Percolation, quantum tunnelling and the integer Hall effect

A model is introduced for Anderson localisation in the integer quantum Hall regime. The model represents a system with a disordered potential that varies slowly on the scale of the magnetic length, but includes quantum tunnelling and interference effects. Numerical calculations indicate that the localisation length diverges only at the centre of each Landau band. The scaling behaviour near the mobility edge is analysed: results suggest that quantum tunnelling induces crossover at the classical percolation threshold to critical behaviour similar to that found previously for a rapidly varying potential.

[1]  An exact effective Hamiltonian for a perturbed Landau level , 1987 .

[2]  K. Klitzing.  The quantized Hall effect , 1986 .

[3]  Fisher,et al.  Finite-size scaling and correlation lengths for disordered systems. , 1986, Physical review letters.

[4]  A. Pippard.  Quantization of coupled orbits in metals II. The two-dimensional network, with special reference to the properties of zinc , 1964, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  M. Tsukada.  On the Tail States of the Landau Subbands in MOS Structures under Strong Magnetic Field , 1976 .

[6]  S. Luryi,et al.  Quantum percolation and quantization of Hall resistance in two-dimensional electron gas , 1982 .

[7]  F. Wegner.  Electrons in disordered systems. Scaling near the mobility edge , 1976 .

[8]  G. Dorda,et al.  New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance , 1980 .

[9]  I. Affleck.  Exact critical exponents for quantum spin chains, non-linear σ-models at θ=π and the quantum hall effect , 1986 .

[10]  J. Chalker.  Scaling and correlations at a mobility edge in two dimensions , 1988 .

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

[12]  S. Iordansky.  On the conductivity of two dimensional electrons in a strong magnetic field , 1982 .

[13]  S. Hikami.  Localization Length and Inverse Participation Ratio of Two Dimensional Electron in the Quantized Hall Effect , 1986 .

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

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

[16]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory , 1980 .

[17]  P. Anderson.  New method for scaling theory of localization. II. Multichannel theory of a , 1981 .

[18]  S. Libby,et al.  Electron delocalization by a magnetic field in two dimensions , 1983 .

[19]  Tsui,et al.  Localization and scaling in the quantum Hall regime. , 1986, Physical review. B, Condensed matter.

[20]  Aoki,et al.  Critical localization in two-dimensional Landau quantization. , 1985, Physical review letters.

[21]  A. Mackinnon,et al.  Magnetic field and electron states in two-dimensional disordered systems , 1984 .

[22]  Romo,et al.  e+e---> gamma + missing neutrals: Neutrino versus photino production. , 1986, Physical review. D, Particles and fields.

[23]  H. Kunz,et al.  The conductance of a disordered wire , 1983 .

[24]  B. Shapiro,et al.  Renormalization-Group Transformation for the Anderson Transition , 1982 .

[25]  J. Pichard,et al.  Finite-size scaling approach to Anderson localisation. II. Quantitative analysis and new results , 1981 .

[26]  S. Trugman.  Localization, percolation, and the quantum Hall effect , 1983 .

[27]  R. Joynt,et al.  Conduction in a strong field in two dimensions: The quantum Hall effect , 1982 .

[28]  J. Chalker.  Anderson localisation in quantum Hall systems , 1987 .

[29]  J. Cardy,et al.  Conformal invariance and universality in finite-size scaling , 1984 .