Non-locally correlated disorder and delocalization in one dimension (II). Localization length

Abstract

We study delocalization transition in a one-dimensional Dirac fermion system with random varying mass by using supersymmetric (SUSY) methods. In a previous paper, we calculated density of states and found that (quasi-)extended states near the band center are enhanced by nonlocal correlation of the random Dirac mass. Numerical studies support this conclusion. In this paper, we shall calculate localization length as a function of correlation length of the disorder. The result shows that the localization length is an increasing function of the correlation of the random mass.

Random-Mass Dirac Fermions in an Imaginary Vector Potential: Delocalization Transition and Localization Length

“…The delocalization transition probably occurs at E = 0. In the previous paper [12] we calculated the localization length for the random mass with the short-range correlation (7). We obtained the "mean" localization length to the 1st order of λ by means of the Green function method.…”

“…System of Dirac fermions with a random-varying mass in one dimension has been studied from this point of view [2][3][4][5][6][7][8]. In the previous papers [9][10][11] we studied the effect of nonlocal correlation of the random mass on the extended states which exist near the band center. For numerical studies, we reformulate the system by transfer-matrix formalism, and obtained eigenvalues and wave functions for various configurations of random telegraphic mass [9].…”

“…Case of nonlocally correlated random mass was studied in Refs. [10,11] and ξ m (E) is obtained as a function of λ in Eq. (7).…”

Amplitude scaling behavior of band center states of Frenkel exciton chains with correlated off-diagonal disorder

“…Many efforts have also been spent on the same off-diagonal tightbinding system using supersymmetric methods (SUSY) [6] where the interactions are formally similar to our dipolar interactions but the authors eventually worked with continuous variables whereas ours are discrete. Later, correlated disorder, in particular the exponential type, was included for the same tight binding model using the SUSY [7,8]. Our results can thus be compared with what has been developed for the SUSY methods.…”

“…where l(c) is the correlation length as a function of "wrong sign" concentration c (see below). Thus the dipolar coupling J n has a non fluctuating part and a fluctuating part as in Dirac fermions with random-varying mass [7,8].…”