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Metal-Insulator Transition in onedimensional lattices with chaotic energy sequences 1 Pinto Instituto Venezolano de Investigaciones Científicas Centro de Física Apartado 21827 Caracas 1020A, Venezuela 1 Medina Ricardo Ernesto 1 2 Miguel E. Rodriguez Jorge A. González 1Laboratorio de Física Estadística de Sistemas Desordenados IVIC, Venezuela, 2Laboratorio de Física Computacional IVIC, Venezuela Abstract It is well known that one-dimensional systems with uncorrelated disorder behave like insulators because their electronic states localize at sufficiently large length scales i.e. for systems whose length is larger than the electronic localization length the conductance vanishes exponentially. We study electronic transport through a one-dimensional array of sites using Tight Binding Hamiltonian, where the distribution of site energies is given by a chaotic numbers generator. The degree of correlation between these energies is controlled by a parameter which regulates the dynamical Lyapunov exponent of the sequence. We observe the effect of such a correlation on transport properties, finding evidences of a Metal-Insulator Transition in the thermodynamic limit, for a certain value of the control parameter of the correlation. Introduction The Model There has been great interest in studying the effect of correlations on Our model [1] describes a one-dimensional lattice with N sites each with electronic states in disordered lattices. There is recent evidence that a one electron state. We describe the Hamiltonian of the system (H) in correlations, in the local energy distribution, yields delocalization of the the Tight-Binding approximation with nearest-neighbour interactions with wave function in these structures. Such phenomena diagonal disorder. The local energies i (i=1,..,N), are could serve to explain electronic transport properties in taken from a chaotic number generator: i+11H n n n V m n certain systems such as polymers, proteins, and more n mn sin(z*asin(i1/2)), whose correlation can be controlled recently, DNA chains. De Moura [2], and more recently, by the parameter z, which is uniquely linked to the Carpena et al [3] proposed a model for a oneLyapunov exponent [4]: =ln(z). The system is dimensional lattice with correlated disorder, where a connected at both ends to ordered one-dimensional disorder-induced Metal-Insulator Transition is found in 0 0 leads, which introduce a self-energy term S in the l 2 the thermodynamic limit. We show that in a lattice with n1 1 sin [ z arcsin( n )] system and, consequently, a finite escape probability. a chaotic energy sequence of known correlation a Metal-Insulator Transition also ensues. Results I II Fig. 1: Bifurcation map corresponding to the chaotic number generator to set the energies of sites. In this sample we used E1 = 0.3. Fig. 2: Localization length as a function of the Fermi’s energy. Note the two regions in which the localization length is larger than the size of the system (N=1500). Fig. 3: Conductance scaling for different values of the parameter z. The system is set to an energy value within the region I in the Fig. 2. Fig. 4: Conductance as a function of the control parameter z for systems of different sizes. Fig. 5: Conductance as a function of the control parameter z for three different sizes of the system. All of the three curves overlap, indicating that the behaviour g(z) is independent from the size. Notice that localization occurs at a value z>1. We recall that z1 represents the trivial case of an ordered system. Fig. 6: Wave function for different values of the control parameter z, where we can see the crossover to a localized state as z increases. References: [1]. H. M. Pastawski and E. Medina, Rev. Mex. Fís. 47, 1 (2001). [2] F. de Moura and M. L. Lyra, Phys. Rev. Lett. 81, 3735 (1998). [3] P. Carpena, P. Bernaloa-Galván, P. Ch. Ivanov & H. E. Stanley, Nature 418, 955 (2002). [4] H. Nazareno, J. A. González, I. F. Costa, Phys. Rev. B 57, 13583 (1998).