Search

This book deals with the discovery and explanation of the quantum Hall effect and its fundamental principles. It is meant for undergraduate and graduate students of physics, engineering, and applied sciences studying condensed matter physics. Doctoral students and researchers of this subject will also find it equally useful. It begins with a historical overview of this effect wherein the experiment and the physical systems are described. It progresses to cover discrete symmetries like inversion symmetry, time reversal symmetry, particle-hole symmetry, and chiral symmetry. It also examines how the Hamiltonian transforms under such symmetry operations. Two 1D models, namely the Su-Schrieffer-Heeger (SSH) model and a Kitaev chain with superconducting correlations, are discussed too. Then, the quantum Hall effect in graphene is explained. Further, the spin Hall effect is studied which may have prospects of using graphene as spintronic devices. The book ends with a brief review on fractional quantum Hall effect.

The book is mainly designed for post-graduate students to learn modern-day condensed matter physics. While emphasizing an experiment called the ‘Quantum Hall effect', it introduces the subject of'Topology'and how the topological invariants are related to the quantization of the Hall plateaus. Thus, the content tries to deliver an account of the topological aspects of materials that have shaped the study of condensed matter physics in recent times. The subject is often quite involved for a student to grasp the fundamentals and relate them to physical phenomena. Further, these topics are mostly left out of the undergraduate curriculum, although they often require a simplistic view of the concepts involved to be presented pedagogically. The book contains examples, worked-out concepts, important derivations, diagrams for illustration, etc. to aid the understanding of the students. The book also emphasizes the experimental discoveries that put the subject in its perspective and elaborate on the applications which are likely to be of interest to scientists and engineers.

The year 2022 has been declared by the United Nations as the “International Year of Basic Sciences for Sustainable Development”. Sustainable development is focused on the UN's 17 Sustainable Development Goals. These require the use of basic sciences. This edited book (volume 1) is a collection of twelve invited and peer-reviewed contributions from chemistry, materials science, energy applications, and artificial intelligence.

The study of Condensed Matter Physics has evolved over the last decade or so. The scope of Modern Condensed Matter Physics has expanded significantly from traditional solid-state physics and has become a highly interdisciplinary field of research. This book connects modern experimental discoveries with theoretical and fundamental concepts. It introduces the interacting and non-interacting aspects of fermionic systems and the role of topology and symmetry in understanding material properties. The text emphasizes quantum Hall effect, topological insulators and how the discovery of graphene has incited brilliant ideas in both fundamental and applied aspects. The role of interactions is discussed to explain topics including Magnetism and Superconductivity. Topics such as Bose Einstein condensation and superfluid properties of atomic systems in optical lattices are also a key feature of the text. The book offers something different to the field due to the range of topics covered in a pedagogical way for students.Key FeaturesProvides a modern perspective of condensed matter physicsAims to be understandable for studentsProvides significant pedagogical content in the form of derivations and illustrationsPresents advanced topics in a pedagogical manner