### Abstract

The authors present some new and interesting results on the localisation of electronic states in a one-dimensional lattice with an incommensurate lattice potential. The system studied is represented by a tight-binding Hamiltonian with diagonal elements given by V_{0} cos(qn). V_{0} is the modulation strength and q is the wavenumber. They introduce the concept of quasilocalisation to clarify inconsistencies in previous work on the existence of mobility edges. Their technique allows very precise calculation of the resolvent operator without the problem of numerical instability. Thus they are able to present accurate results for the density of states even when the widths of the energy bands are extremely small.

Original language | English |
---|---|

Article number | 010 |

Pages (from-to) | 6971-6980 |

Number of pages | 10 |

Journal | Journal of Physics C: Solid State Physics |

Volume | 15 |

Issue number | 34 |

DOIs | |

State | Published - 1 Dec 1982 |

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### Cite this

*Journal of Physics C: Solid State Physics*,

*15*(34), 6971-6980. [010]. https://doi.org/10.1088/0022-3719/15/34/010

}

*Journal of Physics C: Solid State Physics*, vol. 15, no. 34, 010, pp. 6971-6980. https://doi.org/10.1088/0022-3719/15/34/010

**Electronic states in a one-dimensional system with incommensurate lattice potentials.** / Dy, K. S.; Ma, Tzu Chiang Ernest.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Electronic states in a one-dimensional system with incommensurate lattice potentials

AU - Dy, K. S.

AU - Ma, Tzu Chiang Ernest

PY - 1982/12/1

Y1 - 1982/12/1

N2 - The authors present some new and interesting results on the localisation of electronic states in a one-dimensional lattice with an incommensurate lattice potential. The system studied is represented by a tight-binding Hamiltonian with diagonal elements given by V0 cos(qn). V0 is the modulation strength and q is the wavenumber. They introduce the concept of quasilocalisation to clarify inconsistencies in previous work on the existence of mobility edges. Their technique allows very precise calculation of the resolvent operator without the problem of numerical instability. Thus they are able to present accurate results for the density of states even when the widths of the energy bands are extremely small.

AB - The authors present some new and interesting results on the localisation of electronic states in a one-dimensional lattice with an incommensurate lattice potential. The system studied is represented by a tight-binding Hamiltonian with diagonal elements given by V0 cos(qn). V0 is the modulation strength and q is the wavenumber. They introduce the concept of quasilocalisation to clarify inconsistencies in previous work on the existence of mobility edges. Their technique allows very precise calculation of the resolvent operator without the problem of numerical instability. Thus they are able to present accurate results for the density of states even when the widths of the energy bands are extremely small.

UR - http://www.scopus.com/inward/record.url?scp=36149043122&partnerID=8YFLogxK

U2 - 10.1088/0022-3719/15/34/010

DO - 10.1088/0022-3719/15/34/010

M3 - Article

VL - 15

SP - 6971

EP - 6980

JO - Journal of Physics C: Solid State Physics

JF - Journal of Physics C: Solid State Physics

SN - 0022-3719

IS - 34

M1 - 010

ER -