The scaling theory of electrons in disordered solids: Additional numerical results

We present extensive numerical results applying the finite size scaling method to the theory of electrons in disordered systems. A method is developed for studying the localisation length in 1-dimensional systems of finite cross section. By studying these results as a function of cross-section and using scaling ideas, we derive the critical properties of 2-D and 3-D systems. We calculate transport properties as a function of temperature which can then be compared with experiment.

[1]  L. Gor’kov,et al.  Particle Conductivity in a Two-Dimensional Random Potential - JETP Lett. 30, 228 (1979) , 1979 .

[2]  E. N. Economou,et al.  Study of electronic states with off-diagonal disorder in two dimensions , 1982 .

[3]  D. Thouless,et al.  Numerical studies of localization in disordered systems , 1972 .

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

[5]  A. Mackinnon,et al.  MacKinnon and Kramer Respond , 1982 .

[6]  J. Pendry.  The evolution of waves in disordered media , 1982 .

[7]  G. Deutscher,et al.  Two-Dimensional Localization in Thin Copper Films , 1981 .

[8]  D. Weaire,et al.  Numerical study of conductivity for the Anderson model in two and three dimensions , 1981 .

[9]  D. Tsui,et al.  Nonmetallic Conduction in Electron Inversion Layers at Low Temperatures , 1980 .

[10]  J. Sak,et al.  Transmission of particles through a random one-dimensional potential , 1981 .

[11]  H. Fukuyama,et al.  Self-Consistent Treatment of Two-Dimensional Anderson Localization in Magnetic Fields , 1981 .

[12]  Daniel S. Fisher,et al.  Anderson Localization in Two Dimensions , 1981 .

[13]  Philip W. Anderson,et al.  New method for a scaling theory of localization , 1980 .

[14]  A. Mackinnon.  The conductivity of the one-dimensional disordered Anderson model: a new numerical method , 1980 .

[15]  D. Vollhardt,et al.  Diagrammatic, self-consistent treatment of the Anderson localization problem in d<=2 dimensions , 1980 .

[16]  Boris L. Altshuler,et al.  Interaction Effects in Disordered Fermi Systems in Two Dimensions , 1980 .

[17]  R. Markiewicz,et al.  Two-Dimensional Resistivity of Ultrathin Metal Films , 1981 .

[18]  S. Hikami.  Anderson Localization in Nonlinear σ Model Representation , 1981 .

[19]  M. Pepper,et al.  Logarithmic and power law corrections in two-dimensional electronic transport , 1982 .

[20]  D. Weaire,et al.  Numerical methods for electronic properties of disordered solids , 1980 .

[21]  G. Landwehr.  Application of high magnetic fields in semiconductor physics : proceedings of the international conference held in Grenoble, France, September 13-17, 1982 , 1983 .

[22]  R. Stinchcombe,et al.  A renormalisation group approach to a quantum spin system , 1979 .

[23]  I. Morgenstern,et al.  Two-dimensional Ising model in random magnetic fields , 1981 .

[24]  D. Osheroff,et al.  Nonmetallic Conduction in Thin Metal Films at Low Temperatures , 1979 .

[25]  M. Nightingale.  Non-universality for ising-like spin systems , 1977 .

[26]  D. Thouless.  The effect of inelastic electron scattering on the conductivity of very thin wires , 1980 .

[27]  D. Thouless,et al.  Maximum metallic resistance in thin wires , 1977 .

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

[29]  P. Prelovšek.  Diffusion in the Anderson model of a disordered system: A numerical study , 1978 .

[30]  G. Bergmann.  Inelastic life-time of the conduction electrons in some noble metal films , 1982 .

[31]  P. Prelovšek.  Conductor-insulator transition in the Anderson model of a disordered solid , 1981 .

[32]  G. Czycholl,et al.  Conductivity and localization of electron states in one dimensional disordered systems: Further numerical results , 1981 .

[33]  N. Mott,et al.  The conductivity of disordered systems and the scaling theory , 1981 .

[34]  C. Hamer,et al.  Finite-lattice methods in quantum Hamiltonian field theory. I. O(2) and O(3) Heisenberg models , 1981 .

[35]  E. Abrahams,et al.  Resistance fluctuations in disordered one-dimensional conductors , 1980 .

[36]  R. Landauer.  Electrical resistance of disordered one-dimensional lattices , 1970 .

[37]  D. Vollhardt,et al.  Scaling Equations from a Self-Consistent Theory of Anderson Localization , 1982 .

[38]  V. Prigodin,et al.  Localization in a Random System of N Coupled Chains I. Microscopic Model, General Scheme , 1982 .

[39]  Sayaka Yoshino,et al.  Numerical Study of Electron Localization in Anderson Model for Disordered Systems: Spatial Extension of Wavefunction , 1977 .

[40]  A. MacKinnon,et al.  One-Parameter Scaling of Localization Length and Conductance in Disordered Systems , 1981 .

[41]  D. Thouless,et al.  Conductivity and mobility edges for two-dimensional disordered systems , 1975 .

[42]  A. Abrikosov,et al.  Conductivity of quasi-one-dimensional metal systems , 1978 .

[43]  S. Hikami,et al.  Anderson localization in a nonlinear-sigma-model representation , 1981 .

[44]  P. Lee.  Real-Space Scaling Studies of Localization , 1979 .

[45]  Paul Erdös,et al.  Theories of electrons in one-dimensional disordered systems , 1982 .

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

[47]  M. Pepper,et al.  The transition from two- to one-dimensional electronic transport in narrow silicon accumulation layers , 1982 .

[48]  A. Larkin,et al.  Magnetoresistance and Hall effect in a disordered two-dimensional electron gas , 1980 .

[49]  G. Czycholl,et al.  Numerical investigation of the conductivity and electron localization of a one dimensional disordered system , 1980 .

[50]  Scott Kirkpatrick,et al.  Conductivity of the disordered linear chain , 1981 .

[51]  Scaling theory of Anderson localization: A renormalization group approach , 1981 .

[52]  Wave functions in disordered systems , 1981 .