Bulk-boundary correspondence is the emergence of features at the boundary of a material that are dependent on and yet distinct from the properties of the bulk of the material. The diverse applications of this idea in topological insulators as well as high energy physics prove its universality. However, whether a form of bulk-boundary correspondence holds also in soft matter such as gels, polymers, lipids and other biomaterials is thus far unknown. Aerosil-dispersed liquid crystal gels (LC+aerosil) provide a good testing ground to explore the relation between the controlled variations of the aerosil density within the liquid crystal host bulk and the surface topography of the sample.Here we report on one of the earliest if not the first direct observation of such a correspondence where the controlled strength of random disorder created by aerosil dispersion in the bulk liquid crystal is correlated with the fractal dimension of the surface. We obtained the surface topography of our gel samples with different quenched random disorder strengths by using atomic force microscope techniques, and computed the fractal dimension for each sample. We found that an increase of the aerosil gel density in the bulk corresponds to an increase in the fractal dimension at the surface. From our results emerges a new method to acquire the bulk properties of soft matter such as density, randomness and phase merely from the fractal dimension of the surface.The connection between a material's bulk and its boundary has been one of the guiding principles in several branches of physics in the last decade. The main idea is that the boundary of the system would feature excitations that do not occur in the bulk, yet the physics on the boundary is still determined by the properties of the bulk. For example in topological insulators, the index theorem relates the Chern number quantifying the topology of the insulating bulk to the spectrum of the edge states at the boundary [1][2][3][4]. The holographic principle in high energy physics, also known as gauge/gravity duality, is another example of the bulk-boundary correspondence where the spectrum of the strongly interacting gauge theory in four spacetime dimensions is connected to the weakly interacting theory on the three dimensional boundary via duality [5,6].Here we report on the first ever test of whether bulkboundary correspondence holds in soft condensed matter systems [7,8], particularly in aerosil dispersed liquid crystals ( Fig. 1a). We prepared liquid crystal+aerosil (LC+aerosil) gel mixtures with varying amount of aerosil within, and observed that the aerosil gel density ρ s = m SiO2 /V LC in the bulk is correlated with the fractal dimension of the surface. This experimental verification of the bulk-boundary correspondence in soft matter is the main goal of this study.Liquid crystals (LCs) are not only utilized in screens and TVs, but also used to study phase transitions [9]. Since they possess a rich spectrum of different phases with different types of phase transitions, they stand ou...

We study the quenched random disorder (QRD) effects created by aerosil dispersion in the octylcyanobiphenyl (8CB) liquid crystal (LC) using atomic force microscopy technique. Gelation process in the 8CB+aerosil gels yields a QRD network which also changes the surface topography. By increasing the aerosil concentration, the original smooth pattern of LC sample surfaces is suppressed by the emergence of a fractal aerosil surface effect and these surfaces become more porous, rougher and they have more and larger crevices. The dispersed aerosil also serves as pinning centers for the liquid crystal molecules. It is observed that via the diffusion-limitedaggregation process, aerosil nano-particles yield a fractal-like surface pattern for the less disordered samples. As the aerosil dispersion increases, the surface can be described by more aggregated regions, which also introduces more roughness. Using this fact, we show that there is a net correlation between the short-range ordered x-ray peak widths (the results of previous x-ray diffraction experiments) and the calculated surface roughness. In other words, we show that these QRD gels can also be characterized by their surface roughness values.

Low temperature powder inelastic neutron scattering measurements were performed on three different powder samples; parent BaMn2As2,12.5% K-doped Ba0.875K0.125Mn2As2 and 25% K-doped Ba(0.75)K0.25Mn2As2. The Heisenberg Model involving J1-J2-Jz coupling constants were compared to the data by a powder integration routine using Monte Carlo integration methods. The best magnetic parameters were selected using a chi-square test where model intensities were compared to the full (q,E) dependence of magnetic scattering. A key step to this analysis is the characterization of the background which is formed mostly by phonon scattering intensities along with other sources including the magnetic impurity scattering events. The calculated powder magnetic intensities added to the estimated background obtained from the non-magnetic high momentum transfer region. The agreement between the simulated and the raw data enabled us to perform quantitative analysis of the unreacted MnO impurities. Overall, this is another confirmation along with earlier studies using this technique, that magnetic exchange constants can be calculated within an acceptable range with a very quick inelastic neutron powder experiment without need for a single crystal sample.