Cooper-pair delocalization in disordered media

Araújo, M. A. N.; Dzierzawa, Michael; Aebischer, C.; Baeriswyl, D.

doi:10.1016/s0921-4526(97)00454-7

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…However, there the studies were mainly addressed to the properties of excited states while here we will investigate only the properties of the ground state in the case of an attractive interaction. We also note that the attractive case in one-dimension was discussed in [22,23].…”

Section: Ground State Properties Without Magnetic Fieldmentioning

confidence: 94%

Phase of biparticle localized states for the Cooper problem in two-dimensional disordered systems

Lages

Shepelyansky

2001

Phys. Rev. B

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Section: Ground State Properties Without Magnetic Fieldmentioning

confidence: 94%

Phase of biparticle localized states for the Cooper problem in two-dimensional disordered systems

Lages

Shepelyansky

2001

Phys. Rev. B

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“…Arau ´jo et al considered the Cooper problem and found that near the ground state an attractive interaction led to delocalization for small disorder while it enhanced localization for large disorder [117].…”

Section: Eigenstatesmentioning

confidence: 99%

Quantum diffusion and scaling of localized interacting electrons

Halfpap

2001

Annalen der Physik

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A new numerical method is introduced that enables a reliable study of disorder‐induced localization of interacting particles. It is based on a quantum mechanical time evolution calculation combined with a finite size scaling analysis. The time evolution of up to four particles in one dimension is studied and localization lengths are defined via the long‐time saturation values of the mean radius, the inverse participation ratio and the center of mass extension. A systematic study of finite size effects using the finite size scaling method is performed in order to extract the localization lengths in the limit of an infinite system size. For a single particle, the well‐known scaling of the localization length λ1 with disorder strength W is observed, λ1 ∝ W—2. For two particles, an interaction‐induced delocalization is found, confirming previous results obtained by numerically calculating matrix elements of the two‐particle Green's function: in the limit of small disorder, the localization length increases with decreasing disorder as λ2 ∝ W—4 and can be much larger than <$>\mitlambda λ1. For three and four particles, delocalization is even stronger. Based on analytical arguments, an upper bound for the n‐particle localization length λn is derived and shown to be in agreement with the numerical data, λn ∝ λ1. Although the localization length increases superexponentially with particle number and can become arbitrarily large for small disorder, it does not diverge for finite λ1 and n. Hence, no extendedstates exist in one dimension, at least for spinless fermions.

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Localization Length in the Cooper Problem With Disorder

Araújo

2001

Int. J. Mod. Phys. B

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We study the localization properties of a bound state of two electrons in the presence of a Fermi sea of normal electrons which are Anderson localized due to disorder. We describe the bound state as in the s-wave Cooper problem. The localization length of the pair depends on its dispersion relation for small momenta relative to the Fermi surface. Expressions for the pair localization length are derived, for both one and two spatial dimensions, in the limit of large single-particle localization length. In one dimensional we find that there is no considerable enhancement of the pair localization length (L c2 ) over that of a single electron (L c ). In two dimensional there is a large enhancement in the limit of large L c . In three dimensional the pair dispersion relation is obtained in both diffusive and (single-particle) localized regimes and the implications on localization are discussed. In this case the mobility edge of the pair is located below the single-electron mobility edge.

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Cooper-pair delocalization in disordered media

Cited by 3 publications

References 17 publications

Phase of biparticle localized states for the Cooper problem in two-dimensional disordered systems

Phase of biparticle localized states for the Cooper problem in two-dimensional disordered systems

Quantum diffusion and scaling of localized interacting electrons

Localization Length in the Cooper Problem With Disorder

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