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arXiv · 2602.09769

Metallic mean quasicrystals and their topological invariants

Anuradha Jagannathan
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Abstract

Topological invariants govern many important physical properties in condensed matter systems. In this work, we obtain the complete set of topological invariants for a family of one-dimensional quasicrystals. The first and best-studied member of the family is the Fibonacci chain, while the successive ones are known in the literature as silver, bronze... and collectively as the metallic mean chains. By considering rational approximants, and by making use of the relationship between these chains and two dimensional Quantum Hall problems, we write down a gap labeling scheme for finite systems, and extend it to the quasiperiodic limit. We show, by numerical computations on open chains, that the proposed scheme correctly yields the winding numbers of edge states in each of the gaps, in all of the quasicrystals. We observe that their relationship to the 2D model leads, in the strict 1D chains family, to spectra forming a simplified Hofstadter ``butterfly" diagram, with the analogues of Landau levels appearing in the asymptotic limit.

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Anuradha Jagannathan. 2026-02-10. Metallic mean quasicrystals and their topological invariants. https://arxiv.org/abs/2602.09769

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