title: Fractal nematic colloids.
abstract: Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.
authors.affiliation: Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.|Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran 1458889694, Iran.
authors.forename: S M
authors.initials: SM
authors.lastname: Hashemi
authors.affiliation: Department of Condensed Matter Physics, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia.
authors.forename: U
authors.initials: U
authors.lastname: Jagodič
authors.affiliation: Department of Physics, University of Qom, P.O. Box 3716146611, Qom, Iran.
authors.forename: M R
authors.initials: MR
authors.lastname: Mozaffari
authors.affiliation: Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran 1458889694, Iran.|Center of Excellence in Complex Systems and Condensed Matter (CSCM), Sharif University of Technology, Tehran 1458889694, Iran.
authors.forename: M R
authors.initials: MR
authors.lastname: Ejtehadi
authors.affiliation: Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.|Department of Condensed Matter Physics, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia.
authors.forename: I
authors.initials: I
authors.lastname: Muševič
authors.affiliation: Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.|Department of Condensed Matter Physics, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia.
authors.forename: M
authors.identifier: 0000-0001-8883-9318
authors.initials: M
authors.lastname: Ravnik