Cholesteric dislocations in mica wedges

A large part of the scientific legacy of Maurice Kleman concerns topological defects in liquid crystals. Here, we focus on the very first article of Kleman on liquid crystals coauthored with Jacques Friedel and devoted to linear defects in cholesterics discovered in 1921 by François Grandjean who observed them in wedges made from partially cleaved mica sheets. Kleman and Friedel interpreted the thin (single) and thick (double) Grandjean lines as dislocations with Burgers vectors equal respectively to p/2 (half pitch) or p (whole pitch) and have shown that they are composed of pairs of disclinations that they called τ and λ. We report on a recent work accomplished specifically in memoriam of Maurice Kleman, with the aim to show the beauty of nets of Grandjean lines in wedges made of mica sheets. Using crossed cylindrical sheets, we nucleated in a controlled manner dislocation loops of the two kinds persisting indefinitely independently of the local thickness and of the angle of the wedge. In thin wedges, surprisingly, the double dislocation loops are not smooth but contain one or two cusps corresponding to kinks predicted by Kleman and Friedel. Their presence is a fingerprint of the helicoidal symmetry of cholesterics.