Abstract
Electrostatic superlattices have been known to significantly modify the electronic structure of low-dimensional materials. Studies of graphene superlattices were triggered by the discovery of moiré patterns in van der Waals stacks of graphene and hexagonal boron nitride (hBN) layers a few years ago. Very recently, gate-controllable superlattices using spatially modulated gate oxides have been achieved, allowing for Dirac band structure engineering of graphene. Despite these rapid experimental progresses, technical advances in quantum transport simulations for large-scale graphene superlattices have been relatively limited. Here, we show that transport experiments for both graphene/hBN moiré superlattices and gate-controllable superlattices can be well reproduced by transport simulations based on a scalable tight-binding model. Our finding paves the way to tuning-parameter-free quantum transport simulations for graphene superlattices, providing reliable guides for understanding and predicting novel electric properties of complex graphene superlattice devices.
Highlights
Electrostatic superlattices have been known to significantly modify the electronic structure of low-dimensional materials
As shown in the following, our transport simulations based on the real-space Green’s function method for twoterminal structures with the superlattice potential arising either from the graphene/hexagonal boron nitride (hBN) moiré pattern or from periodically modulated gating are consistent with transport experiments as well as mini-band structures based on the continuum model
To perform quantum transport simulations for graphene working in real-space, the scalable tight-binding model[29] has been proved to be a very convenient numerical tool[30,31,32,33,34]: the physics of a real graphene system can be captured by a graphene lattice scaled by a factor of s such that the lattice spacing and nearest-neighbor hopping parameter are given by a = sa[0] and t = t0/s, respectively, where a0 ≈ 0.142 nm and t0 ≈ 3 eV are the tight-binding parameters for a genuine graphene lattice
Summary
Electrostatic superlattices have been known to significantly modify the electronic structure of low-dimensional materials. Other exciting transport experiments have been reported[7,8,9,10,11,12,13], as well as a dynamic band structure tuning[14,15] Another approach for inducing a superlattice potential in graphene has been demonstrated by using patterned dielectrics[16], allowing for mini-band structure engineering. Our transport simulations based on the real-space Green’s function method for twoterminal structures with the superlattice potential arising either from the graphene/hBN moiré pattern or from periodically modulated gating are consistent with transport experiments as well as mini-band structures based on the continuum model. Our method is applicable well to multi-terminal structures for simulating, for example, four-probe measurements using the Landauer–Büttiker approach[28]
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