Information Length and Localization in One Dimension

The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical results obtained by assuming an exponential envelope function. A perfect agreement is obtained already for systems of $10^3$--$10^4$ sites over a very wide range of disorder parameter $10^{-4}<W<10^4$. Implications for higher dimensions are also presented.Comment: 11 pages (+3 Figures upon request), Plain TE

Transitions from the Quantum Hall State to the Anderson Insulator: Fa te of Delocalized States

Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon) gauge, the weak magnetic field regime is explored numerically. The regime is closely related to the continuum model. The change of the Hall conductance and the trajectoy of the delocalized states are investigated by the topological arguments and the Thouless number study.Comment: 10 pages RevTeX, 14 postscript figure

Perturbation Study of the Conductance through an Interacting Region Connected to Multi-Mode Leads

We study the effects of electron correlation on transport through an interacting region connected to multi-mode leads based on the perturbation expansion with respect to the inter-electron interaction. At zero temperature the conductance defined in the Kubo formalism can be written in terms of a single-particle Green's function at the Fermi energy, and it can be mapped onto a transmission coefficient of the free quasiparticles described by an effective Hamiltonian. We apply this formulation to a two-dimensional Hubbard model of finite size connected to two noninteracting leads. We calculate the conductance in the electron-hole symmetric case using the order $U^2$ self-energy. The conductance shows several maximums in the $U$ dependence in some parameter regions of $t_y/t_x$, where $t_x$ ($t_y$) is the hopping matrix element in the $x$- ($y$-) directions. This is caused by the resonance occurring in some of the subbands, and is related with the $U$ dependence of the eigenvalues of the effective Hamiltonian.Comment: 17 pages, 12 figures, to be published in J.Phys.Soc.Jpn. 71(2002)No.

The random magnetic flux problem in a quantum wire

The random magnetic flux problem on a lattice and in a quasi one-dimensional (wire) geometry is studied both analytically and numerically. The first two moments of the conductance are obtained analytically. Numerical simulations for the average and variance of the conductance agree with the theory. We find that the center of the band $\epsilon=0$ plays a special role. Away from $\epsilon=0$, transport properties are those of a disordered quantum wire in the standard unitary symmetry class. At the band center $\epsilon=0$, the dependence on the wire length of the conductance departs from the standard unitary symmetry class and is governed by a new universality class, the chiral unitary symmetry class. The most remarkable property of this new universality class is the existence of an even-odd effect in the localized regime: Exponential decay of the average conductance for an even number of channels is replaced by algebraic decay for an odd number of channels.Comment: 16 pages, RevTeX; 9 figures included; to appear in Physical Review

Localization Transition in Multilayered Disordered Systems

The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation expansion, we estimate the mean free paths in the main directions and verify by scaling of the conductance that the states remain extended for any finite $p$, despite the interlayer disorder. In the presence of additional diagonal disorder ($W > 0$) we obtain an Anderson transition with critical disorder $W_c$ and localization length exponent $\nu$ independently of the direction. The critical conductance distribution $P_{c}(g)$ varies, however, for the parallel and the perpendicular directions. The results are discussed in connection to disordered anisotropic materials.Comment: 10 pages, Revtex file, 8 postscript files, minor change

Charge Localization in Disordered Colossal-Magnetoresistance Manganites

The metallic or insulating nature of the paramagnetic phase of the colossal-magnetoresistance manganites is investigated via a double exchange Hamiltonian with diagonal disorder. Mobility edge trajectory is determined with the transfer matrix method. Density of states calculations indicate that random hopping alone is not sufficient to induce Anderson localization at the Fermi level with 20-30% doping. We argue that the metal-insulator transtion is likely due to the formation of localized polarons from nonuniform extended states as the effective band width is reduced by random hoppings and electron-electron interactions.Comment: 4 pages, RevTex. 4 Figures include

Mesoscopic Effects in the Quantum Hall Regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behaviour in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behaviour for strong disorder. This behaviour may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.Comment: 13 pages, 6 figures, Proceedings of the International Meeting on Mesoscopic and Disordered Systems, Bangalore December 2000, to appear in Pramana, February 200

Scaling near the upper critical dimensionality in the localization theory

The phenomenon of upper critical dimensionality d_c2 has been studied from the viewpoint of the scaling concepts. The Thouless number g(L) is not the only essential variable in scale transformations, because there is the second parameter connected with the off-diagonal disorder. The investigation of the resulting two-parameter scaling has revealed two scenarios, and the switching from one to another scenario determines the upper critical dimensionality. The first scenario corresponds to the conventional one-parameter scaling and is characterized by the parameter g(L) invariant under scale transformations when the system is at the critical point. In the second scenario, the Thouless number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation of the Wegner relation s=\nu(d-2) between the critical exponents for conductivity (s) and for localization radius (\nu), which takes the form s=\nu(d_c2-2). The resulting formulas for g(L) are in agreement with the symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous version of Mott's argument concerning localization due topological disorder has been proposed.Comment: PDF, 7 pages, 6 figure

Crossover from the chiral to the standard universality classes in the conductance of a quantum wire with random hopping only

The conductance of a quantum wire with off-diagonal disorder that preserves a sublattice symmetry (the random hopping problem with chiral symmetry) is considered. Transport at the band center is anomalous relative to the standard problem of Anderson localization both in the diffusive and localized regimes. In the diffusive regime, there is no weak-localization correction to the conductance and universal conductance fluctuations are twice as large as in the standard cases. Exponential localization occurs only for an even number of transmission channels in which case the localization length does not depend on whether time-reversal and spin rotation symmetry are present or not. For an odd number of channels the conductance decays algebraically. Upon moving away from the band center transport characteristics undergo a crossover to those of the standard universality classes of Anderson localization. This crossover is calculated in the diffusive regime.Comment: 22 pages, 9 figure

Integer Quantum Hall Effect in Double-Layer Systems

We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models and on transfer matrix calculations for phenomenological network models. The microscopic calculations indicate a crossover regime for weak interlayer tunneling in which the correlation length exponent appears to increase. Comparison of network model calculations with microscopic calculations casts doubt on their generic applicability.Comment: 14 pages, 12 figures included, RevTeX 3.0 and epsf. Additional reference