dissipative nonreciprocal devices, a circulator
that is controlled by a single quantum system
also enables operation in coherent superposition states of routing light in one and the other
direction, providing a route toward its application in future photonic quantum protocols. The
demonstrated operation principle is universal in
the sense that it can straightforwardly be implemented with a large variety of different quantum emitters provided that they exhibit circularly
polarized optical transitions and that they can
be spin-polarized. Using state-of-the-art WGM
microresonators (29), one could realize a circulator with optical losses below 7% and close-to-unit
operation fidelity (26). This would then allow one
to almost deterministically process and control
photons in an integrated optical environment.
Arranging N circulators so that they form a linear
array allows one to realize a (2N + 2)-port optical
circulator. Moreover, two- and three-dimensional
networks of quantum circulators are potential
candidates for implementing lattice-based quantum computation (30). Such networks would
enable the implementation of artificial gauge
fields for photons (31–33), in which a nonlinearity
at the level of single quanta allows for the flux
to become a dynamical degree of freedom that
interacts with the particles themselves (34).
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The authors are grateful to J. Simon and M. Levy for helpful
discussions. We gratefully acknowledge financial support by the
Austrian Science Fund (FWF; SFB FoQuS project no. F 4017
and DK CoQuS project no. W 1210-N16) and the European
Commission (IP SIQS, no. 600645). A.H. acknowledges financial
support from the Austrian Science Fund (FWF; Meitner
Program Project M 1970).
Materials and Methods
Figs. S1 and S2
13 September 2016; accepted 21 November 2016
Published online 8 December 2016
Emergence of hierarchical structural
complexities in nanoparticles and
Chenjie Zeng,1 Yuxiang Chen,1 Kristin Kirschbaum,2
Kelly J. Lambright,2 Rongchao Jin1*
We demonstrate that nanoparticle self-assembly can reach the same level of hierarchy,
complexity, and accuracy as biomolecules. The precise assembly structures of gold
nanoparticles (246 gold core atoms with 80 p-methylbenzenethiolate surface ligands) at
the atomic, molecular, and nanoscale levels were determined from x-ray diffraction studies.
We identified the driving forces and rules that guide the multiscale assembly behavior. The
protecting ligands self-organize into rotational and parallel patterns on the nanoparticle surface
via C-H⋅⋅⋅p interaction, and the symmetry and density of surface patterns dictate directional
packing of nanoparticles into crystals with orientational, rotational, and translational orders.
Through hierarchical interactions and symmetry matching, the simple building blocks evolve
into complex structures, representing an emergent phenomenon in the nanoparticle system.
Hierarchical self-assembly of nanoparticles (NPs) into complex architectures across different length scales is an important ca- pability in nanotechnology (1–4), especially for the bottom-up fabrication for electronics, sensors, energy conversion, and storage devices.
Such self-assembly can be driven by entropy-dictated maximization of the packing density,
as demonstrated in close packing of spheres,
binary NPs, rods, and hard polyhedrons (5–9).
Interparticle interactions, such as the electrostatic
attraction (10), cDNA binding (11, 12), and patchy
NP surfaces (13–15), have also been exploited to
guide assembly into diverse lattice structures.
Despite these advances, NP assembly has not
achieved the same level of atomic accuracy
as in biological systems.
We now demonstrate that NP-assembled struc-
tures can reach the same hierarchy and atomic
accuracy as biomolecules at the interparticle
and intraparticle levels. Through crystalliza-
tion of uniform 2.2-nm gold NPs bearing p-
methylbenzenethiolate (p-MBT) surface ligands
[Au246(p-MBT)80], we fully resolve the entire self-
assembled structures at atomic (packing of gold
atoms), molecular (packing of surface ligands),
and nanoscale (packing of NPs) levels by single-
crystal x-ray diffraction (SC-XRD) (16). The precise
structural information across scales allows an in-
depth examination of the forces and the rules that
govern the assembly behavior at each level. We
reveal that the simple structure of protecting
ligands can generate complex patterns on the
NP surfaces, and the symmetry and density of
the surface patterns further guide the packing
of NPs into lattices with orientational, rotational,
and translational order.
The Au246(p-MBT)80 NPs were synthesized by
a two-step “size-focusing” method (16). Briefly,
the ligand-coated NPs in a narrow size range from
~10 to ~70 kilodaltons were first made, and then
the size focusing process gradually led to the stable
Au246(p-MBT)80 NPs (figs. S1 and S2). The as-obtained product (~90% purity) was subject to
further solvent fractionation to reach molecularly pure Au246 NPs. Optical absorbance spectra
showed a prominent peak at 470 nm and several weak humps at 400 and 600 nm (fig. S3),
indicating the nonplasmonic nature of the Au246
(p-MBT)80 NPs. Single crystals were grown by diffusion of antisolvent (acetonitrile) into a toluene
solution of the pure Au246 NPs. The structure was
determined at the resolution of 0.96 Å by SC-XRD
1580 23 DECEMBER 2016 • VOL 354 ISSUE 6319 sciencemag.org SCIENCE
1Department of Chemistry, Carnegie Mellon University,
Pittsburgh, PA 15213, USA. 2Department of Chemistry and
Biochemistry, University of Toledo, Toledo, OH 43606, USA.
*Corresponding author. Email: firstname.lastname@example.org