Introduction to Topological Defects and Solitons: In Liquid Crystals, Magnets, and Related Materials

by Jonathan V. Selinger

Overview

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.

Product Details

ISBN-13:	9783031701993
Publisher:	Springer Nature Switzerland
Publication date:	10/15/2024
Series:	Lecture Notes in Physics , #1032
Edition description:	2024
Pages:	213
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Jonathan Selinger is Professor of Physics and Ohio Eminent Scholar in Theoretical Liquid Crystal Physics at Kent State University. His research focuses on liquid crystals and other soft materials, and seeks to make connections between fundamental statistical mechanics and technological applications.

Selinger studied physics at Harvard University, receiving his A.B. in 1983 and Ph.D. in 1989. He then did postdoctoral research in Los Angeles, with positions at the UCLA Department of Physics and Caltech Department of Chemical Engineering. In 1992 he moved to the Naval Research Laboratory in Washington, DC, where he worked as Research Physicist in the Center for Bio/Molecular Science and Engineering. In 2005 he came to his current position at Kent State. In addition to these research and teaching positions, he has also served as Associate Editor of Physical Review E, responsible for the liquid-crystal section of the journal, and he is currently Treasurer of the International Liquid Crystal Society.

Selinger's previous book is Introduction to the Theory of Soft Matter: From Ideal Gases to Liquid Crystals, published by Springer in 2016.

Table of Contents

Chapter 1. Introduction to Defects.- Chapter 2. Introduction to Solitons.- Chapter 3. Free Energy.- Chapter 4. Dynamics and Statistical Mechanics.- Chapter 5. Prequel to Defects: Variable Magnitude of Order.- Chapter 6. Further Issues: Defect Phase/Orientation, Charge Density, Curvature.- Chapter 7. 2D Nematic Order, Active Liquid Crystals.- Chapter 8. 3D Polar or Nematic Order.- Chapter 9. Defects in Crystals.- Chapter 10. 2D Measuring Surface: Hedgehogs, Skyrmions.- Chapter 11. 3D Measuring Surface: Hopfions.- Chapter 12. Phases With Regular Arrays of Defects or Solitons.

What People are Saying About This

From the Publisher

“Notwithstanding their name, defects turn out to be, as Selinger’s book shows, very useful in a variety of fields, particularly in the study of liquid crystals, magnets, and other ordered matter systems. The topic has become increasingly important, as shown by the more than twofold increase in the number of papers dealing with topological defects listed by Web of Science in the last ten years, making the book certainly timely. Selinger has managed to introduce the subject in a way that is accessible to a wide audience of students and researchers, starting with simple physical examples, relatively straightforward maths, and helpful illustrations to arrive at complex and often unfamiliar concepts, such as Skyrmions and Hopfions. I appreciate the book's pragmatic yet elegant approach and have no hesitation in recommending it.” (Claudio Zannoni, Emeritus Professor of Physical Chemistry, University of Bologna, Italy)

“In this elegant, concise book, Jonathan Selinger allows readers to reap insights gained during a distinguished career focused on understanding liquid crystals, magnets and other complex materials. With a minimum of fancy mathematics and a maximum of physical intuition (rendered in part through beautiful illustrations), he leads the reader with lucid prose to a basic understanding of the essential features of topological defects and solitons in condensed matter physics.” (David R. Nelson, Arthur K. Solomon Professor, Harvard University)

“In his book Introduction to Topological Defects and Solitons Jonathan Selinger brings the reader from the basic notions concerning topological defects and solitons all the way to the more sophisticated ones of “hedgehogs,” “skirmions,” “hopfions,” etc. They are exposed with clarity, avoiding unnecessary difficulties, but pointing at all aspects of the fascinating domain of topological singularities and solitons in magnetic systems, liquid crystals and also superconductors on occasion. Upon reading the book, one has the impression of listening to the master explaining at the blackboard the concepts with the use of well-designed drawings and well-chosen words. Without any doubts, this book will be useful to our community and beyond.” (Jacques Prost, Institut Curie, France)