Dimensional Crossover of the Dephasing Time in Disordered Mesoscopic Rings: From Diffusive through Ergodic to 0D Behavior

Abstract

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]

Thermal noise and dephasing due to electron interactions in nontrivial geometries

“…1, including connected rings and grids. 3,4 It has been found (both experimentally 5 and theoretically [6][7][8][9][10] ) that dephasing depends not only on the dimensionality, but also on the geometry of the system. The noise correlation function is well-understood for macroscopically homogeneous systems such as infinite wires or isolated rings, but has sofar not been studied in multiply-connected networks with leads attached at arbitrary points.…”

Transport and dephasing in a quantum dot: Multiply connected graph model

“…One possibility to improve the effective precision of the measurements is related to extracting τ ϕ from the T -dependence of the Aronov-Altshuler-Spivak oscillations of the magnetoconductivity in almost closed mesoscopic rings. This option was discussed in recent papers [6,22] where all effects of the environment were taken into account via a constant dwelling time. We plan to study in more detail the sensitivity of the AAS oscillations on the distortions from the environment using a ring model similar to the model of the dot presented here [23].…”

“…4(a) for several values of the origin of the Cooperon, x 0 , which can belong either to the central region (solid blue lines) or the contact (dashed red lines). To check the validity of the results, we compare τ ϕ at high and small temperatures with earlier results for an almost isolated quasi-1D ring of total length 4L and total conductance g 1 [22].…”

“…In the ring, the high-T regime appears at T g 1 E Th . The formula for τ ϕ in this regime, including sub-leading terms, reads [22]:…”

“…The geometry of the system is not important in this case and, therefore, the low-T regime is usually referred to as the regime of 0D dephasing. In the ring, it occurs at T E Th with τ ϕ given by [22] τ ϕ…”