VOLUME 50, NUMBER 10 PHYSICAL REVIEW LETTERS 7 MARCH 1983 National Science Foundation; the U. S. Office of Naval Research, under Grant No. N00014-81-K- 0438; and the U. S. National Science Foundation, under Grant No. DMR77-23776. Also at Istituto di Fisica Teorica, University, di Trieste, I-34014 Trieste, Italy. ermanent address: Institut fiir Physikalische Chemic, University of Vienna, Wahringerstrasse 42, A-1090 Vienna, Austria. P. Pfluger and H. J. QGntherodt, I estkorperprob- leme: Advances in Solid State Physics, edited by J. Treusch (Vieweg, Braunschweig, 1981), Vol. 21, p. 271 and references therein. ~E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys. Rev. B 24, 864 (1981). 3N. A. W. Holzwarth, S. Rabii, and L. A. Qirifalco, Phys. Rev. B 18, 5190 (1978). The three systems studied in this work have D6„ symmetry. The irreducible representations of this group are labeled according to the notations of Q. F. Koster, J. O. Dimmock, R. Q. Wheeler, and H. Statz, Properties of the Thirty-To Point Groups (MIT Press, Cambridge, Mass. , 1963). According to Ref. 3, the bottom of the Li band in LiC6 is -1. 7 eV above EF. Notice, however, that, assuming rigid bands, we calculate that EF (LiC6) = Ep(C6-Li-C6) + 0.4 eV since the concentration of Li atoms in LiC6 is twice that in C6-Li-C6. 60bservation of K 4s states in KC8 at about this en- ergy has been reported by J. J. Ritsko and C. F. Brucker, Bull. Am. Phys. Soc. 27, 405 (1982). VL. Samuelson and I. P. Batra, J. Phys. C 13, 5105 (1980), and reference therein. W. van Haeringen and H. Q. Junginger, Solid State Commun. 7, 1723 (1969). ~C. P. Mallet, J. Phys. C 14, L213 (1981). ' Y. Baer, J. Electron Spectrosc. Relat. Phenom. 24, 95 (1981). Localization in One-Dimensional Disordered Systems in the Presence of an Electric Field C. M. Soukoulis, Jorge V. Josd, '" E. N. Economou, ' ' and Ping Sheng Corporate Research Science Laboratories, Exxon Research and Engineering Company, Linden, New Jersey 07036 (Received 16 December 1982) The influence of an electric field E on the nature of electronic states in a one-dimensional disordered Kronig-Penney model is studied. By study of the Poincare map of the Kronig- Penney model in a field, the transmission coefficient T was calculated as a function of sys- tem size L. T is found to behave as L "(s), with n-I/P, for small F which indicates pow- er-law localization. In this regime, it is predicted that the resistance R(E) =R(0)(l-b~P~), which may be checked experimentally. PACS numbers: 72. 10. Bg, 71. 50. +t, 71. 55. Jv The question of localization of the eigenstates in one dimensional (1D) disordered systems has been extensively studied both numerically and analytically. ' lt is by now well established that in a 1D model all eigenstates are localized regard- less of the amount of disorder. ' Experiments on quasi one-dimensional disordered metallic sys- tems (thin wires) are in qualitative agreement with localization theory. ' %bile much work has been done for the study of the energy spectrum of an electron in a finite or semi-infinite periodic lattice in the presence of an electric field, ' very little is known for the problem of a 1D disordered system in an electric field, " especially regard- ing the nature of the localized states. It is the purpose of this Letter to examine the size dependence of the transmission coefficient T in a 1D disordered system when an electric field I is present. The study of the transmission coefficient has been used successfully to analyze the nature of the electronic states. ' " The model studied in this paper is + Q b„5(x — n) — Fx g(x) =Kg(x), d2 where b„ is the strength of the nth 6-function po- tential, taken to be a random variable with rec- tangular probability distribution of width O'. Here F is the product of the electric field by the elec- tron charge e. The numerical study of Eq. (1) can be simplified if we use the Poincard map representation of the Schrodinger equation. This consists in relating the wave-function amplitudes at different lattice sites. Specifically, defining 764 1983 The American Physical Society