Topological defect
= Topological defect
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A topological defect is a spatial configuration whose surrounding ordered field cannot be smoothly extended through a core while staying everywhere in its <order-parameter space>. The field may lose its order or leave that space inside the core. Winding around a phase vortex is a simple example.
The topology of a surrounding loop can protect a line defect in three dimensions; a surrounding sphere can characterize a point defect. A <nematic disclination> uses an unoriented director, whereas a phase vortex uses an angle defined modulo $2\pi$, so their possible charges differ. Protection prevents a local smooth removal under the stated conditions, but a defect can still annihilate with another defect, escape through a boundary or disappear when order is destroyed. Its core and long-range distortion also have an energy cost, which affects formation and motion.