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Chiral assemblies of pinwheel superlattices on substrates


The unique topology and physics of chiral superlattices make their self-assembly from nanoparticles highly sought after yet challenging in regard to (meta)materials1,2,3. Here we show that tetrahedral gold nanoparticles can transform from a perovskite-like, low-density phase with corner-to-corner connections into pinwheel assemblies with corner-to-edge connections and denser packing. Whereas corner-sharing assemblies are achiral, pinwheel superlattices become strongly mirror asymmetric on solid substrates as demonstrated by chirality measures. Liquid-phase transmission electron microscopy and computational models show that van der Waals and electrostatic interactions between nanoparticles control thermodynamic equilibrium. Variable corner-to-edge connections among tetrahedra enable fine-tuning of chirality. The domains of the bilayer superlattices show strong chiroptical activity as identified by photon-induced near-field electron microscopy and finite-difference time-domain simulations. The simplicity and versatility of substrate-supported chiral superlattices facilitate the manufacture of metastructured coatings with unusual optical, mechanical and electronic characteristics.

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Fig. 1: Chiral symmetry breaking in superlattices from tetrahedra undergoing phase transition from low- to high-packing fraction states.
Fig. 2: Corner-sharing and pinwheel bilayer superlattices with corner-to-edge connections from gold tetrahedral NPs.
Fig. 3: Chirality of pinwheel bilayer lattices deposited on solid substrates.
Fig. 4: Formation mechanism and controllability of self-assembled chiral superlattices from tetrahedral NPs.

Data availability

The datasets generated during and/or analysed during the current study are available in the Illinois Data Bank (

Code availability

The codes used for data analysis during the current study are available from GitHub (


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Experiments were carried out in part in the Materials Research Laboratory (MRL) Central Research Facilities, University of Illinois. We thank J. Spear and H. Zhou (MRL) for assistance with SEM measurements. We are grateful to D. Vecchio for participation in the calculation of CI. This research was supported by the Office of Naval Research (no. MURI N00014-20-1-2479). S.Z. and Q.C. thank the Alfred Sloan Foundation for support via the Sloan fellowship. We also thank the Center for Nanoscale Materials, a US Department of Energy Office of Science User Facility, supported by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DE-AC02-06CH11357. N.A.K., J. Lu and J.-Y.K. thank the Vannevar Bush DoD Fellowship (to N.A.K.) entitled ‘Engineered Chiral Ceramics’ (no. ONR N000141812876). FDTD simulations and OPD calculations were supported by NSF (no. 1463474, entitled ‘Energy- and Cost-Efficient Manufacturing Employing Nanoparticles’). Research by A.T. was supported by the US Department of Energy (US DoE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Ames National Laboratory is operated for the US DoE by Iowa State University under contract DE-AC02-07CH11358.

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Authors and Affiliations



S.Z., J. Li, J. Lu and Q.C. designed the experiments. S.Z. and J. Li performed the experiments and data analysis. J. Li performed interaction calculations. J. Lu and N.A.K. performed FDTD simulations and analysed simulation data. H.L., Z.D.H., T.E.G. and I.A. performed PINEM experiments. J-Y.K. performed OPD calculations. S.Z. and A.K. performed tetrahedron purification. L.Y. developed protocols for image analysis and particle tracking. C.L., C.Q. and J. Li performed liquid-phase TEM experiments. N.A.K. built the GT model of the superlattices and calculated the CI values of the superlattices. W.C. contributed to property discussions. X.L. and A.T. contributed to geometric calculation and analysis. K.S. contributed to Maxwell lattice construction and discussion. All authors contributed to the writing of the paper. Q.C. and N.A.K. supervised the work.

Corresponding authors

Correspondence to Nicholas A. Kotov or Qian Chen.

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Nature thanks Ou Chen, Andrei Petukhov and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary information

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This file contains Supplementary Notes 1–6, Tables 1–7, Figs. 1–27 and references.

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Supplementary Video 1. Animations of lattice transformation of tetrahedron mono- and bilayers under effective in-plane ‘compression’.

Animations showing the tetrahedron monolayer forming into a disordered structure under effective in-plane ‘compression’ (left) and the achiral honeycomb bilayer lattice transforming into a pinwheel bilayer lattice by switching from corner-to-corner connections to corner-to-edge connections (right) in top and perspective views.

Supplementary Video 2. Animations showing that the tetrahedron pinwheel bilayer lattice is chiral with the substrate.

Without substrate, the pinwheel bilayer lattice can overlap with its mirror image by flipping whereas, with substrate, the pinwheel bilayer lattice can no longer overlap with the mirror image through flipping.

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Zhou, S., Li, J., Lu, J. et al. Chiral assemblies of pinwheel superlattices on substrates. Nature 612, 259–265 (2022).

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