Half-integer point defects in the $Q$-tensor theory of nematic liquid crystals

Abstract

We investigate prototypical profiles of point defects in two dimensional liquid crystals within the framework of Landau-de Gennes theory. Using boundary conditions characteristic of defects of index $k/2$, we find a critical point of the Landau-de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, $b^2$ small, we prove that this critical point is the unique global minimiser of the Landau-de Gennes energy. We investigate in greater detail the regime of vanishing elastic constant $L\to 0$, where we obtain three explicit point defect profiles, including the global minimiser.

15 pages, 16 figures

References in corpus (2)

• Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals
• Instability of point defects in a two-dimensional nematic liquid crystal model

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