中国物理B ›› 2009, Vol. 18 ›› Issue (3): 1214-1220.doi: 10.1088/1674-1056/18/3/062

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State vector evolution localized over the edges of a square tight-binding lattice

何良明1, 石端文2   

  1. (1)College of Physics and Electronic Engineering, Guangxi University for Nationalities, Nanning 530006, China; (2)Department of Physics, Hainan Normal University, Haikou 571158, China
  • 收稿日期:2008-07-05 修回日期:2008-09-10 出版日期:2009-03-20 发布日期:2009-03-20

State vector evolution localized over the edges of a square tight-binding lattice

He Liang-Ming(何良明)a) and Shi Duan-Wen (石端文)b)   

  1. a College of Physics and Electronic Engineering, Guangxi University for Nationalities, Nanning 530006, China; b Department of Physics, Hainan Normal University, Haikou 571158, China
  • Received:2008-07-05 Revised:2008-09-10 Online:2009-03-20 Published:2009-03-20

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摘要： We study the time evolution of a state vector in a square tight-binding lattice, focusing on its evolution localized over the system surfaces. In this tight-binding lattice, the energy of atomic orbital centred at surface site is different from that at the interior (bulky) site by an energy shift U. It is shown that for the state vector initially localized on a surface, there exists an exponential law (y=a\ex/b+y0) determined by the absolute value of the energy shift, |U|, which describes the transition of the state evolving on the square tight-binding lattice, from delocalized over the whole lattice to localized over the surfaces.

关键词: Anderson localization, surface states, state vector evolution

Abstract: We study the time evolution of a state vector in a square tight-binding lattice, focusing on its evolution localized over the system surfaces. In this tight-binding lattice, the energy of atomic orbital centred at surface site is different from that at the interior (bulky) site by an energy shift U. It is shown that for the state vector initially localized on a surface, there exists an exponential law (y=aex/b+y0) determined by the absolute value of the energy shift, |U|, which describes the transition of the state evolving on the square tight-binding lattice, from delocalized over the whole lattice to localized over the surfaces.

Key words: Anderson localization, surface states, state vector evolution

中图分类号:  (Surface states, band structure, electron density of states)

  • 73.20.At
71.15.Ap (Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.))