Critical parameters for the disorder-induced metal-insulator transition in FCC and BCC lattices

We use a transfer-matrix method to study the disorder-induced metal-insulator transition. We take isotropic nearest-neighbor hopping and an onsite potential with uniformly distributed disorder. Following the previous work done on the simple-cubic lattice, we perform numerical calculations for the body-centered cubic and face-centered cubic lattices, which are more common in nature. We obtain the localization length from calculated Lyapunov exponents for different system sizes. This data is analyzed using finite-size scaling to find the critical parameters. We create an energy-disorder phase diagram for both lattice types, noting that it is symmetric about the band center for the body-centered cubic lattice but not for the face-centered cubic lattice. We find a critical exponent of approximately 1.5-1.6 for both lattice types for transitions occurring either at fixed energy or at fixed disorder, agreeing with results previously obtained for other systems belonging to the same orthogonal universality class. We notice an increase in critical disorder with the number of nearest neighbors, which agrees with intuition.

[1]  E. Economou,et al.  Localization in Disordered Materials: Existence of Mobility Edges , 1970 .

[2]  Bernhard Kramer,et al.  Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition , 1997 .

[3]  CORRECTIONS TO SCALING AT THE ANDERSON TRANSITION , 1998, cond-mat/9812065.

[4]  Stupp,et al.  Possible solution of the conductivity exponent puzzle for the metal-insulator transition in heavily doped uncompensated semiconductors. , 1993, Physical review letters.

[5]  Frank Milde,et al.  Energy level statistics at the metal‐insulator transition in the Anderson model of localization with anisotropic hopping , 1998 .

[6]  A new criterion for localization in Anderson's model for disordered lattices☆ , 1974 .

[7]  Cummings,et al.  Hopping Conduction and Metal-Insulator Transition in Isotopically Enriched Neutron-Transmutation-Doped 70Ge:Ga. , 1996, Physical review letters.

[8]  P. Anderson.  Absence of Diffusion in Certain Random Lattices , 1958 .

[9]  M. V. Sadovskii,et al.  Self-consistent theory of localization for the Anderson model , 1983 .

[10]  Scaling of level statistics at the disorder-induced metal-insulator transition. , 1995, Physical review. B, Condensed matter.

[11]  M. Schreiber,et al.  Multifractal analysis of the metal-insulator transition in anisotropic systems , 1996, cond-mat/9609276.

[12]  Michael Schreiber,et al.  Localization of electronic states in 2D disordered systems , 1992 .

[13]  Galam,et al.  Universal formulas for percolation thresholds. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  A. MacKinnon,et al.  The scaling theory of electrons in disordered solids: Additional numerical results , 1983 .

[15]  M. Schreiber,et al.  Energy-level statistics at the metal-insulator transition in anisotropic systems , 1999, cond-mat/9909210.

[16]  E. Economou,et al.  Existence of Mobility Edges in Anderson's Model for Random Lattices , 1972 .

[17]  Review of recent progress on numerical studies of the Anderson transition , 1999, cond-mat/9911213.

[18]  CRITICAL EXPONENTS FOR THE METAL-INSULATOR-TRANSITION , 1993, cond-mat/9312024.

[19]  C. A. Murray,et al.  Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions , 1979 .

[20]  D. Thouless,et al.  Electrons in disordered systems and the theory of localization , 1974 .

[21]  M. Schreiber,et al.  Critical properties of the metal-insulator transition in anisotropic systems , 1999, cond-mat/9911029.

[22]  E. Haller,et al.  Electrical properties of isotopically enriched neutron-transmutation-doped 70 Ge:Ga near the metal-insulator transition , 1998, cond-mat/9806267.

[23]  J. Pichard,et al.  Finite size scaling approach to Anderson localisation , 1981 .

[24]  David Alan Drabold,et al.  Universal features of localized eigenstates in disordered systems , 2005 .

[25]  C. Pfleiderer,et al.  Critical Behavior of the Conductivity of Si:P at the Metal-Insulator Transition under Uniaxial Stress , 1999, cond-mat/9905297.

[26]  B. Kramer,et al.  Localization: theory and experiment , 1993 .

[27]  Ohtsuki,et al.  Topology dependent quantities at the anderson transition , 2000, Physical review letters.