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Anisotropic band flattening in graphene with one-dimensional superlattices


Patterning graphene with a spatially periodic potential provides a powerful means to modify its electronic properties1,2,3. In particular, in twisted bilayers, coupling to the resulting moiré superlattice yields an isolated flat band that hosts correlated many-body phases4,5. However, both the symmetry and strength of the effective moiré potential are constrained by the constituent crystals, limiting its tunability. Here, we have exploited the technique of dielectric patterning6 to subject graphene to a one-dimensional electrostatic superlattice (SL)1. We observed the emergence of multiple Dirac cones and found evidence that with increasing SL potential the main and satellite Dirac cones are sequentially flattened in the direction parallel to the SL basis vector, behaviour resulting from the interaction between the one-dimensional SL electric potential and the massless Dirac fermions hosted by graphene. Our results demonstrate the ability to induce tunable anisotropy in high-mobility two-dimensional materials, a long-desired property for novel electronic and optical applications7,8. Moreover, these findings offer a new approach to engineering flat energy bands where electron interactions can lead to emergent properties9.

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Fig. 1: Transport anisotropy in graphene subjected to a 1D superlattice.
Fig. 2: Band structure calculations for an L = 55 nm graphene 1D SL system.
Fig. 3: Anisotropic band flattening.
Fig. 4: Magnetotransport in a 1D SL device.

Data availability

Presented measurement data are available from the corresponding author upon reasonable request.

Code availability

The computer code for calculating band structures and simulating Rxx and Ryy values is available from the corresponding author upon reasonable request.


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This research was supported primarily by the Office of Naval Research (ONR) Young Investors Program (no. N00014-17-1-2832). P.M. was supported by the Science and Technology Commission of Shanghai Municipality (grant no. 19ZR1436400) and NYU-ECNU Institute of Physics at NYU Shanghai. This research was carried out using the High Performance Computing resources at NYU Shanghai.

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Authors and Affiliations



Y.L., P.M. and C.R.D. conceived the experiment. Y.L. fabricated the samples, performed transport measurements and analysed transport data. P.M. provided theoretical modelling of the system and helped interpret transport data. S.D. and C.F. performed preliminary studies on a van der Pauw sample. Y.L., P.M. and C.R.D. co-wrote the paper. K.W. and T.T. provided hBN material for device fabrication.

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Correspondence to Cory R. Dean.

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The authors declare no competing interests.

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Supplementary Information

Supplementary Figs. S1–S7 and Discussions S1–S8.

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Li, Y., Dietrich, S., Forsythe, C. et al. Anisotropic band flattening in graphene with one-dimensional superlattices. Nat. Nanotechnol. 16, 525–530 (2021).

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