Localized and extended states in one-dimensional disordered system: random-mass Dirac fermions

A system of Dirac fermions with random-varying mass is studied in detail. W e reformulate the system by transfer-matrix formalism. Eigenvalues and wave functions are obtained numerically for various configurations of random te legraphic mass m(x). Localized and extended states are identified. For quas i-periodic m(x), low-energy wave functions are also quasi-periodic and exte nded, though we are not imposing the periodic boundary condition on wave fu nction. On increasing the randomness of the varying mass, states lose perio dicity and most of them tend to localize. At the band centre or the low-ene rgy limit, there exist extended states which have more than one peak spatia lly separate with each other comparatively large distance. Numerical calcul ations of the density of states and ensemble averaged Green's functions are explicitly given. They are in good agreement with analytical calculations by using the supersymmetric methods and exact form of the zero-energy wave functions. (C) 1999 Elsevier Science B.V. All rights reserved.