3D Polar or Nematic Order

This chapter extends the concept of topological defects to 3D orientational order. A system with 3D polar order cannot have any disclinations, because any apparent disclination can escape into the third dimension. By contrast, a system with 3D nematic order can have half-charged disclinations, but there is no topological distinction between winding number of \(+1/2\) or \(-1/2\) . Although the topology of 3D nematic disclinations is simple, the geometric and physical properties are much more complex. The chapter explains how these properties can be characterized in terms of the local tangent vector, local rotation vector, and other vectors and tensors. It also shows that disclinations have a biaxial nematic core structure, surrounded by the uniaxial nematic bulk.