Alexander, Gareth P., Chen, Bryan, Matsumoto, Elisabetta and Kamien, Randall. (2012) Colloquium : disclination loops, point defects, and all that in nematic liquid crystals. Reviews of Modern Physics, Vol.84 (No.2). pp. 497-514. ISSN 0034-6861

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Abstract

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Centre for Complexity Science Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Topological defects (Physics), Homotopy theory, Liquid crystals -- Mathematical models
Journal or Publication Title:	Reviews of Modern Physics
Publisher:	American Physical Society
ISSN:	0034-6861
Date:	9 April 2012
Volume:	Vol.84
Number:	No.2
Page Range:	pp. 497-514
Identification Number:	10.1103/RevModPhys.84.497
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	National Science Foundation (U.S.) (NSF)
Grant number:	DMR05-47230 (NSF)
References:	Abrikosov, A. A., 1957, \On the Magnetic Properties of Superconductors of the Second Group," Zh. Eksp. i Teor. Fiz. 32, 1442-1452; [JETP 5, 1174-1182 (1957)]. Bechluft-Sachs, S., and M. Hien, 1999, \The Global Defect Index," Commun. Math. Phys. 202, 403-409. Chaikin, P. M. and T. C. Lubensky, 1995, Principles of Con- densed Matter Physics, (Cambridge University Press, Cambridge). Chen, B. G., G. P. Alexander, and R. D. Kamien, 2009, \Symmetry breaking in smectics and surface models of their singularities," Proc. Natl. Acad. Sci. USA 106, 15577-15582. Chen, B. G., G. P. Alexander, E. A. Matsumoto, and R. D. Kamien, unpublished. Cladis, P. E., and M. Kl�eman, 1972, \Non-singular disclinations of strength s = +1 in nematics," J. Phys. France 33, 591-598. Coleman, S., 1975, \Quantum sine-Gordon equation as the massive Thirring model," Phys. Rev. D 11, 2088-2097. Coleman, S. 1988 Aspects of Symmetry: Selected Erice Lec- tures, (Cambridge University Press, Cambridge). �Copar, S., and S. �Zumer, 2011, \Nematic braids: topological invariants and rewiring of disclinations," Phys. Rev. Lett. 106, 177801. Dupuis, A., D. Marenduzzo, and J. M. Yeomans, 2005, \Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals," Phys. Rev. E 71, 011703. Frank, F. C., 1958, \I. Liquid crystals. On the theory of liquid crystals," Faraday Discuss. 25, 19-28. Grebel, H., R. M. Hornreich, and S. Shtrikman, 1983, \Landau theory of cholesteric blue phases," Phys. Rev. A 28, 1114-1138. Guzm�an, O., E. B. Kim, S. Grollau, N. L. Abbott, and J. J. de Pablo, 2003, \Defect Structure around Two Colloids in a Liquid Crystal," Phys. Rev. Lett. 91, 235507. Harris, A. B., R. D. Kamien, and T. C. Lubensky, 1999, \Molecular chirality and chiral parameters," Rev. Mod. Phys. 71, 1745-1757. Hatcher, A., 2002, Algebraic Topology, Cambridge University Press, Cambridge. J�anich, K., 1987, \Topological properties of ordinary nematics in 3-space," Acta Appl. Math. 8, 65-74. Kamien, R. D., 2002, \The geometry of soft materials: A primer," Rev. Mod. Phys. 74, 953-971. Kamien, R. D., 2011, \Knot your simple defect lines," Science 333, 46-47. Kitaev, A. Yu., 2003, \Fault-tolerant quantum computation by anyons," Ann. Phys. 303, 2-30. Kosterlitz, J. M., and D. J. Thouless, 1973, \Ordering, metastability and phase transitions in two-dimensional systems," J. Phys. C: Solid State Phys., 6, 1181-1203. Kurik, M. V., and O. D. Lavrentovich, 1988, \Defects in liquid crystals: homotopy theory and experimental studies," Phys. Usp. 31, 196-224. Lintuvuori, J. S., D. Marenduzzo, K. Stratford, and M. E. Cates, 2010, \Colloids in liquid crystals: a lattice Boltzmann study," J. Mater. Chem. 20, 10547-10552. Mermin, N. D., 1979, \The topological theory of defects in ordered media," Rev. Mod. Phys. 51, 591-648. Mermin, N. D, and T. L. Ho, 1976, \Circulation and angular momentum in the A phase of super uid Helium-3," Phys. Rev. Lett. 36, 594-597; 36, 832(E). Meyer, R. B., 1973, \On the existence of even indexed disclinations in nematic liquid crystals," Phil. Mag. 27, 405-424. Michel, L., 1980, \Symmetry defects and broken symmetry. Con�gurations hidden symmetry," Rev. Mod. Phys. 52, 617-651. M�uhlbauer, S., B. Binz, F. Jonitez, C. P eiderer, A. Rosch, A. Neubauer, R. Georgii, and P. B�oni, 2009, \Skyrmion Lattice in a Chiral Magnet," Science 323, 915-919. Mu�sevi�c, I., M. �Skarabot, U. Tkalec, M. Ravnik, and S. �Zumer, 2006, \Two-dimensional nematic colloidal crystals self-assembled by topological defects," Science 313, 954- 958. Nakanishi, H., K. Hayashi, and H. Mori, 1988, \Topological classi�cation of unknotted ring defects," Commun. Math. Phys. 117, 203-213. Nayak, C., S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, 2008, \Non-Abelian anyons and topological quantum computation," Rev. Mod. Phys. 80, 1083-1159. Nelson, D. R., 1988, \Vortex Entanglement in High-Tc Superconductors," Phys. Rev. Lett. 60, 1973-1976. Po�enaru, V., and G. Toulouse, 1977, \The crossing of defects in ordered media and the topology of 3-manifolds," J. Phys. France 38, 887-895. Polyakov, A. M., 1974, \Particle spectrum in quantum �eld theory," ZhETF Pis. Red. 20, 430-433; [JETP 20, 194-195 (1974)]. Poulin, P., H. Stark, T. C. Lubensky, and D. A. Weitz, 1997, \Novel Colloidal Interactions in Anisotropic Fluids," Science 275, 1770-1773. Priest, R. G. and T. C. Lubensky, 1974, \Biaxial model of cholesteric liquid crystals," Phys. Rev. A 9 893-898. Ravnik, M., M. �Skarabot, S. �Zumer, U. Tkalec, I. Poberaj, D. Babi�c, N. Osterman, and I. Mu�sevi�c, 2007, \Entangled Nematic Colloidal Dimers and Wires," Phys. Rev. Lett. 99, 247801. Ravnik, M., and S. �Zumer, 2009, \Nematic colloids entangled by topological defects," Soft Matter 5, 269-274. R�o�ler, U. K., A. N. Bogdanov, and C. P eiderer, 2006, \Spontaneous skyrmion ground states in magnetic metals," Nature 442, 797-801. �Skarabot, M., M. Ravnik, S. �Zumer, U. Tkalec, I. Poberaj, D. Babi�c, N. Osterman, and I. Mu�sevi�c, 2007, \Twodimensional dipolar nematic colloidal crystals," Phys. Rev. E 76, 051406. �Skarabot, M., M. Ravnik, S. �Zumer, U. Tkalec, I. Poberaj, D. Babi�c, N. Osterman, and I. Mu�sevi�c, 2008, \Interactions of quadrupolar nematic colloids," Phys. Rev. E 77, 031705. Smalyukh, I. I., Y. Lansac, N. A. Clark, and R. P. Trivedi, 2009, \Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic uids," Nat. Mater. 9, 1-7. Terentjev, E. M., 1995, \Disclination loops, standing alone and around solid particles, in nematic liquid crystals," Phys. Rev. E 51, 1330-1337. Tkalec, U., M. Ravnik, S. �Copar, S. �Zumer, and I. Mu�sevi�c, 2011, \Recon�gurable knots and links in chiral nematic colloids," Science 333, 62-65. Trebin, H. R., 1982, \The topology of non-uniform media in condensed matter physics," Adv. Phys. 31, 195-254. Williams, C., and Y. Bouligand, 1974, \Fils et disinclinaisons dans un n�ematique en tube capillaire," J. Phys. France 35, 589-593. Wright, D. C. and N. D. Mermin, 1989, \Crystalline liquids: the blue phases," Rev. Mod. Phys. 61, 385-432.
URI:	http://wrap.warwick.ac.uk/id/eprint/49307

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