Topological Insulators in Amorphous Systems

  • Adhip AgarwalaEmail author
Part of the Springer Theses book series (Springer Theses)


In this chapter, we will theoretically establish that amorphous systems can host topologically insulating phases. We will provide a demonstration of this by constructing models (using familiar ingredients) on random lattices where fermions hop between sites within a finite range. By tuning parameters (such as the density of sites), we show that the system undergoes a quantum phase transition from a trivial to a topological phase. We characterize the topological nature by obtaining the topological invariant and associated quantized transport signatures. We also address interesting features of such quantum phase transitions. This is achieved through a detailed study of all nontrivial symmetry classes (A, AII, D, DIII and C) in two dimensions. We will also provide a demonstration of a topological insulator in three dimensions. This work opens a new direction in the experimental search for topological quantum matter, by demonstrating their possibility in, as yet unexplored, amorphous systems. We discuss several examples including glassy systems and other engineered random systems.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.International Centre for Theoretical SciencesTata Institute of Fundamental ResearchBangaloreIndia

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