skyrmions are particle-like topological entities in a continuous field that have an important role in various condensed matter systems, including two-dimensional electron gases exhibiting the quantum Hall effect, chiral ferromagnets and Bose-Einstein condensates. Here we show theoretically, with the aid of numerical methods, that a highly chiral nematic liquid crystal can accommodate a quasi-two-dimensional skyrmion lattice as a thermodynamically stable state, when it is confined to a thin film between two parallel surfaces imposing normal alignment. A chiral nematic liquid crystal film can thus serve as a model skyrmion system, allowing direct investigation of their structural properties by a variety of optical techniques at room temperatures that are less demanding than skyrmion systems discussed previously.

We investigate effects of the electric field on diblock copolymers by assuming an induced dipolar interaction among the composition fluctuations. First, we show that, when an electric field is applied perpendicularly to lamellae, undulations start to grow if their in-plane wavenumbers are smaller than an electric wavenumber qe proportional to the field. Subsequently, the undulations grow into larger spatial structures, eventually leading to a final square-lattice pattern. Second, we calculate the Maxwell stress tensor due to the electric field to predict a finite shear modulus in a lamellar state oriented by the electric field. Third, we examine form birefringence in disordered and ordered phases. In particular, the lamellar and hexagonal phases are shown to become birefringent on spatial scales longer than the spacing of lamellae or cylinders, even if the constituent monomers are optically isotropic. This gives rise to enhancement of depolarized light scattering from lamellar microstructures, which has indeed been observed recently. Most predictions in this paper are applicable to many situations other than those in the electric field.

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