Periodic, quasi-periodic, fractal, Kolakoski and random binary polymers: Energy structure and carrier transport

TL;DR

This study investigates how different binary sequence structures, including periodic, aperiodic, fractal, Kolakoski, and random, influence energy levels, localization, and charge transport in a DNA-inspired tight-binding model.

Contribution

It provides a comprehensive analysis of the impact of sequence intricacy and correlations on physical properties like energy structure and charge transport in various binary sequences.

Findings

Periodic segments enhance transport properties.

Homogeneous sequences maximize transport efficiency.

Random sequences exhibit the lowest transport efficiency.

Abstract

We study periodic, quasi-periodic (Thue-Morse, Fibonacci, Period Doubling, Rudin-Shapiro), fractal (Cantor, generalized Cantor), Kolakoski and random binary sequences using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We use B-DNA as our prototype system. All sequences have purines, guanine (G) or adenine (A) on the same strand, i.e., our prototype binary alphabet is (G,A). Our aim is to examine the influence of sequence intricacy and magnitude of parameters on energy structure, localization and charge transport. We study quantities such as autocorrelation function, eigenspectra, density of states, Lyapunov exponents, transmission coefficients and current-voltage curves. We show that the degree of sequence intricacy and the presence of correlations decisively affect the aforementioned physical properties. Periodic segments have enhanced transport properties. Specifically, in homogeneous sequences transport efficiency is maximum. There are several deterministic aperiodic sequences that can support significant currents, depending on the Fermi level of the leads. Random sequences is the less efficient category.