Electron localization in disordered systems: critical behavior and macroscopic manifestations

Sadovskiǐ, M. V.

doi:10.3367/ufnr.0133.198102b.0223

Cited by 31 publications

(22 citation statements)

References 11 publications

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“…One of the main problems is the qualitative behavior of conductivity when the Fermi level E F crosses the mobility edge E c (at T = 0). While Mott assumed the discontinuous drop of conductivity from σ c to zero 2,3 modern approach [4][5][6]29 based mainly on the scaling theory to localization 31 demonstrates continuous transition. Experiments at low temperatures clearly confirm this type of behavior 6 , and σ c acts as a characteristic conductivity scale close to transition.…”

Section: Anderson Localization and Metal-insulator Transition In mentioning

confidence: 99%

“…For d = 3 this is sometimes refered to as Gotze's 35 law ω 1/3 , although this particular derivation was later acknowledged to be wrong 36 . The spatial dimension d = 2 is the so called "lower critical dimensionality" [4][5][6][7] . For d = 2 all electronic states are localized for infinitesimal disorder 31 , and there is no Anderson transition.…”

Section: Anderson Localization and Metal-insulator Transition In mentioning

confidence: 99%

“…The concept of electron localization 1 is basic for the understanding of electron properties of disordered systems 2,3 . In recent years a number of review papers had appeared, extensively discussing this problem [4][5][6][7] . According to this concept introduction of sufficiently strong disorder into a metallic system leads to spatial localization of electronic states near the Fermi level and thus to a transition to dielectric state (Anderson transition).…”

Section: Introductionmentioning

confidence: 99%

“…Also we believe that better understanding of their properties under disordering may be important for the development of the general theory of high-temperature superconductivity. In recent years a number of review papers had appeared dealing with basic aspects of Anderson localization [4][5][6][7][27][28][29] . Here we shall remind the main points of this theory and introduce the accepted terminology.…”

Section: Introductionmentioning

confidence: 99%

“…We assume that the magnetic field is low enough, so that N 0 ≫ 1, i.e. Scaling description of a system close to Anderson transition can be developed also on the basis of some analogies with usual phase transitions 4,7,6 . Most successful in this respect is an approach initially proposed by Wegner 82-84 .…”

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confidence: 99%

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Superconductivity and localization

1997

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We present a review of theoretical and experimental works on the problem of mutual interplay of Anderson localization and superconductivity in strongly disordered systems. Superconductivity exists close to the metalinsulator transition in some disordered systems such as amorphous metals, superconducting compounds disordered by fast neutron irradiation etc. Hightemperature superconductors are especially interesting from this point of view. Only bulk systems are considered in this review. The superconductor-insulator transition in purely two-dimensional disordered systems is not discussed.We start with brief discussion of modern aspects of localization theory including the basic concept of scaling, self-consistent theory and interaction effects. After that we analyze disorder effects on Cooper pairing and superconducting transition temperature as well as Ginzburg-Landau equations for superconductors which are close to the Anderson transition. A necessary generalization of usual theory of "dirty" superconductors is formulated which allows to analyze anomalies of the main superconducting properties close to disorder-induced metal-insulator transition. Under very rigid conditions superconductivity may persist even in the localized phase (Anderson insulator).Strong disordering leads to considerable reduction of superconducting transition temperature T c and to important anomalies in the behavior of the upper critical field H c2 . Fluctuation effects are also discussed. In the vicinity of Anderson transition inhomogeneous superconductivity appears due to statistical fluctuations of the local density of states.We briefly discuss a number of experiments demonstrating superconductivity close to the Anderson transition both in traditional and high-T c superconductors. In traditional systems superconductivity is in most cases destroyed before metal-insulator transition. In case of high-T c superconductors a number of anomalies show that superconductivity is apparently conserved in the localized phase before it is suppressed by strong enough disorder. The concept of electron localization 1 is basic for the understanding of electron properties of disordered systems 2,3 . In recent years a number of review papers had appeared, extensively discussing this problem [4][5][6][7] . According to this concept introduction of sufficiently strong disorder into a metallic system leads to spatial localization of electronic states near the Fermi level and thus to a transition to dielectric state (Anderson transition). After this transition dc conductivity (at zero temperature, T = 0) vanishes, despite the finite value of electronic density of states at the Fermi level (at least in one-electron approximation).At the same time it is well-known that even the smallest attraction of electrons close to the Fermi level leads to formation of Cooper pairs and the system becomes superconducting at sufficiently low temperatures 8,9 . It is known that the introduction of disorder which does not break the time-reversal invariance (normal, nonm...

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Section: Anderson Localization and Metal-insulator Transition In mentioning

confidence: 99%

Section: Anderson Localization and Metal-insulator Transition In mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Superconductivity and localization

1997

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Localization of Electronic States in Disordered Tight‐Binding Systems. II. Mobility Edges

Unger

1984

Physica Status Solidi (b)

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The model of a "partially disordered semi-infinite chain" for disordered real systems which was obtained from first principles in a foregoing paper is further investigated. The existence of mobilit,y edges in the spectrum is shown if t.hc recursion coefficients tend to constant limiting values. The convergence of t.hc sequence of recursion coefficients is discussed. Interesting relations to the theory of critical phenomena and to the percolation theory lire found. The physical picture behind converging rccursion coefficients, i.c. the existcncc of short-range order, is cleared up. A the0re.tical foundation for the Mott-CFO-niodel is givcn. Within t,he framewrrrk of the recursion method the dependence of the dcgrce of localization on the dimensionality is discussed.

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Calculation of the electronic structure in disordered semiconductors

Shunin¹,

Shvarts

1986

Physica Status Solidi (b)

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Contents1. Theoretical problems of the electronic structure of disordered solids 1.1 From crystals t o amorphous solids 1.2 The tight binding approximation : LCAO 1.3 APW, KKR, and KKPZ methods for electronic states calculations 1.4 The multiple scattering theory and disordered systems 1.5 Potential, pseudopotential, and random field 2. Calculation of the electronic structure of disordered covalent solids b y the cluster model 2.1 The cluster model for disordered solids 2.2 Choice of potentials 2.3 Calculation of the electronic density of states 2.4 Electronic structure of Se, Si, and AS 2.5 Approach to the binary compounds of AszSelPz and AszS1-, type 3. Conclusion References T a b l e 1 Development and evolution of the main theoretical concepts of the electronic and band structures ~ -authors subject date ref.

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Electron localization in disordered systems: critical behavior and macroscopic manifestations

Cited by 31 publications

References 11 publications

Superconductivity and localization

Superconductivity and localization

Localization of Electronic States in Disordered Tight‐Binding Systems. II. Mobility Edges

Calculation of the electronic structure in disordered semiconductors

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