Localization-delocalization transition in the quasi-one-dimensional ladder chain with correlated disorder

TL;DR

This paper investigates the localization-delocalization transition in a quasi-one-dimensional ladder chain with correlated disorder, combining analytical and numerical methods to identify critical points and characterize the transition.

Contribution

It introduces a generalized dimer model on a two-leg ladder and provides analytical and numerical analysis of localization properties and transition behavior.

Findings

Presence of a delocalization point at the band center confirmed analytically and numerically.

Analytical expressions for Landauer resistance and localization length index derived.

Numerical results show how the transition affects the distribution of Wigner delay times.

Abstract

The generalization of the dimer model on a two-leg ladder is defined and investigated both, analytically and numerically. For the closed system we calculate the Landauer resistance analytically and found the presence of the point of delocalization at the band center which is confirmed by the numerical calculations of the Lyapunov exponent. We calculate also analytically the localization length index and present the numerical investigations of the density of states (DOS). For the open counterpart of this model the distribution of the Wigner delay times is calculated numerically. It is shown how the localization-delocalization transition manifest itself in the behavior of the distribution.