Abstract
We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is determined by the disorder and interference effects, leading to interesting sharp features in conductance as the energy, disorder, and boundary conditions are varied. To aid understanding of this phenomenon, we develop a visualization method whereby the progression of a wave packet entering the cluster through a lead on one side and exiting from another lead on the other side can be tracked dynamically. Using this method, we investigate the localization-delocalization transition in a 2D system for various boundary conditions. Our results indicate the existence of two different kinds of localized regimes, namely exponential and power law localization, depending on the amount of disorder. Our study further suggests that there may be a delocalized state in the 2D quantum percolation system at very low disorder. These results are based on a finite size scaling analysis of the systems of size up to 70 × 70 (containing 4900 sites) on the square lattice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Cuansing, H. Nakanishi, Phys. Rev. E 70, 066142 (2004)
M.F. Islam, H. Nakanishi, Eur. Phys. J. B 65, 555 (2008)
C.M. Soukoulis, E.N. Economou, G.S. Grest, Phys. Rev. B 36, 8649 (1987)
Th. Koslowski, W. von Niessen, Phys. Rev. B 44, 9926 (1991)
R. Berkovits, Y. Avishai, Phys. Rev. B 53, R16125 (1996)
E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)
However, a recent work of N. Goldenfeld, R. Haydock, Phys. Rev. B 73, 045118 (2006), concludes that a transition between two localized states exists for the 2D Anderson model
G.J. Dolan, D.D Osheroff, Phys. Rev. Lett. 43, 721 (1979)
D.J. Bishop, D.C. Tsui, R.C Dynes, Phys. Rev. Lett. 44, 1153 (1980)
M.J. Uren, R.A. Davies, M. Papper, J. Phys. C 13, L985 (1980)
E. Abrahams, S.V. Kravchenko, M.P. Sarachik, Rev. Mod. Phys. 73, 251, (2001)
D. Daboul, I. Chang, A. Aharony, Eur. Phys. J. B 16, 303 (2000)
T. Odagaki, K.C. Chang, Phys. Rev. B 30, 1612 (1984)
V. Srivastava, M. Chaturvedi, Phys. Rev. B 30, 2238 (1984)
M. Letz, K. Ziegler, Phil. Mag. B 79, 491 (1999)
H.N. Nazareno, P.E. de Brito, E.S. Rodrigues, Phys. Rev. B 66, 012205 (2002)
A. Eilmes, R.A. Römer, M. Schreiber, Physica B 296, 46 (2001)
G. Hałdaś, A. Kolek, A.W. Stadler, Phys. Status Solidi B 230, 249 (2002)
A. Bunde, J.W. Kantelhardt, L. Schweitzer, Ann. Phys. (Leipzig) 7, 372 (1998)
C.M. Soukoulis, G.S. Grest, Phys. Rev. B 44, 4685 (1991)
A. Mookerjee, I. Dasgupta, T. Saha, Int. J. Mod. Phys. B 9, 2989 (1995)
M. Inui, S.A. Trugman, E. Abrahams, Phys. Rev. B 49, 3190 (1994)
E. Cuansing, H. Nakanishi, Physica A 387, 806 (2008)
M.F. Islam, H. Nakanishi, Phys. Rev. E 77, 061109 (2008)
N.J. Giordano, H. Nakanishi, Computational Physics, 2nd edn. (Pearson Prentice Hall, 2005), pp. 334–335
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Islam, M., Nakanishi, H. Dynamical method for studying localization-delocalization transition in two dimensional percolating systems. Eur. Phys. J. B 68, 123–131 (2009). https://doi.org/10.1140/epjb/e2009-00076-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2009-00076-8