Application of braid groups in 2D Hall system physics. Composite fermion structure. (Q2911421)

The phenomenon of fractional quantum Hall effect (FQHE) was discovered by Daniel Tsui and Horst Störmer in 1982. It occurs in two dimensional electron systems in the presence of a strong orthogonal magnetic field, and corresponds to fractional filling of the lowest Landau level. In this book, the main goal of the authors is to understand the Laughlin correlations and the structure of the composite fermions in terms of braid groups.NEWLINENEWLINEThe book begins with a short introductory chapter on the role of topological effects in physics, which sets the tone for what follows. In Chapter 2, the authors describe the Laughlin correlation function and the traditional way of viewing composite fermions. This is then followed by a chapter on topological methods in which we find an introduction to the braid group, its one dimensional unitary representations and the role they play in quantization via Feynman propagators. Chapter 4 is the heart of the book. In this chapter, the authors introduce the cyclotron braid subgroup of the full braid group and make use of it to understand various aspects of the FQHE. Chapter 5 is concerned with a number of recent progress in the field initiated by the discovery of Tsui and Störmer. Here we find descriptions of several recent graphene experiments as well as an introduction to the novel concept of topological insulators. The authors then give a summary of the book in Chapter 6. The last chapter, Chapter 7, is essentially an appendix where some of the background information on 2D Hall systems and the fundamental group are given.