Year: 2025
Type: article
Abstract: We study the localization properties of the quasiperiodic one-dimensional helical chain with two tunneling paths: nearest-neighbor and a long-range hop that connects sites of consecutive helical turns. Using exact diagonalization, we quantify localization employing the inverse participation ratio (IPR) and the normalized participation ratio (NPR) and combine them into a single measure to create a phase map. The resulting diagrams reveal three regimes: a completely extended phase, a completely localized phase, and a mixed domain where localized and extended states coexist. In the diagrams, we investigate the behaviors of tightly and loosely wound helices and examine a special case where the number of sites per turn is a Fibonacci number. For moderate numbers of sites per helical turn, the mixed region is broad and also shifts with the long-range coupling. When the turn size is a Fibonacci number, the phase boundary becomes nearly horizontal and the mixed region fades out, effectively recovering the standard Aubry–André model behavior.
Authors: Taylan Yildiz, B. Tanatar
Institution: Bilkent University
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
Funder: Türkiye Bilimler Akademisi
OpenAlex ID: W4416042220