J. Phys. I France
Volume 2, Numéro 11, November 1992
Page(s) 2039 - 2045
DOI: 10.1051/jp1:1992265
J. Phys. I France 2 (1992) 2039-2045

Behaviour of the electronic states in the Harper model in one dimension

Abhijit Kar Gupta and Asok K. Sen

Low Temperature Physics Section, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064, India

(Received 22 June 1992, accepted 20 August 1992)

In contrast to a recent claim that the metal-insulator transition in the Harper model in one dimension does not occur sharply at $\lambda_{\rm C}=2t$, we find in a numerical study involving transmittances that there exists a sharp boundary between the localized and extended spectra in the parameter space (of $\lambda$, the amplitude of the incommensurate site potential). Further more, the multifractal behaviour of the normalized transmittances as a function of length has been studied in support of our work. The multifractal spectra along with the resistance as a function of length prompts us to conjecture that the nature of the extended states in a finite sized system for values of $\lambda$, very near to $\lambda_{\rm C}$ are different from that of typical Bloch states.

© Les Editions de Physique 1992