The Double Twist

Technical Bulletin

Introduction to Topological Defects and Solitons

This textbook introduces topological defects and solitons at a level suitable for advanced undergraduates and beginning graduate students in physics and materials science. It avoids the formal mathematics of topology, and instead concentrates on the physical properties of these topological structures. The first half of the book concentrates on fundamental principles of defects and solitons, and illustrates these principles with a single example—the xy model for 2D magnetic order. It begins by defining the concept of a winding number, and uses this concept to describe the topology of defects (vortices or disclinations) and solitons (domain walls), carefully identifying the similarities and differences between these two types of topological structures. It then goes on to discuss physical properties of defects and solitons, including free energy, dynamics, statistical mechanics, and coupling with curvature. It shows how these concepts emerge from a theory with variable magnitude of order, and hence how topology can be viewed as an approximation to physics. The second half goes on to explore a wider range of topological defects and solitons. First, it considers more complex types of order—2D nematic liquid crystals, 3D magnetic or liquid-crystal order, 2D or 3D crystalline solids—and shows how each type of order leads to specific topological structures. Next, it discusses defects and solitons that are characterized by 2D or 3D measuring surfaces, not just 1D loops, including hedgehogs, skyrmions, and hopfions. These structures are more complex, but they can still be understood using the same fundamental principles. A final chapter describes the formation of phases with regular arrays of defects or solitons.

Fundamentals of Liquid Crystal Devices

Liquid Crystal Devices are crucial and ubiquitous components of an ever-increasing number of technologies. They are used in everything from cellular phones, eBook readers, GPS devices, computer monitors and automotive displays to projectors and TVs, to name but a few. This second edition continues to serve as an introductory guide to the fundamental properties of liquid crystals and their technical application, while explicating the recent advancements within LCD technology. This edition includes important new chapters on blue-phase display technology, advancements in LCD research significantly contributed to by the authors themselves. This title is of particular interest to engineers and researchers involved in display technology and graduate students involved in display technology research. Key features: Updated throughout to reflect the latest technical state-of-the-art in LCD research and development, including new chapters and material on topics such as the properties of blue-phase liquid crystal displays and 3D liquid crystal displays; Explains the link between the fundamental scientific principles behind liquid crystal technology and their application to photonic devices and displays, providing a thorough understanding of the physics, optics, electro-optics and material aspects of Liquid Crystal Devices; Revised material reflecting developments in LCD technology, including updates on optical modelling methods, transmissive LCDs and tunable liquid crystal photonic devices; Chapters conclude with detailed homework problems to further cement an understanding of the topic.