Bistable Defect Structures In Blue Phase Devices

Blue phases are liquid crystals made up by networks of defects, or disclination lines. While existing phase diagrams show a striking variety of competing metastable topologies for these networks, very little is known as to how to kinetically reach a target structure, or how to switch from one to the other, which is of paramount importance for devices. We theoretically identify two confined blue phase I systems in which by applying an appropriate series of electric field it is possible to select one of two bistable defect patterns. Our results may be used to realize new generation and fast switching energy-saving bistable devices in ultrathin surface treated blue phase I wafers.

Figure 1

Equilibrium disclination networks for BPI when (a) the structure is strongly anchored at both walls and when (b) there is homeotropic anchoring at both walls.

Figure 2

Free-energy evolution (top panel) of the BPI device with FBCs, with (triangles) and without (circles) backflow. Parameters were $A_0=0.0034$, $K=0.005$, $\gamma =3.775$, $e^2\sim 0.2$ (corresponding to a field of $\sim 8\mathrm{V}/\mu \mathrm{m}$). The evolution of the defects under an applied field is reported in the bottom panel. The step function in the top panel is $\ne 0$ when the field is on. From $t=0$ up to $t=35000$ the system relaxes to the stable BPI configuration in Fig. 1a. An electric field along $\widehat{x}$ is switched on at $t=35\times {10}^3$ and the equilibrium field-induced state is reached at $t_4=30\times {10}^4$. The corresponding free energy is shown in (a), top panel. Then the field is switched off and the system relaxes to a new metastable state ($t_8=80\times {10}^4$) [(b) in the bottom panel] characterized by a new free energy, slightly higher than the bulk BPI value. An electric field along $\widehat{y}$ is then switched on and off at $t_{12}=120\times {10}^4$ [(c) and (d) in the top panel]. Strikingly, the relaxation process brings the system back to the equilibrium state without field.

Figure 3

Defect evolution with homeotropic anchoring under an applied electric field. Parameters are the same as in Fig. 2. The electric field ($\sim 4.5\mathrm{V}/\mu \mathrm{m}$, i.e., with $e^2\sim 0.06$) is switched on along $\widehat{x}$ at time $t=10\times {10}^4$ [Fig. 1b for the steady state] and the evolution dynamics is reported in the first row. A steady state double-helix defect is attained at time $t_4=98.7\times {10}^4$. When the field is switched off the defect structure is almost unaltered (steady state reached at time $t_8=117.7\times {10}^4$). Then field ($\sim 4\mathrm{V}/\mu \mathrm{m}$, i.e., with $e^2\sim 0.05$) is switched on along $\widehat{y}$. The double-helix disclination transforms into a steady state with twisted ring defects ($t_{12}=155.6\times {10}^4$) stable after switching off ($t_{16}=194.2\times {10}^4$). Bistability requires a route back to the double-helix state: this is provided by a further application of a field along $\widehat{x}$ (steady state at $t_{20}=223.4\times {10}^4$).