Effects of Long-Range Correlations in Random-Mass Dirac Fermions

TL;DR

This paper investigates how long-range correlations in random-mass Dirac fermions influence localization, delocalization transitions, and singular behaviors at the band center, revealing a phase transition driven by correlation length.

Contribution

It provides new insights into the effects of long-range correlations on localization phenomena in one-dimensional Dirac fermions, extending previous short-range correlation studies.

Findings

Identification of a phase transition driven by correlation length

Demonstration of long-range correlations affecting localization lengths

Analysis of density of states near the band center

Abstract

In the previous paper, we studied the random-mass Dirac fermion in one dimension by using the transfer-matrix methods. We furthermore employed the imaginary vector potential methods for calculating the localization lengths. Especially we investigated effects of the nonlocal but short-range correlations of the random mass. In this paper, we shall study effects of the long-range correlations of the random mass especially on the delocalization transition and singular behaviours at the band center. We calculate localization lengths and density of states for various nonlocally correlated random mass. We show that there occurs a "phase transition" as the correlation length of the random Dirac mass is varied. The Thouless formula, which relates the density of states and the localization lengths, plays an important role in our investigation.