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Optically-active optoelectronic materials are of great interest for many applications, including chiral sensing and circularly polarized light emission. Traditionally, such applications have been enabled by synthetic strategies to design chiral organic semiconductors and conductors. Here, centrosymmetric tetrathiafulvalene (TTF) crystals are rendered chiral on the mesoscale by crystal twisting. During crystallization from the melt, helicoidal TTF fibers were observed to grow radially outwards from a nucleation centre as spherulites, twisting in concert about the growth direction. Because molecular crystals exhibit orientation-dependent refractive indices, periodic concentric bands associated with continually rotating crystal orientations were observed within the spherulites when imaged between crossed polarizers. Under certain conditions, concomitant crystal twisting and bending was observed, resulting in anomolous crystal optical behavior. X-ray diffraction measurements collected on different spherulite bands indicated no difference in the molecular packing between straight and twisted TTF crystals, as expected for microscopic twisting pitches between 20–200 μm. Mueller matrix imaging, however, revealed preferential absorption and refraction of left- or right-circularly polarized light in twisted crystals depending on the twist sense, either clockwise or counterclockwise, about the growth direction. Furthermore, hole mobilities of 2.0 ± 0.9 × 10 −6 cm 2 V −1 s −1 and 1.9 ± 0.8 × 10 −5 cm 2 V −1 s −1 were measured for straight and twisted TTF crystals deposited on organic field-effect transistor platforms, respectively, demonstrating that crystal twisting does not negatively impact charge transport in these systems.
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On higher level Kirillov–Reshetikhin crystals, Demazure crystals, and related uniform models
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Billinge, Simon (Ed.)Periodic space crystals are well established and widely used in physical sciences. Time crystals have been increasingly explored more recently, where time is disconnected from space. Periodic relativistic spacetime crystals on the other hand need to account for the mixing of space and time in special relativity through Lorentz transformation, and have been listed only in 2-dimensions. This work shows that there exists a transformation between the conventional Minkowski spacetime (MS) and what is referred to here as renormalized blended spacetime (RBS); they are shown to be equivalent descriptions of relativistic physics in flat spacetime. There are two elements to this reformulation of MS, namely, blending and renormalization. When observers in two inertial frames adopt each other’s clocks as their own, while retaining their original space coordinates; the observers become blended. This process reformulates the Lorentz boosts into Euclidean rotations while retaining the original spacetime hyperbola describing worldlines of constant spacetime length from the origin. By renormalizing the blended coordinates with an appropriate factor that is a function of the relative velocities between the various frames, the hyperbola is transformed into a Euclidean circle. With these two steps, one obtains the RBS coordinates complete with new light lines, but now with a Euclidean construction. One can now enumerate the RBS point and space groups in various dimensions with their mapping to the well-known space crystal groups. The RBS point group for flat isotropic RBS spacetime is identified to be that of cylinders in various dimensions: mm2 which is that of a rectangle in 2D, (∞⁄m)m which is that of a cylinder in 3D, and that of hypercylinder in 4D. An antisymmetry operation is introduced that can swap between space-like and time-like directions, leading to color spacetime groups. The formalism reveals RBS symmetries that are not readily apparent in the conventional MS formulation. Mathematica® script is provided for plotting the MS and RBS geometries discussed in the work.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jalgebra.2019.07.036
