Defects in the cholesteric phase

The order tensor of the cholesteric liquid crystal is a symmetrical matrix, or a set of three orthogonal vectors n, q and n x q. 

It is known that there is no topological stable singular wall and point but there are topological stable singular lines which are characterized by the Q group, Q C0,C0,C1,C2,C 5). The classification of the cholesteric 

Compared with the homotopy classification, each element in the homotopy Q group corresponds to the above defects in the following way 

It is apparent that the two classifications are consistent, but the homotopy approach is more powerful in further analysis because there is a relation between the group elements, which is associated with the interactions between the defects. 

The cholesteric liquid crystal can be regarded as a layered structure so that it also shows the focal-conic texture, especially for large pitch cholesteric liquid crystals. 

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As already discussed, there are no isolated point defects in the cholesteric phase, 7r2(9 = SO 3)/D2) = 0. However, singular point defects can serve as the ends of linear solitons, as in the case of the monopole structure, in which the nonsingular disclinations can be considered as linear solitons. 

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