Localization in one-dimensional disordered systems with electric field: An analytical approach

作者: Dar̆o Castello , Alfredo Caro , Arturo López

DOI: 10.1103/PHYSREVB.36.3002

关键词: Exponential growthTransmission coefficientStatistical physicsPower (physics)Condensed matter physicsElectric fieldTransfer (group theory)Expression (mathematics)PhysicsChain (algebraic topology)

摘要: We perform an analytic calculation of the transmission coefficient for a finite disordered Kronig-Penney chain with electric field, using some interesting properties transfer matrices \ensuremath{\delta}-function potential. They allow us to give closed-form approximate expression which clearly shows existence three regions wave-function behavior: exponentially localized, power and extended states. The current-voltage characteristics such system are also evaluated, together precise numerical evaluation comparison.

参考文章(10)
Gregory H. Wannier, Wave Functions and Effective Hamiltonian for Bloch Electrons in an Electric Field Physical Review. ,vol. 117, pp. 432- 439 ,(1960) , 10.1103/PHYSREV.117.432
J. E. Avron, J. Zak, A. Grossmann, L. Gunther, Instability of the continuous spectrum: The N‐band Stark ladder Journal of Mathematical Physics. ,vol. 18, pp. 918- 921 ,(1977) , 10.1063/1.523360
C. M. Soukoulis, Jorge V. José, E. N. Economou, Ping Sheng, Localization in One-Dimensional Disordered Systems in the Presence of an Electric Field Physical Review Letters. ,vol. 50, pp. 764- 767 ,(1983) , 10.1103/PHYSREVLETT.50.764
Francois Delyon, Barry Simon, Bernard Souillard, From Power-Localized to Extended States in a Class of One-Dimensional Disordered Systems Physical Review Letters. ,vol. 52, pp. 2187- 2189 ,(1984) , 10.1103/PHYSREVLETT.52.2187
Ernesto Cota, Jorge V. José, M. Ya. Azbel, Delocalization transition in random electrified chains with arbitrary potentials. Physical Review B. ,vol. 32, pp. 6157- 6165 ,(1985) , 10.1103/PHYSREVB.32.6157
T. R. Kirkpatrick, Anderson localization and delocalization in an electric field. Physical Review B. ,vol. 33, pp. 780- 788 ,(1986) , 10.1103/PHYSREVB.33.780
Dieter Vollhardt, Peter Wölfle, Diagrammatic, self-consistent treatment of the Anderson localization problem ind≤2dimensions Physical Review B. ,vol. 22, pp. 4666- 4679 ,(1980) , 10.1103/PHYSREVB.22.4666
Rolf Landauer, Electrical resistance of disordered one-dimensional lattices Philosophical Magazine. ,vol. 21, pp. 863- 867 ,(1970) , 10.1080/14786437008238472
A.A. Abrikosov, The paradox with the static conductivity of a one-dimensional metal Solid State Communications. ,vol. 37, pp. 997- 1000 ,(1981) , 10.1016/0038-1098(81)91203-5