Multifractal wave functions at the Anderson transition
作者： Michael Schreiber , Heiko Grussbach
DOI: 10.1103/PHYSREVLETT.67.607
关键词:
摘要: Electronic wave functions in disordered systems are studied within the Anderson model of localization. At critical disorder 3D we diagonalize very large (103 823\ifmmode\times\else\texttimes\fi{}103 823) secular matrices by means Lanczos algorithm. On all length scales obtained strong spatial fluctuations amplitude eigenstates display a multifractal character, reflected set generalized fractal dimensions and singularity spectrum measure. An analysis 1D shows multifractality too, contrast to previous claims.
harvard.edu
sci-hub.se 参考文章(21)
N.F. Mott, W.D. Twose, The theory of impurity conduction Advances in Physics. ,vol. 10, pp. 107- 163 ,(1961) , 10.1080/00018736100101271
E. Abrahams, P. W. Anderson, D. C. Licciardello, T. V. Ramakrishnan, Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions Physical Review Letters. ,vol. 42, pp. 673- 676 ,(1979) , 10.1103/PHYSREVLETT.42.673
B. Kramer, K. Broderix, A. Mackinnon, M. Schreiber, The Anderson transition: New numerical results for the critical exponents Physica A: Statistical Mechanics and its Applications. ,vol. 167, pp. 163- 174 ,(1990) , 10.1016/0378-4371(90)90050-3
H Aoki, Critical behaviour of extended states in disordered systems Journal of Physics C: Solid State Physics. ,vol. 16, ,(1983) , 10.1088/0022-3719/16/6/007
C. M. Soukoulis, E. N. Economou, Fractal Character of Eigenstates in Disordered Systems Physical Review Letters. ,vol. 52, pp. 565- 568 ,(1984) , 10.1103/PHYSREVLETT.52.565
M. Schreiber, Fractal character of eigenstates in weakly disordered three-dimensional systems Physical Review B. ,vol. 31, pp. 6146- 6149 ,(1985) , 10.1103/PHYSREVB.31.6146
T. Ohtsuki, B. Kramer, Y. Ono, On the fractal dimensionality of the extended states in disordered two-dimensional systems in a strong magnetic field Surface Science. ,vol. 196, pp. 127- 133 ,(1988) , 10.1016/0039-6028(88)90674-7
Yoshiyuki Ono, Tomi Ohtsuki, Bernhard Kramer, Inverse Participation Number and Fractal Dimensionality of Electronic States in a Two Dimensional System in Strong Perpendicular Magnetic Field Journal of the Physical Society of Japan. ,vol. 58, pp. 1705- 1716 ,(1989) , 10.1143/JPSJ.58.1705
Michael Schreiber, Fractal eigenstates in disordered systems Physica A: Statistical Mechanics and its Applications. ,vol. 167, pp. 188- 198 ,(1990) , 10.1016/0378-4371(90)90052-T
Hideo Aoki, Fractal dimensionality of wave functions at the mobility edge: Quantum fractal in the Landau levels Physical Review B. ,vol. 33, pp. 7310- 7313 ,(1986) , 10.1103/PHYSREVB.33.7310