Quantum decoherence of interacting electrons in arrays of quantum dots and diffusive conductors

Abstract

We develop a new unified theoretical approach enabling us to non-perturbatively study the effect of electron-electron interactions on weak localization in arbitrary arrays of quantum dots. Our model embraces (i) weakly disordered conductors (ii) strongly disordered conductors and (iii) metallic quantum dots. In all these cases at T → 0 the electron decoherence time is determined by the universal formula τ ϕ0 ∼ gτ D / ln(E C /δ), where g, τ D , E C and δ are respectively dimensionless conductance, dwell time, charging energy and level spacing of a single dot. In the case (i) this formula yields τ ϕ0 ∝ D 3 / ln D (D is the diffusion coefficient) and matches with our previous quasiclassical results [D.S. Golubev, A.D. Zaikin, Phys. Rev. Lett. 81 (1998) 1074], while in the cases (ii) and (iii) it illustrates new physics not explored earlier. A detailed comparison between our theory and numerous experiments provides an overwhelming evidence that zero temperature electron decoherence in disordered conductors is universally caused by electron-electron interactions rather than by magnetic impurities.

Dephasing of Cooper pairs and subgap electron transport in superconducting hybrids

“…Note that up to an unimportant prefactor of order one, τ ϕ coincides with zero-temperature electron decoherence time evaluated, e.g., for the WL problem. [15][16][17] At this point we emphasize that the agreement between the low-temperature dephasing length scales L ϕ found here for Cooper pairs and previously [15][16][17][18][19] for single electrons is by no means a pure coincidence. Rather, this agreement 144529-3 reflects fundamental and universal nature of low-temperature quantum decoherence caused by electron-electron interactions in various types of disordered conductors.…”

“…We will evaluate Andreev conductance G for NS structures in the presence of electron-electron interactions and demonstrate that in the low-temperature limit, G essentially depends on L ϕ . This dependence allows to directly measure the dephasing length L ϕ in transport experiments with NS hybrids.It is also interesting to point out that the dephasing length L ϕ derived here for NS systems up to a numerical prefactor coincides with zero-temperature decoherence length obtained within totally different theoretical framework [15][16][17][18][19] for a different physical quantity-the so-called weak localization (WL) correction to the normal metal conductance. This agreement demonstrates fundamental nature of low-temperature dephasing by electron-electron interactions, which universally occurs in different types of disordered conductors, including normal-superconducting hybrids.…”

“…At high temperatures, T 1/τ ϕ , the penetration length of Cooper pairs into the N metal is defined by L T , while L ϕ is irrelevant and dephasing is only due to spatially uniform fluctuations described by the first term in Eq. (19). In this case, the results of Ref.…”

“…The remaining terms in Eq. (19) originate from nonuniform in space fluctuations in the N metal and define the scales in our problem-Cooper pair decoherence time τ ϕ = 2πνa 2 √ 2Dτ c and decoherence length L ϕ = Dτ ϕ , where τ c ∼ l/v F sets a short time cutoff [15][16][17] and also τ ϕ τ RC . Note that up to an unimportant prefactor of order one, τ ϕ coincides with zero-temperature electron decoherence time evaluated, e.g., for the WL problem.…”

“…2 and the corresponding discussion above); (iii) already at T = 0 the Cooperon studied here decays differently as compared to the Cooperon in the WL problem, cf., e.g., our Eq. (19) and Eq. (28) in Ref.…”