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

Abstract

In this and subsequent papers, one dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the delocalization transition. Especially 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 the relation between the localization length of states and the correlation length of the random mass. In subsequent paper, we shall study Dirac fermions with a random mass of long-ranged correlations.