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.
We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered metals and give a microscopic derivation of the correlation function of the scalar electric potentials in real space. Starting from the interacting Hamiltonian for electrons in a metal and the random phase approximation, we find a relation between the correlation function of the electric potentials and the density fluctuations which is valid for arbitrary geometry and dimensionality. We show that the potential fluctuations are proportional to the solution of the diffusion equation, taken at zero frequency. As an example, we consider networks of quasi-1D disordered wires and give an explicit expression for the correlation function in a ring attached via arms to absorbing leads. We use this result in order to develop a theory of dephasing by electronic noise in multiply-connected systems.
We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads, where we recently predicted a crossover for the dephasing time τϕ(T ) from diffusive or ergodic 1D (τ −1 ϕ ∝ T 2/3 , T 1 ) to 0D behavior (τ −1 ϕ ∝ T 2 ) as T drops below the Thouless energy E Th . 1 We provide a detailed derivation of our results, based on an influence functional for quantum Nyquist noise, and calculate all leading and subleading terms of the dephasing time in the three regimes. Explicitly taking into account the Pauli blocking of the Fermi sea in the metal allows us to describe the 0D regime on equal footing as the others. The crossover to 0D, predicted by Sivan, Imry and Aronov for 3D systems, 2 has so far eluded experimental observation. We will show that for T E Th , 0D dephasing governs not only the T -dependence for the smooth part of the magnetoconductivity but also for the amplitude of the Altshuler-Aronov-Spivak oscillations, which result only from electron paths winding around the ring. This observation can be exploited to filter out and eliminate contributions to dephasing from trajectories which do not wind around the ring, which may tend to mask the T 2 behavior. Thus, the ring geometry holds promise of finally observing the crossover to 0D experimentally. arXiv:1001.0479v2 [cond-mat.mes-hall]
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