Liquid crystal cells with "dirty" substrates

Abstract

We explore liquid crystal order in a cell with a "dirty" substrate imposing a random surface pinning. Modeling such systems by a random-field xy-model with surface heterogeneity, we find that orientational order in the three-dimensional system is marginally unstable to such surface pinning. We compute the Larkin length scale, and the corresponding surface and bulk distortions. On longer scales we calculate correlation functions using the functional renormalization group and matching methods, finding a universal logarithmic and double-logarithmic roughness in two and three dimensions, respectively. For a finite thickness cell, we explore the interplay of homogeneous-heterogeneous substrate pair and detail crossovers as a function of disorder strength and cell thickness.

4 pages, 1 figure, Published in PRL, with minor typos corrected

References in corpus (4)

• Elastic theory of flux lattices in presence of weak disorder
• Destruction of bulk ordering by surface randomness
• Thermal depinning and transverse-field tilting transitions in a planar vortex array pinned by a columnar defect
• Disordered periodic systems at the upper critical dimension

Cited by in corpus (7)

• Topological order generated by random field in a 2D exchange model
• Stability and distortions of liquid crystal order in a cell with a heterogeneous substrate
• Transverse Quantum Fluids
• Pseudo-Casimir interactions and surface anchoring duality in bookshelf geometry of smectic-A liquid crystals
• Smectic order, pinning, and phase transition in a smectic liquid crystal cell with a random substrate
• Fluctuation-induced interactions in nematics with disordered anchoring energy
• Surface alignment disorder and pseudo-Casimir forces in smectic-A liquid crystalline films