There is evidence that the pseudogap phase in the cuprates breaks time reversal symmetry. Here we show that pair density wave (PDW) states give rise to a translational invariant nonsuperconducting order parameter that breaks time reversal and parity symmetries, but preserves their product. This secondary order parameter has a different origin, but shares the same symmetry properties as a magnetoelectric loop current order that has been proposed earlier in the context of the cuprates to explain the appearance of intra-cell magnetic order. We further show that, due to fluctuations, this secondary loop current order, which breaks only discrete symmetries, can preempt PDW order, which breaks both continuous and discrete symmetries. In such a phase, the emergent loop current order coexists with spatial short range superconducting order and possibly short range charge density wave (CDW) order. Finally, we propose a PDW phase that accounts for intra-cell magnetic order and the Kerr effect, has CDW order consistent with x-ray scattering and nuclear magnetic resonance observations, and quasi-particle properties consistent with angle resolved photoemission scattering.

Developing mechanically flexible composite materials with high electrical conductivity is currently hindered by the need to use high loading of conductive filler, which severely limits flexibility. Here, acoustic focusing is used to control arrangement of conductive particles in photopolymer matrices to create composites with both tunable conductivity and flexibility. Acoustophoresis patterns filler particles into highly efficient percolated networks which utilize up to 97% of the particles in the composite, whereas the inefficient stochastic networks of conventional dispersed‐fiber composites utilize <5%. These patterned materials have conductivity an order of magnitude higher than conventional composites made with the same ink, reaching 48% the conductivity of bulk silver within the assembled silver‐particle networks (at 2.6 vol% loading). They also have low particle loading so that they are flexible, withstanding >500 bending cycles without losses in conductivity and changing conductivity only 5% within cycles on average. In contrast, conventional unpatterned composites with the same conductivity require such high loading that they are prohibitively brittle. Finally, modulating the applied acoustic field controls the anisotropy of the conductive networks and produces materials which are either 2D conductive, 1D conductive, or insulating, using the same nozzle and ink, paving the way for versatile multifunctional 3D printing.

Liquid crystal shells have attracted considerable attention in recent years. In such systems, a combination of confinement and curvature generates topological defect structures that do not exist in the bulk. Past studies, however, have largely focused on perfectly spherical shells, and little attention has been devoted to the impact of core geometry on the configuration and arrangement of topological defects. In this work, a microfluidic glass capillary device is used to encapsulate spherical and prolate ellipsoidal particles in nematic liquid crystal (LC) droplets dispersed in aqueous media. Our experimental studies show that, when trapped inside a radial LC droplet, spherical particles with both homeotropic and planar anchoring are highly localized at the droplet's center. While the radial configuration of the LC droplets is not altered by a homeotropic particle, polystyrene particles with strong planar anchoring disturb the radial ordering, leading to a twisted structure. Experiments indicate that off-center particle positions can also arise, in which defects are displaced towards the vicinity of the droplet's surface. In contrast, when prolate ellipsoidal particles are encapsulated in a thick radial LC shell, the minimum free energy corresponds to configurations where the particle is positioned at the droplet center. In this case, defects arise at the two ends of the prolate ellipsoid, where the curvature of the particle is maximal, leading to the formation of peculiar hybrid and twisted structures.