On Discrete Soliton and Soliton Lattice at SmC_α∗-SmC Transition Driven by an Electric Field

Abstract

Unwinding process of Smectic C_α∗ phase (SmC_α∗) to smectic C phase (SmC) in an electric field looks similar to a transition from chiral smectic C phase (SmC∗) to SmC which is interpreted as a soliton condensation. As a pitch of the helical structure is quite short in the former, a discrete description is required and the soliton accompanying with should be a discrete type, while in the latter, the soliton is a kink of sine-Gordon equation. Under the condition of constant tilt at SmC_α∗, it has been elucidated that for the helical pitch larger than four-layer the transition is second order and a wave number versus field relation makes a devil's staircase. Here, a free energy curve for the wave number is proved to be non-differentiable at any rational wave number, monotonous and convex, corresponding to the devil's staircase structure of the wave number. This non-analytic property contrasts with the case of continuous description in SmC∗, where the free energy curve is analytic. In the framework of the present model, a change of apparent optical axis and switching current is calculated, which are compared with experimental results reported so far.

Keywords:

• Devil's staircase
• discrete soliton
• non-differentiability of free energy
• SmC_α∗-SmC transition
• switching current

The authors would like to thank Professor Atsuo Fukuda for his invaluable discussions. One of the authors (M. Y.) also thanks Professor Kazuo Sasaki for notifying him of Ref [16].