Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators

TL;DR

This paper explores how Fibonacci modulation induces multiple topological Anderson insulator phases in a one-dimensional spin-orbit coupled chain, revealing fractal energy spectra and multifractal wave functions with potential experimental realizations.

Contribution

It demonstrates the emergence of multiple TAIs driven by Fibonacci modulation and characterizes their multifractal properties, expanding understanding of topological phases in disordered systems.

Findings

Number of TAI phases increases as SOC decreases

Fibonacci modulation induces fractal energy spectra

Wave functions exhibit multifractal properties

Abstract

Topological Anderson insulators (TAIs) provide a mechanism for topological phase transitions in disordered systems and have implications for quantum material design. In this work, we investigate the emergence of multiple TAIs in a one-dimensional spin-orbit coupled (SOC) chain subject to Fibonacci modulation, which transforms a trivial band structure into a sequence of topologically nontrivial phases. This behavior is characterized by the appearance of zero-energy modes and changes in the $Z_2$ topological quantum number. As the SOC amplitude decreases, the number of TAI phases increases, a feature that is closely related to the fractal structure of the energy spectrum induced by Fibonacci modulation. In contrast to conventional TAI phases with fully localized eigenstates, the wave functions in the Fibonacci-modulated TAI phases display multifractal properties. This model can be experimentally realized using a Bose-Einstein condensate in a momentum-space lattice, where its topological transitions and multifractal features can be explored through quench dynamics.