Inverse Design of Strongly Localized Topological $\pi$ Modes in One-Dimensional Nonperiodic Systems

TL;DR

This paper presents an inverse design method for creating one-dimensional topological $\pi$-modes with enhanced spatial confinement, using a generative model under topological constraints, leading to compact, strongly localized states.

Contribution

The study introduces a generative inverse design approach for topological states that achieves stronger localization while maintaining topological properties.

Findings

Generated potential sequences with enhanced confinement ($\xi=0.85$).

Constructed a minimal heterostructure reducing localization length to $\xi=0.75$.

Provided a compact design principle for localized topological states.

Abstract

This study investigates the spatial confinement of topological $\pi$-modes in one-dimensional chiral-symmetric systems. In conventional periodic and quasiperiodic structures, edge-mode wave functions inevitably penetrate the bulk. To suppress this, inverse design of a potential sequence is performed using a generative model under a global topological constraint. The generated sequence reveals a characteristic structure consisting of a topological boundary layer and a macroscopic S-dense domain, leading to enhanced confinement ($\xi=0.85$) while preserving topology. Based on the physical principle extracted from this result, a minimal heterostructure composed of only two S-blocks is manually constructed, which further reduces the localization length to $\xi=0.75$. These results provide a compact design principle for strongly localized topological states.