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

In this paper, one dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix method. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the delocalization transition. In particular, we numerically calculate both the “typical” and “mean” localization lengths as a function of energy and the correlation length of the random mass. To this end we introduce an imaginary vector potential as suggested by Hatano and Nelson and solve the eigenvalue problem. Numerical calculations are in good agreement with the results of the analytical calculations. We obtain a relation between the localization length of states and the correlation length of the random mass.