Radzihovsky Leo, Lubensky T C
Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051701. doi: 10.1103/PhysRevE.83.051701. Epub 2011 May 2.
General symmetry arguments, dating back to de Gennes, dictate that at scales longer than the pitch, the low-energy elasticity of a chiral nematic liquid crystal (cholesteric) and of a Dzyaloshinskii-Morya (DM) spiral state in a helimagnet with negligible crystal symmetry fields (e.g., MnSi, FeGe) is identical to that of a smectic liquid crystal, thereby inheriting its rich phenomenology. Starting with a chiral Frank free energy (exchange and DM interactions of a helimagnet) we present a transparent derivation of the fully nonlinear Goldstone mode elasticity, which involves an analog of the Anderson-Higgs mechanism that locks the spiral orthonormal (director or magnetic moment) frame to the cholesteric (helical) layers. This shows explicitly the reduction of three orientational modes of a cholesteric down to a single-phonon Goldstone mode that emerges on scales longer than the pitch. At a harmonic level our result reduces to that derived many years ago by Lubensky and collaborators.
可追溯到德热纳的一般对称性论证表明，在大于螺距的尺度上，手性向列型液晶（胆甾相）以及晶体对称场可忽略不计的螺旋磁体（如锰硅化物、铁锗）中的季亚洛欣斯基 - 莫利亚（DM）螺旋态的低能弹性与近晶型液晶相同，从而继承了其丰富的现象学。从手性弗兰克自由能（螺旋磁体的交换和DM相互作用）出发，我们给出了完全非线性戈德斯通模弹性的清晰推导，其中涉及将螺旋正交归一（指向矢或磁矩）框架锁定到胆甾相（螺旋）层的安德森 - 希格斯机制的类似物。这明确显示了胆甾相的三个取向模在大于螺距的尺度上简化为单个声子戈德斯通模。在谐波层面，我们的结果简化为卢本斯基及其合作者多年前得出的结果。
