Smoke, fog, jelly, paints, milk and shaving cream are common everyday examples of colloids 1 , a type of soft matter consisting of tiny particles dispersed in chemically distinct host media. Being abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses 2 to fabrication of third-generation quantum-dot solar cells 3 . Because naturally occurring colloids have a shape that is typically determined by minimization of interfacial tension (for example, during phase separation) or faceted crystal growth 1 , their surfaces tend to have minimum-area spherical or topologically equivalent shapes such as prisms and irregular grains (all continuously deformable-homeomorphic-to spheres). Although toroidal DNA condensates and vesicles with different numbers of handles can exist 4-7 and soft matter defects can be shaped as rings 8 and knots 9 , the role of particle topology in colloidal systems remains unexplored. Here we fabricate and study colloidal particles with different numbers of handles and genus g ranging from 1 to 5. When introduced into a nematic liquid crystal-a fluid made of rod-like molecules that spontaneously align along the so-called "director" 10 -these particles induce threedimensional director fields and topological defects dictated by colloidal topology. Whereas electric fields, photothermal melting and laser tweezing cause transformations between configurations of particle-induced structures, three-dimensional nonlinear optical imaging reveals that topological charge is conserved and that the total charge of particle-induced defects always obeys predictions of the Gauss-Bonnet and Poincaré-Hopf index theorems [11][12][13] . This allows us to establish and experimentally test the procedure for assignment and summation of topological charges in threedimensional director fields. Our findings lay the groundwork for new applications of colloids and liquid crystals that range from topological memory devices 14 , through new types of self-assembly [15][16][17][18][19][20][21][22][23] , to the experimental study of low-dimensional topology 6,7,[11][12][13] .Although a coffee mug and a doughnut look different to most of us, they are topologically equivalent solid tori or handlebodies of genus g = 1, both being different from, say, balls and solid cylinders of genus g = 0, to which they cannot be smoothly morphed without cutting 11,12 . In a similar way, molecules can form topologically distinct structures including rings, knots and other molecular configurations satisfying the constraints imposed by chemical bonds 24 . Although the topology of shapes, fields and defects is important in many phenomena and in theories ranging from the nature of elementary particles to early-Universe cosmology 25,26 , topological aspects of colloidal systems (composed of particles larger than molecules and atoms but much smaller than the objects that we encounter in our everyday life) are rarely explored. Typically dealing with...

We demonstrate the bulk self-alignment of dispersed gold nanorods imposed by the intrinsic cylindrical micelle selfassembly in nematic and hexagonal liquid crystalline phases of anisotropic fluids. External magnetic field and shearing allow for alignment and realignment of the liquid crystal matrix with the ensuing long-range orientational order of well-dispersed plasmonic nanorods. This results in a switchable polarization-sensitive plasmon resonance exhibiting stark differences from that of the same nanorods in isotropic fluids. The device-scale bulk nanoparticle alignment may enable optical metamaterial mass production and control of properties arising from combining the switchable nanoscale structure of anisotropic fluids with the surface plasmon resonance properties of the plasmonic nanorods.KEYWORDS Nanorods, liquid crystals, optical metamaterials, self-assembly, plasmonic nanoparticles H aving predesigned structural units different from those in a conventional matter, metamaterials exhibit many unusual properties of interest from both fundamental science and applications standpoints. However, manufacturing such bulk optical metamaterials with three-dimensional (3D) structure 1-4 using lithography techniques presents a significant challenge, especially for the large-scale production. Mass production of bulk optical metamaterials from self-aligning and self-assembling nanoparticles is poised to revolutionize scientific instruments, technologies,andconsumerdevices.5-7 Althoughthemetamaterial self-assembly from nanoparticles remains a significant challenge, recent advances in colloidal science show that it may be realized and the emerging nanoscale alignment and assembly approaches utilize surface monolayers, 8,9 stretched polymer films, 10,11 and functionalized nanoparticles 12,13 but are usually restricted to only short-range ordering, twodimensional rather than three-dimensional assembly, and limited switching.7 Tunable metamaterials may potentially be obtained by nanoparticle self-assembly in liquid crystals (LCs) 14 through the LC-mediated realignment and rearrangement of incorporated nanoparticles in response to applied fields. However, experimental realization of such self-assembling switchable metamaterial composites is lacking. In this work, we demonstrate spontaneous long-range orientational ordering of gold nanorods (GNRs) dispersed in surfactant-based lyotropic LCs and use polarizing optical microscopy, darkfield microscopy, spectroscopy, and freezefracture transmission electron microscopy (FFTEM) to study these composites on the scales ranging from nanometers to millimeters. We find that the anisotropic fluids in both columnar hexagonal and nematic LC phases impose nematic-like long-range orientational ordering of GNRs with no correlation of their centers of mass but with the GNRs aligning along the LC director n (a unit vector describing the average local orientation of cylindrical micelles forming the LC), Figure 1. The unidirectional alignment of nanorods with high order parameter is...

Practical guest-host devices in which dichroic dye molecules follow electrical switching of a liquid crystal host remain elusive for decades despite promising efficient displays and emergent applications such as smart windows. This is mainly because of poor stability, surface precipitation, and limited means for property engineering of the dyes. To overcome these challenges, we develop plasmonic metal nanoparticle analogues of dichroic guest-host liquid crystals. Nematic dispersions of aligned anisotropic gold nanoparticles are obtained by polymer passivation of their surfaces to impose weak tangential boundary conditions for orientation of anisotropic host molecules. Control of the ensuing surface interactions leads to long-range ordered colloidal dispersions, allowing for collective optical and electrical switching of rod- and platelet-like nanoparticles. This facile control of mesostructured plasmonic medium's optical properties in visible and infrared spectral ranges is of interest for many applications.