We present a numerically accurate procedure for the study of the electronic structure of one-dimensional incommensurate systems. Our method is used to infer the localized or extended nature of the electronic states by considering, at the same time, both diagonal and off-diagonal matrix elements of an appropriate effective Hamiltonian; we work out a convenient expression of the Lyapunov coefficient in terms of the off-diagonal effective matrix elements. With the further implementation of separately processing (though interdependently) the appropriate segments of the infinite chain, we provide a simple method to reach any desired numerical precision, so that physical aspects can be clearly worked out. Our procedure is tested on an incommensurate potential that exhibits mobility edges.

ELECTRONIC-STRUCTURE IN INCOMMENSURATE POTENTIALS OBTAINED USING A NUMERICALLY ACCURATE RENORMALIZATION SCHEME

GROSSO, GIUSEPPE;
1992

Abstract

We present a numerically accurate procedure for the study of the electronic structure of one-dimensional incommensurate systems. Our method is used to infer the localized or extended nature of the electronic states by considering, at the same time, both diagonal and off-diagonal matrix elements of an appropriate effective Hamiltonian; we work out a convenient expression of the Lyapunov coefficient in terms of the off-diagonal effective matrix elements. With the further implementation of separately processing (though interdependently) the appropriate segments of the infinite chain, we provide a simple method to reach any desired numerical precision, so that physical aspects can be clearly worked out. Our procedure is tested on an incommensurate potential that exhibits mobility edges.
Farchioni, R; Grosso, Giuseppe; PASTORI PARRAVICINI, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/18756
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