Superconductivity and localization

Abstract

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...

DMFT+Σ approach to disordered hubbard model

“…In particular, the behavior of coefficient C is qualitatively changed at Anderson localization transition [41]. Thus, the coefficient C is basically determined by two -particle charateristics of the system and does not demopnstrate the universal dependence on disorder due only to changes of the effective bandwidth.…”

“…Cooper instability, determining T c is related to divergence of two -particle loop in Cooper channel. In the weak coupling limit, when superconductivity is due to the appearance of Cooper pairs at T c , disorder only slightly influences superconductivity with s-wave pairing [41,42]. This is the essence of the so called Anderson theorem and changes of T c are due only to the relatively small changes of the density of states at the Fermi level induced by disorder.…”

Superconductivity in the system MoxCyGazOδ prepared by focused ion beam induced deposition

“…However, in using this amorphous superconductor an important issue has not been adequately addressed, namely the high degree of structural disorder of this material which puts it close to a disorder-induced metal-insulator or Anderson transition 6 . This has severe consequences with regard to various key quantities of the superconducting state, such as the dependence of the critical temperature, T c , on the degree of disorder and the growing importance of statistical fluctuations of the superconducting order parameter leading to a spatial variation of the critical temperature T c (r) 7 . In this case the usability of such a superconductor is severely limited.…”

“…For these samples the self-averaging of the superconducting order parameter over the complete sample volume is not complete any more. Very close to the critical resistivity value statistical fluctuations of the order parameter can lead to a spatial inhomogeneity of the critical temperature T c (r) which becomes apparent as appreciably broadened or multi-step transitions 7 . The R(T )-curves furthermore exhibit a pronounced rounding already far above the actual superconducting onset which we consider as a signature of the broadened critical region above T c in which fluctuational Cooper pair formation occurs and which is quite typical for disordered systems 7,10 .…”

Self-consistent theory of localization and Coulomb drag effect

“…The interaction effects on the Anderson transition in disordered systems have been discussed by Sadovskii. 29 In summary, we have considered the Coulomb drag effect between two parallel quantum wells in the presence of disorder treated phenomenologically. The temperature dependence of the drag rate is known to be significantly enhanced with increasing disorder as the system evolves from a metallic state toward an insulating state.…”