Articles written in Resonance – Journal of Science Education
Volume 25 Issue 6 June 2020 pp 765-786 General Article
Topological insulators are a new class of materials that have attracted signiﬁcant attention in contemporary condensed mat-ter physics. They are diﬀerent from regular insulators, and they display novel quantum properties that involve the idea of ‘topology’, an area of mathematics. Some of the fundamental concepts behind topological insulators, particularly in low-dimensional condensed matter systems such as poly-acetylene chains, can be understood using a simple one-dimensional toy model popularly known as the Su-Schrieﬀer-Heeger (SSH) model. This model can also be used as an introduction to the topological insulators of higher dimensions. Here, we give a concise description of the SSH model along with a brief re-view of the background physics and attempt to understand the ideas of topological invariants, edge states, and bulk-boundary correspondence using the model.
Volume 27 Issue 1 January 2022 pp 93-122 General Article
Based on the nature of the quantum statistics they follow, the quantum particles in the universe can be divided into two broad categories, the bosons, and the fermions. Indistinguishability leads to the invariance of the wave functions of the bosons and the fermions, up to a sign, under pairwise exchange. For fermions, Pauli's exclusion principle makes it impossible to put more than one identical particle in the same state. One consequence of this is the existence of different elements in the periodic table. On the other hand, many identical bosons can occupy a single state leading to exotic phases of matter like the Bose--Einstein condensates. In two dimensions, it is also possible to realize special quantum particles called the `anyons', the particles that are neither bosons nor fermions! The world-lines$^1$ representing the exchange of anyons appear to be different from those of the bosons and the fermions and they show `braiding' (like braiding hairs) leading to more sophisticated quantum statistics. Though the space around us is three-dimensional (at least), we can create special artificial two-dimensional spaces in the form of surfaces and interfaces where anyons can exist, and cleverly designed experiments can even detect them. In this article, we attempt to understand the fundamentals of anyons and find out how anyons can emerge in a two-dimensional fractional quantum Hall system.
Volume 27 | Issue 6