Abstract
Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological phase can also be fruitfully applied to plasmas. Here, the theory of topological phase is introduced, including a discussion of Berry phase, Berry connection, Berry curvature and Chern number. One of the clear physical manifestations of topological phase is the bulk-boundary correspondence, the existence of localized unidirectional modes at the interface between topologically distinct phases. These concepts are illustrated through examples, including the simple magnetized cold plasma. An outlook is provided for future theoretical developments and possible applications.
Highlights
The aim of this article is to introduce the concepts and physics of topological phase in the context of plasma physics
An important feature of topological invariants is that they are constrained by topological quantization and are generally not altered under smooth deformations, and so their physical consequences may be robust against perturbations
The purpose of this paper is to provide an accessible introduction to these concepts and their applications, without requiring any background in condensed matter physics or differential geometry
Summary
The aim of this article is to introduce the concepts and physics of topological phase in the context of plasma physics. It was realized that this integer multiple corresponded to a topological invariant called the Chern number that described the sample bulk, with corresponding electron edge states that allowed conduction. The periodic metamaterial structure of a photonic crystal gives rise to Bloch states and Bloch bands analogous to those in condensed matter systems. This field of topological photonics may offer novel disorder-robust routes to controlling light (Lu, Joannopoulos & Soljacic 2014; Ma et al 2015; Ozawa et al 2019). Plasmas and fluids are typically described mathematically as a smooth continuum, coarse-grained over the length scale of individual particles This distinction gives rise to a very different structure of the wave vector space. Mathematical background we review the mathematical background for topological phase
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