Topology of smectic order on compact substrates.
Topology of smectic order on compact substrates.
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致密基板上的近晶有序拓扑。
DOI：
10.1103/physrevlett.101.147801
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发表时间：
2007
影响因子：
8.6
通讯作者：
Xiangjun Xing
中科院分区：
文献类型：
--
作者：
Xiangjun Xing
弯曲衬底上的近晶有序可以用一阶(1-形式)的微分形式来描述，其几何意义是密度调制的局域相场的微分。1-形式的外导数为局域位错密度。弹性变形用精确的微分形式叠加来描述。应用这种形式研究了环面和球面上的近晶有序，我们发现这两个系统都表现出许多拓扑上不同的低能态，这些态可以用两个整数拓扑荷来表征。低能态的总数以衬底面积的平方根为尺度。对于球面上的近晶，我们还探讨了作为可能的低能激发的位错运动及其拓扑含义。
Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of the 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on a torus as well as on a sphere, we find that both systems exhibit many topologically distinct low energy states that can be characterized by two integer topological charges. The total number of low energy states scales as the square root of the substrate area. For a smectic on a sphere, we also explore the motion of disclinations as possible low energy excitations, as well as its topological implications.