h/2eOscillations for Correlated Electron Pairs in Disordered Mesoscopic Rings

Abstract

The full spectrum of two interacting electrons in a disordered mesoscopic one{dimensional ring threaded by a magnetic ux is calculated numerically. For ring sizes far exceeding the one{particle localization length L1 we nd several h=2e{periodic states whose eigenfunctions exhibit a pairing e ect. This represents the rst direct observation of interaction{assisted coherent pair propagation, the pair being delocalized on the scale of the whole ring.PACS numbers: 72.15, 73.20 For more than three decades Anderson localization has been a subject of intensive research (for a review see 1]). Among the rst results in this eld was the fact that noninteracting electrons in one dimension (1d) are always localized and that their wave{functions decay exponentially on the scale of the localization length L 1 . Very recently, Shepelyansky 2] and later Imry 3] considered two interacting electrons in a 1d random potential. Both authors suggest that in a regime of not too strong disorder correlated electron pair states may extend over a distance L 2 / L 2 1 much larger than L 1 . This completely novel e ect could very well have a fundamental impact on our understanding of the localization problem and other related areas. However, the methods employed in 2,3], though powerful and suggestive, are partly approximate and partly qualitative. Shepelyansky's original reasoning relied on certain assumptions of a statistical nature, allowing him to map the problem onto a random band matrix model. A numerical study of this model together with additional evidence from a variety of other models formed the basis for his claim. Imry, on the other hand, invoked the Thouless scaling block picture to arrive at precisely the same results as Shepelyansky. Moreover, Imry's approach seems to be very suitable to generalize the e ect to higher dimensions.The key quantity in 2,3] was the distribution of interaction matrix elements in the disorder{diagonal basis. This distribution de nes the statistical properties of the band matrix model and provides the interblock coupling in the scaling approach. In a recent study 4] employing the transfer matrix technique we investigated numerically both nite and in nite systems starting from rst principles. In this work, the principal e ect was con rmed, but the two{particle localization length L 2 was found to scale with a smaller exponent, L 2 / L 1:65 1 , in the parameter range investigated. This modi cation could be attributed to particular properties of the above{mentioned distribution which had not been taken into account in 2,3].In the present paper, we demonstrate the existence of h=2e{periodic states in the spectrum of a disordered mesoscopic ring with two interacting electrons by direct diagonalization. Inspection of the two{electron eigenfunctions reveals that this period halving is indeed due to a pairing e ect: Both electrons propagate coherently around the ring, staying within a distance of a few L 1 from each other. This is the rst direct observation of interaction{assisted coherent pair propagation ...

Sparse-random-matrix configurations for two or three interacting electrons in a random potential

“…This conclusion was confirmed and extended to higher dimensions via Thouless block scaling picture by Imry [2]. The subsequent numerical studies [3,4,5,6,7,8,9,10] verified the main qualitative results concerning the presence of Shepelyansky states, mostly by supressing single particle transport via efficient Green function or bag model methods which examine pair propagation [8].The deviations from the predicted behavior of the two-particle localization length ξ found were usually attributed to the oversimplified statistical assumptions concerning the band random matrix model of the original Shepelyansky construction.However, there is an ongoing debate whether coherent pair propagation actually exists for two interacting electrons in infinite disordered systems [11,12], which began by a recent transfer matrix study where no propagation enhancement is found at E = 0 for an infinite chain [11]. Moreover, it was pointed out that the reduction to a SBRM relies on questionable assumptions regarding chaoticity of the non-interacting electron localized states within ξ 1 , so that the relevant matrix model could be prob-2 ably different [13,14].…”

“…This conclusion was confirmed and extended to higher dimensions via Thouless block scaling picture by Imry [2]. The subsequent numerical studies [3,4,5,6,7,8,9,10] verified the main qualitative results concerning the presence of Shepelyansky states, mostly by supressing single particle transport via efficient Green function or bag model methods which examine pair propagation [8].…”

Chaotic delocalization of two interacting particles in the classical Harper model

“…It is possible that the semiclassical description can work even at moderate values of n q ∼ 3 but a detailed analysis of semiclassical description of such cases is required. The quantum interference effects may lead to the quantum localization of chaon diffusion in a similar way as for the Anderson localization of TIP in 1D and 2D (see discussions for TIP in disordered potential in [14,15,16,21]). However, in the care of quasiperiodic potential, appearing for irrational values, the situation is rather nontrivial as show the results of subdiffusive spreading for TIP in the 2D quantum Harper model [26].…”

“…Further studies also found enhancement of localization effects in presence of interactions [12,13]. This localization enhancement is opposite to the TIP effect in disordered systems where the interactions increase the TIP localization length in 1D [14,15,16,17,18,20,23] or even lead to delocalization of TIP pairs for dimensions d ≥ 2 [19,21,22]. Thus interactions between two particles in systems with disorder can even destroy the Anderson localization existing for noninteracting particles.…”

Mesoskopische Systeme mit Wechselwirkung und Unordnung: Erhöht die Coulomb‐Wechselwirkung die Leitfähigkeit ungeordneter Festkörper?

“…Die Unordnung ist so gewählt, dass die Einteilchen-Lokalisierungslänge L 1 Ϸ Ϸ 11 viel kleiner ist als der Umfang L = 100 des Rings [8]. Man erkennt deutlich, dass die Wellenfunktion entlang der Diagonalen (die der Schwerpunktsachse entspricht) ausgedehnt ist.…”