Dimensional crossover of the dephasing time in disordered mesoscopic rings

Abstract

We study dephasing by electron interactions in a small disordered quasi-one-dimensional ͑1D͒ ring weakly coupled to leads. We use an influence functional for quantum Nyquist noise to describe the crossover for the dephasing time ͑T͒ from diffusive or ergodic 1D ͑ −1 ϰ T 2/3 , T 1 ͒ to zero-dimensional ͑0D͒ behavior ͑ −1 ϰ T 2 ͒ as T drops below the Thouless energy. The crossover to 0D, predicted earlier for two-dimensional and three-dimensional systems, has so far eluded experimental observation. The ring geometry holds promise of meeting this long-standing challenge, since the crossover manifests itself not only in the smooth part of the magnetoconductivity but also in the amplitude of Altshuler-Aronov-Spivak oscillations. This allows signatures of dephasing in the ring to be cleanly extracted by filtering out those of the leads.

Dephasing by a Zero-Temperature Detector and the Friedel Sum Rule

“…À for the applicability of Eq. (12). We have argued that passage of an interfering electron transforms the Slater determinant of ji into a Slater determinant of j i.…”

“…Standard detection schemes involve an out-of-equilibrium detector, e.g., a currentcarrying quantum point contact, electrostatically coupled to the interferometer. Dephasing is directly related to entanglement between the state of the system and that of the detector [6] and has been observed [7,8] and discussed [9][10][11][12][13] in the context of electronic interferometers. Special features arise when the system-detector coupling is strong [14][15][16].…”

“…It is known that coupling to a dissipative environment may give rise to dephasing through thermal fluctuations [10][11][12][13]17,18]. It may also give rise to a change of the ground state [19] through an Anderson orthogonality catastrophe mechanism [5,20,21].…”

Quantum corrections to the polarizability and dephasing in isolated disordered metals

“…It is in sharp contrast to the quantum corrections to the conductivity, which always saturate at γ ∆. 4,31 Let us illustrate our unexpected statement with the help of Fig. 8: We know the exact value of ∆α in the limit γ → 0 from the RMT+σ-model and the correct behavior of ∆α for γ being of order of (and slightly below) ∆.…”

“…The theory predicts a 0D dephasing rate, γ 0D = a∆T 2 /E 2 Th , 3 at low temperatures and an ergodic dephasing rate, γ erg = b∆T /E Th , 33,34 at higher temperatures, where a and b are system-specific, dimensionless coefficients of order ∼ 1, see Ref. [31] and [35]. The crossover between the two regimes occurs at a temperature T cross = b a E Th .…”