Nonequilibrium dynamics of the Anderson impurity model

Abstract

The M -channel Anderson impurity model (M = 1, 2) is studied in the Kondo limit with a finite voltage bias applied to the conduction electron reservoirs. Using the Non-Crossing Approximation (NCA), we calculate the local spectral functions, the differential conductance, and susceptibility at non-zero bias for symmetric as well as asymmetric coupling of the impurity to the leads. We describe an effective procedure to solve the NCA integral equations which enables us to reach temperatures far below the Kondo scale. This allows us to study the scaling regime where the conductance depends on the bias only via a scaling function. Our results are applicable to both tunnel junctions and to point contacts. We present a general formula which allows one to go between the two cases of tunnel junctions and point contacts. Comparison is also made between the conformal field theory and the NCA conduction electron self-energies in the two channel case.

The 2-Channel Kondo Model

“…6. When our results are combined with recent numerical results of Hettler et al [12,13], quantitative agreement with the experimental scaling curve is obtained.…”

“…Some of the most recent advances were made by Affleck and Ludwig (AL) (see [10] and references therein), who developed an exact conformal field theory (CFT) solution for the T = 0 fixed point of the multichannel Kondo models. On the experimental front, an experiment performed by two of us (RB) [1,11], that investigated certain zero-bias anomalies (ZBAs) in the conductance of quenched Copper nanoconstrictions, has emerged as a potential experimental realization of the 2-channel Kondo (2CK) model and the corresponding non-Fermi-liquid physics [2,12,13,14]. Although criticisms of the 2CK interpretation [15,16] and alternative mechanisms for the ZBAs have been offered [17,18], the 2CK scenario has recently received important additional suppport from experimental results on ZBAs in constrictions made from Titanium [19] and from metallic glasses [20,21].…”

Universal scaling in transport out of equilibrium through a single quantum dot using the noncrossing approximation

“…It yields an accurate quantitative description of the equilibrium single channel Anderson model down to low temperatures, although it does not capture the correct Fermi-liquid behavior. As an additional advantage of the method, the NCA can be generalized out of equilibrium in a straightforward way [10,13] and it results in a reliable approximation for quantities involving the ρ d (ω) such as the conductance as a function of temperature and bias voltage [14,15]. In the numerical procedure to solve the NCA equations, we have used a set of self-adjusting meshes (rather than the fixed one used in Ref.…”

“…In the numerical procedure to solve the NCA equations, we have used a set of self-adjusting meshes (rather than the fixed one used in Ref. [13]) to describe the spectral densities and lesser Green's functions of the auxiliary particles. The procedure guarantees the resolution of the sets of integral equations for the auxiliary particles self-energies to a high degree of accuracy.…”

Resonance Kondo tunneling through a double quantum dot at finite bias

“…Following the poor man's scaling approach, we derive the system of coupled renormalization group (RG) equations for (7). The equations for LL co-tunneling are: Hatched boxes and circles stand for triplet-triplet and singlettriplet vertices respectively.…”