Calculations of layer structure

We performed calculations of CLC structure within layer of chiral nematic. We used the extended Frank elastic continuum approach to find energy-optimal layer structures. This approach includes the effects of the director field distortion and the formation of defects:

where K11, K22 and K33 are the splay, twist and bend elasticity constants, respectively, q0=2π/p0, W is the surface anchoring energy density, θnk is the tilt angle of local director n from the surface plane, θ0 is the preferred tilt angle, and Fdef is the energy of defects calculated by the summation of the point and linear defect energies (see the details in ref.⁴⁴). The ratio between elasticity constants was set to K11:K22:K33=1:0.51:1.31 to simulate the studied cholesteric liquid crystal mixture. To take into account potential formation of the disclination lines with core, its linear energy density was set to fcoreline=K11. The bottom surface was set with strong planar aligned boundaries characterized by the dimensionless anchoring strength μ1=W1d/K11=1000 and θ0=0, where d is the thickness of the layer. The top surface had weak conical boundary conditions (μ2=W2d/K11=40, θ0=50∘). The equilibrium characteristic ratio d/p0=0.6 was set according to the experimental data. To simulate thin layer, we used cuboid simulation box with periodic boundary conditions over two dimensions (namely, x and y). We varied the first dimension Lx from 2d to 4d with 0.1d step to find energy-optimal stripped structure period. The volume was rendered in a lattice from 32×4×16 to 64×4×16, correspondingly. The second dimension of the simulations box was fixed at Ly=0.25d to constrain a possible direction of strips parallel to y. For each simulation box size, we varied the direction of easy axis on bottom plane from 0 to 180∘ with 5∘ degree step to determine the energy-optimal mutual orientation of defect lines and rubbing direction. We used Monte-Carlo annealing optimization with 16 independent runs for each setup to find the energy-optimal structures. To simulate electrically-induced transformation of LC structure, we applied the Monte-Carlo relaxation after switching the electric field on or off. The data shown in dimensionless electric field were calculated as e=|E|dε0Δε/K111/2.