Localization in a strongly disordered system: A perturbation approach

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent is $\nu=1$ in agreement with the Chayes criterion $\nu\ge 1$. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.Comment: 5 pages, no figures. Version accepted for publication on International Journal of Modern Physics

Measurements of conductivity near the metal-insulator critical point

We present measurements of the electrical conductivity at low temperatures of bulk samples of Si:P under uniaxial stress controlled to bring the samples within 0.1% of the metal-insulator transition. As the metal approaches the critical point, we find that the power law of the temperature correction to the conductivity predicted for weak Coulomb interactions continues to fit, but that its sign, size, and range of validity change. Its size defines a diffusion temperature which tends towards zero at the critical density, at which point the power law itself appears to change

Annealed disorder, rare regions, and local moments: A novel mechanism for metal-insulator transitions

Local magnetic moments in disordered sytems can be described in terms of annealed magnetic disorder, in addition to the underlying quenched disorder. It is shown that for noninteracting electron systems at zero temperature, the annealed disorder leads to a new mechanism, and a new universality class, for a metal-insulator transition. The transition is driven by a vanishing of the thermodynamic density susceptibility rather than by localization effects. The critical behavior near two-dimensions is determined, and the underlying physics is discussed.Comment: 4 pp., LaTeX, no figs., final version as publishe

Transport in strongly disordered multiwalled carbon nanotubes

We have studied magnetic field and temperature dependence of electron transport in chemical vapor deposition synthesized highly resistive multiwalled carbon nanotubes. The analysis of the weak-localization magnetoresistance according to electron-electron interaction theories leads to very small mean free paths, l<10 nm. At lowest temperatures the sheet resistance is near RK=h/e exp 2. Both of these observations suggest that our samples are close to the strong-localization limit.Peer reviewe

Tunneling spectroscopy of disordered multiwalled carbon nanotubes

The tunneling density of states has been studied on disordered multiwalled carbon nanotubes. The tunneling conductance shows a large zero-bias anomaly, whose temperature and voltage dependence is successfully compared with the non-perturbative theory of electron tunneling into a disordered 1D electrode. The environmental Coulomb blockade is expected to set in at lower energies, where junctions can be considered to be zero-dimensional. In one of the samples, Coulomb blockade behavior is revealed over a wide range of temperatures. In this sample the tunneling is also studied using a superconducting counterelectrode, and the observed reduction of the conductivity is found to be in quantitative agreement with the theory.Peer reviewe

Critical Scaling of the Conductance in a Disordered Insulator

A critical scaling of the real and imaginary parts of the low-frequency ac conductance of insulating phosphorus-doped silicon near the metal-insulator transition has been observed. The results are interpreted as evidence of an electron glass, i.e., glasslike behavior, intimately connected with the scaling description of the transition, in which Coulomb interactions play a significant role

Stress Tuning of the Metal-Insulator Transition at Millikelvin Temperatures

A high-resolution scan of the metal-insulator transition in Si:P at millikelvin temperatures has been obtained by applying uniaxial stress. A sharp, but continuous, metal-insulator transition is resolved, with conductivities below Mott's "minimum" value σ_M. These measurements join smoothly with previous low-resolution experiments, ruling out any discontinuity at σ_M. The reproducible critical behavior disagrees with predictions of existing scaling theories of localization

Particle-Hole Symmetry and the Effect of Disorder on the Mott-Hubbard Insulator

Recent experiments have emphasized that our understanding of the interplay of electron correlations and randomness in solids is still incomplete. We address this important issue and demonstrate that particle-hole (ph) symmetry plays a crucial role in determining the effects of disorder on the transport and thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that the low-temperature conductivity decreases with increasing disorder when ph-symmetry is preserved, and shows the opposite behavior, i.e. conductivity increases with increasing disorder, when ph-symmetry is broken. The Mott insulating gap is insensitive to weak disorder when there is ph-symmetry, whereas in its absence the gap diminishes with increasing disorder.Comment: 4 pages, 4 figure