The Geometry of the Cholesteric Phase

Daniel A. Beller, Thomas Machon, Simon Čopar, Daniel M. Sussman, Gareth P. Alexander, Randall D. Kamien, Ricardo A. Mosna

Research output: Contribution to journalArticle (Academic Journal)peer-review


We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot be, in general, translated from one phase to the other.
Original languageUndefined/Unknown
JournalPhysical Review X
Publication statusPublished - 12 Jun 2014

Bibliographical note

5 pages, the full catastrophe


  • cond-mat.soft

Cite this