Extended State to Localization in Random Aperiodic Chains |
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Authors: | GAO Hui-Fen and TAO Rui-Bao |
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Institution: | 1. Department of Physics, Fudan University, Shanghai 200433, China
;2. China Center of Advanced Science and Technology (World Laboratory), P.O. Box 8730, Beijing 100080, China |
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Abstract: | The electronic states in Thus-Morse chain (TMC) and generalized Fibonacci
chain (GFC) are studied by solving eigenequation and using transfer matrix
method. Two model Hamiltonians are studied. One contains the nearest
neighbor (n.n.) hopping terms only and the other has additionally next
nearest neighbor (n.n.n.) hopping terms. Based on the transfer matrix
method, a criterion of transition from the extended to the localized states
is suggested for GFC and TMC. The numerical calculation shows the existence of both extended and localized states in pure aperiodic system. A random potential is introduced to the diagonal term of the Hamiltonian and then the
extended states are always changed to be localized. The exponents related to
the localization length as a function of randomness are calculated. For
different kinds of aperiodic chain, the critical value of randomness for
the transition from extended to the localized states are found to be zero,
consistent with the case of ordinary one-dimensional systems. |
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Keywords: | localization transfer matrix method localized length |
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