# Topological charge density waves at half-integer filling of a moiré superlattice

Polshyn H, Zhang Y, Kumar MA, Soejima T, Ledwith P, Watanabe K, Taniguchi T, Vishwanath A, Zaletel MP, Young AF. 2021. Topological charge density waves at half-integer filling of a moiré superlattice. Nature Physics.

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Polshyn, Hryhoriy

^{ISTA}^{}; Zhang, Y.; Kumar, M. A.; Soejima, T.; Ledwith, P.; Watanabe, K.; Taniguchi, T.; Vishwanath, A.; Zaletel, M. P.; Young, A. F.Abstract

When a flat band is partially filled with electrons, strong Coulomb interactions between them may lead to the emergence of topological gapped states with quantized Hall conductivity. Such emergent topological states have been found in partially filled Landau levels1 and Hofstadter bands2,3; however, in both cases, a large magnetic field is required to produce the underlying flat band. The recent observation of quantum anomalous Hall effects in narrow-band moiré materials4,5,6,7 has led to the theoretical prediction that such phases could be realized at zero magnetic field8,9,10,11,12. Here we report the observation of insulators with Chern number C = 1 in the zero-magnetic-field limit at half-integer filling of the moiré superlattice unit cell in twisted monolayer–bilayer graphene7,13,14,15. Chern insulators in a half-filled band suggest the spontaneous doubling of the superlattice unit cell2,3,16, and our calculations find a ground state of the topological charge density wave at half-filling of the underlying band. The discovery of these topological phases at fractional superlattice filling enables the further pursuit of zero-magnetic-field phases that have fractional statistics that exist either as elementary excitations or bound to lattice dislocations.

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2021-12-09

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Nature Physics

Acknowledgement

We are grateful to J. Zhu for fruitful discussions. A.F.Y. acknowledges support from the Office of Naval Research under award N00014-20-1-2609, and the Gordon and Betty Moore Foundation under award GBMF9471. M.P.Z. acknowledges support from the ARO under MURI W911NF-16-1-0361. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, via grant no. JPMXP0112101001; JSPS KAKENHI grant no. JP20H00354; and the CREST(JPMJCR15F3), JST. A.V. was supported by a Simons Investigator Award. P.L. was supported by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program.

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### Cite this

Polshyn H, Zhang Y, Kumar MA, et al. Topological charge density waves at half-integer filling of a moiré superlattice.

*Nature Physics*. 2021. doi:10.1038/s41567-021-01418-6Polshyn, H., Zhang, Y., Kumar, M. A., Soejima, T., Ledwith, P., Watanabe, K., … Young, A. F. (2021). Topological charge density waves at half-integer filling of a moiré superlattice.

*Nature Physics*. Springer Nature. https://doi.org/10.1038/s41567-021-01418-6Polshyn, Hryhoriy, Y. Zhang, M. A. Kumar, T. Soejima, P. Ledwith, K. Watanabe, T. Taniguchi, A. Vishwanath, M. P. Zaletel, and A. F. Young. “Topological Charge Density Waves at Half-Integer Filling of a Moiré Superlattice.”

*Nature Physics*. Springer Nature, 2021. https://doi.org/10.1038/s41567-021-01418-6.H. Polshyn

*et al.*, “Topological charge density waves at half-integer filling of a moiré superlattice,”*Nature Physics*. Springer Nature, 2021.Polshyn, Hryhoriy, et al. “Topological Charge Density Waves at Half-Integer Filling of a Moiré Superlattice.”

*Nature Physics*, Springer Nature, 2021, doi:10.1038/s41567-021-01418-6.**All files available under the following license(s):**

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arXiv 2104.01178