Anderson localization problems in gapless superconducting phases

Oppermann, R.H.

doi:10.1016/0378-4371(90)90061-v

Cited by 46 publications

(44 citation statements)

References 13 publications

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“…We begin with perturbation theory at weak coupling, that is largeκ xx . This was considered previously for classes C and CI [51,53], and for class D is mentioned in Ref. [54].…”

Section: Effects Of Disorder On the Transitionsmentioning

confidence: 99%

“…The case of spin-singlet paired states with disorder was considered in more detail [51,53,54]. The symme- try classes are CI (with time reversal symmetry), and C (without time reversal).…”

Section: Effects Of Disorder On the Transitionsmentioning

confidence: 99%

“…We also consider disorder within the same approximation, making use of recent results on noninteracting BCS quasiparticles with disorder [51][52][53][54][55][56][57][58], and in particular we find that in the spinless p-wave case, there can be an intermediate phase with the thermal properties of a metal, between the two localized phases which correspond to the weak (MR) and strong-pairing phases of the pure case. A disordered version of the MR phase still exists in the presence of disorder, though its properties, including nonabelian statistics, may become more subtle.…”

Section: Introductionmentioning

confidence: 99%

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Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect

2000

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We analyze pairing of fermions in two dimensions for fully-gapped cases with broken parity (P) and time-reversal (T), especially cases in which the gap function is an orbital angular momentum (l) eigenstate, in particular l = −1 (p-wave, spinless or spin-triplet) and l = −2 (d-wave, spinsinglet). For l = 0, these fall into two phases, weak and strong pairing, which may be distinguished topologically. In the cases with conserved spin, we derive explicitly the Hall conductivity for spin as the corresponding topological invariant. For the spinless p-wave case, the weak-pairing phase has a pair wavefunction that is asympototically the same as that in the Moore-Read (Pfaffian) quantum Hall state, and we argue that its other properties (edge states, quasihole and toroidal ground states) are also the same, indicating that nonabelian statistics is a generic property of such a paired phase. The strong-pairing phase is an abelian state, and the transition between the two phases involves a bulk Majorana fermion, the mass of which changes sign at the transition. For the d-wave case, we argue that the Haldane-Rezayi state is not the generic behavior of a phase but describes the asymptotics at the critical point between weak and strong pairing, and has gapless fermion excitations in the bulk. In this case the weak-pairing phase is an abelian phase which has been considered previously. In the p-wave case with an unbroken U(1) symmetry, which can be applied to the double layer quantum Hall problem, the weak-pairing phase has the properties of the 331 state, and with nonzero tunneling there is a transition to the Moore-Read phase. The effects of disorder on noninteracting quasiparticles are considered. The gapped phases survive, but there is an intermediate thermally-conducting phase in the spinless p-wave case, in which the quasiparticles are extended.

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“…We begin with perturbation theory at weak coupling, that is largeκ xx . This was considered previously for classes C and CI [51,53], and for class D is mentioned in Ref. [54].…”

Section: Effects Of Disorder On the Transitionsmentioning

confidence: 99%

“…The case of spin-singlet paired states with disorder was considered in more detail [51,53,54]. The symme- try classes are CI (with time reversal symmetry), and C (without time reversal).…”

Section: Effects Of Disorder On the Transitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect

2000

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“…First attempts to explore this peculiar situation were undertaken in Refs. [166][167][168][169] . These results are easily generalized for the case of strongly anisotropic quasi-twodimensional systems such as high-T c superconducting oxides.…”

Section: General Analysismentioning

confidence: 99%

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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“…Here I mention only a few: The complete classification of ten symmetry classes of random matrix theories, σ-models, and Cartan's symmetric spaces was given by Zirnbauer and Altland [24,25] and by Schnyder, Ryu, Furusaki, and Ludwig [26] after several occurences of chiral and Bogolubov-de Gennes classes [27,28,29,30,31,32,33,34]. These classes are listed in table 1 since I will refer later to this nomenclature.…”

Section: Inhomogeneous Fixed Point Ensemble (Ihfpe)mentioning

confidence: 99%

Inhomogeneous Fixed Point Ensembles Revisited

Wegner¹

2010

50 Years of Anderson Localization

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The density of states of disordered systems in the Wigner-Dyson classes approaches some finite non-zero value at the mobility edge, whereas the density of states in systems of the chiral and Bogolubov-de Gennes classes shows a divergent or vanishing behavior in the band centre. Such types of behavior were classified as homogeneous and inhomogeneous fixed point ensembles within a real-space renormalization group approach. For the latter ensembles the scaling law µ = dν − 1 was derived for the power laws of the density of states ρ ∝ |E| µ and of the localization length ξ ∝ |E| −ν . This prediction from 1976 is checked against explicit results obtained meanwhile.

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Anderson localization problems in gapless superconducting phases

Cited by 46 publications

References 13 publications

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect

Superconductivity and localization

Inhomogeneous Fixed Point Ensembles Revisited

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