, , China
4, National Institute for Materials Science, Tsukuba, , Japan
5, Osaka University, Osaka, , Japan
6, Harvard University, Cambridge, Massachusetts, United States

The ability to manipulate two-dimensional electrons with external electric fields provides a route to band engineering. By imposing artificially designed and spatially periodic superlattice potentials, two-dimensional electronic properties can be further engineered beyond the constraints of naturally occurring atomic crystals [1, 2]. Recently, we reported a new approach to fabricate high mobility superlattice devices by integrating surface dielectric patterning with atomically thin van der Waals materials [3]. By separating the device assembly and superlattice fabrication processes, we addressed the intractable tradeoff between device processing and mobility degradation that constrains superlattice engineering in conventional systems.
In this talk, we will theoretically investigate the electronic band structures of graphene on patterned dielectric superlattices [3]. We will show the effects of different superlattice symmetries (square or triangular) and interaction strengths on the band structures, such as the width of bands and the size of gaps. The fundamental difference between the different superlattice symmetries becomes more evident when external magnetic fields are applied to the superlattices. We developed a general effective theoretical model of graphene superlattices under magnetic fields. The calculated fractal evolution of electron energy gap structures, aka Hofstadter’s butterfly [4], 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. The research findings open a route to engineer electronic structures beyond the constraints of the intrinsic symmetry of atomic layers.
[1] L. Esaki and R. Tsu, IBM J. Res. Dev. 14, 61 (1970).
[2] D. Weiss, K. von Klitzing, K. Ploog, and G. Weimann, EPL 8, 179 (1989).
[3] C. Forsythe et al., arXiv:1710.01365 (2017).
[4] D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).