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Seeking Topological Phases in Fractals

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

Abstract

As we had seen in Table  1.1, the classification of topological systems is described by a tenfold scheme and a periodicity in spatial dimensions d. Notions of integral dimensions and bulk-boundary correspondence lies at the heart of the topological band theory [1, 2, 3, 4]. A nontrivial invariant calculated for a periodic system signals existence of robust boundary states for the same system with a boundary. This correspondence is the progenitor of formulations of various invariants such as TKNN invariant (Chern number) [5], the Pfaffian and others (for a recent review see [3]) which lead to exotic boundary physics. However, not every system has a well defined “bulk” or “boundary”. Neither does every system have a well defined dimension. Is there a notion of a topological state in such systems? If yes, how can they be characterized?

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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