Conductance of closed and open long Aharonov-Bohm-Kondo rings

Abstract

We calculate the finite temperature linear DC conductance of a generic single-impurity Anderson model containing an arbitrary number of Fermi liquid leads, and apply the formalism to closed and open long Aharonov-Bohm-Kondo (ABK) rings. We show that, as with the short ABK ring, there is a contribution to the conductance from the connected 4-point Green's function of the conduction electrons. At sufficiently low temperatures this contribution can be eliminated, and the conductance can be expressed as a linear function of the T-matrix of the screening channel. For closed rings we show that at temperatures high compared to the Kondo temperature, the conductance behaves differently for temperatures above and below $v_F/L$ where $v_F$ is the Fermi velocity and $L$ is the circumference of the ring. For open rings, when the ring arms have both a small transmission and a small reflection, we show from the microscopic model that the ring behaves like a two-path interferometer, and that the Kondo temperature is unaffected by details of the ring. Our findings confirm that ABK rings are potentially useful in the detection of the size of the Kondo screening cloud, the $\pi /2$ scattering phase shift from the Kondo singlet, and the suppression of Aharonov-Bohm oscillations due to inelastic scattering.

arXiv comment52 pages, 14 figures; v2; discussion added on particle-hole symmetric dot for the open long ring

References in corpus (51)

• Fano resonances in nanoscale structures
• Kondo Physics in a Single Electron Transistor
• Time-dependent transport in interacting and non-interacting mesoscopic systems
• A Tunable Kondo Effect in Quantum Dots
• Renormalization Group Approach to Interacting Fermions
• The Kondo Effect in the Unitary Limit
• Observation of the two-channel Kondo effect
• Kondo Correlations and the Fano Effect in Closed AB-Interferometers
• Kondo effect in quantum dots
• Phase Evolution in a Kondo Correlated System
• Anomalous Kondo-effect in Quantum Dot at non-zero bias
• Detecting the Kondo screening cloud around a quantum dot
• The Kondo Box: A Magnetic Impurity in an Ultrasmall Metallic Grain
• Crossover from mesoscopic to universal phase for electron transmission in quantum dots
• Transmission Phase of a Quantum Dot with Kondo Correlation Near the Unitary Limit
• Transmission Phase Shift of a Quantum Dot with Kondo Correlations
• Phase transitions in the pseudogap Anderson and Kondo models: Critical dimensions, renormalization group, and local-moment criticality
• Aharonov-Bohm oscillations and resonant tunneling in strongly correlated quantum dots
• Kondo effect induced by a magnetic field
• On the applicability of the equations-of-motion technique for quantum dots
• Which phase is measured in the mesoscopic Aharonov-Bohm interferometer?
• Detecting the Kondo screening cloud in conductance measurements on quantum dots
• Friedel oscillations and the Kondo screening cloud
• Upper-critical dimension in a quantum impurity model: Critical theory of the asymmetric pseudogap Kondo problem
• Dephasing by extremely dilute magnetic impurities revealed by Aharonov-Bohm oscillations
• Theory of inelastic scattering from magnetic impurities
• Kondo screening cloud effects in mesoscopic devices
• Bosonization and Scale Invariance on Quantum Wires
• Universal dephasing rate due to diluted Kondo impurities
• Persistent currents through a quantum dot
• Theory of inelastic scattering from quantum impurities
• Kondo impurities in nanoscopic systems: new confinement-induced regimes
• Transmission Phase in the Kondo Regime Revealed in a Two-Path Interferometer
• Kondo effect in complex mesoscopic structures
• Transmission phase of a singly occupied quantum dot in the Kondo regime
• How to directly measure a Kondo cloud's length
• Transport through quantum dots in mesoscopic circuits
• Spectroscopy of the Kondo Problem in a Box
• Flux-dependent Kondo temperature in an Aharonov-Bohm interferometer with an in-line quantum dot
• Kondo screening cloud and the charge staircase in one-dimensional mesoscopic devices
• The Enhanced Sensitivity of the Transmission Phase of a Quantum Dot to Kondo Correlations
• Measuring the Kondo effect in the Aharonov-Bohm interferometer
• Mesoscopic Kondo Problem
• Transport Spectroscopy of a Kondo quantum dot coupled to a finite size grain
• The Influence of Interference on the Kondo Effect in a Quantum Dot
• Transport through a multiply connected interacting meso-system using the Keldysh formalism
• Scaling analysis of Kondo screening cloud in a mesoscopic ring with an embedded quantum dot
• Transmission phase shifts of Kondo impurities
• Mesoscopic Anderson Box: Connecting Weak to Strong Coupling
• Interaction effects in Aharonov-Bohm-Kondo Rings
• From Weak- to Strong-Coupling Mesoscopic Fermi Liquids

Cited by in corpus (1)

• Fano-Kondo resonance versus Kondo plateau in an Aharonov-Bohm ring with an embedded quantum dot