M. Ya. Azbel

Quantum oscillations in small rings at low temperatures

The transmission coefficient between two terminals of an effectively one-dimensional (1D) ring with arbitrary scatterers is calculated exactly as a function of enclosed magnetic flux, φ. At low temperatures, where the inelastic diffusion length is larger than the size of the ring, its conductance follows from the Landauer formula. Oscillations of the conductance as a function of the characteristics of the scatterers and of φ are found and results are presented in typical cases, for various parameters. The period of the oscillations in the magnetoresistance is φ0 = hce, though for weak scattering higher harmonics may develop. The oscillations persist even when the elastic scattering is strong. A consequence of this calculation is the inapplicability of the classical addition of resistances in the quantum case. Conditions for the observability of these effects are discussed.

Temperature dependent conductance of one dimensioanal systems

Abstract The eigenstates tunneling theory leads to some unexpected results for the temperature dependence of the conductance G(T). While G(T) sometimes obeys the usual Mott variable range hopping law, it may sometimes be metallic or even non-monotonic. Thus G(T) for a set of quasi-one-dimensional samples connected in parallel should be T independent. The energy dependence of the localization length and of the density of states have unusual effects on G(T) at higher T.

Localization and dimensionality

Abstract Localization of eigenstates depends not only on dimensionality but also on the nature of the disorder. Thus the states in two dimensions may or may not be exponentially localized. Grain boundaries may localize all states in any dimensionality. It is shown that there exists an exact scaling of the transfer matrix, which is valid in any dimensionality.

Impurities in semimetals

Abstract Localization in semimetals and semiconductors strongly depends on the character of disorder. The resistance may decrease when the concentration of vacancies increases, and may be anomalously low for small size substitutions.

Theory of Fluctuation Phenomena in Kinetics

Localization leads to an unusual kind of kinetics. At sufficiently low temperatures transport in a macroscopic system is dominated by a single quenched fluctuation (“flucton”). Kinetic coefficients are unique for each system and exhibit huge oscillations. Even the effective dimensionality of the system may fluctuate. Some manifestations of flucton kinetics are discussed in the paper.