Universal dephasing rate due to diluted Kondo impurities

TL;DR

This paper derives a universal formula for the dephasing rate caused by magnetic impurities in disordered metals, showing it depends on impurity density and the Kondo temperature, with results obtained via numerical renormalization group methods.

Contribution

It provides a universal expression for the dephasing rate due to magnetic impurities, incorporating inelastic scattering effects and using exact numerical solutions for the T-matrix.

Findings

Dephasing rate is a universal function of impurity density and temperature.

Inelastic vertex corrections are suppressed at low energy transfers.

The T-matrix is computed exactly using numerical renormalization group.

Abstract

We calculate the dephasing rate due to magnetic impurities in a weakly disordered metal as measured in a weak localization experiment. If the density n_S of magnetic impurities is sufficiently low, the dephasing rate 1/tau_phi is a universal function, 1/tau_phi = (n_S/nu) f(T/T_K), where T_K is the Kondo temperature and nu the density of states. We show that inelastic vertex corrections with a typical energy transfer Delta E are suppressed by powers of 1/(tau_phi Delta E) proportional to n_S. Therefore the dephasing rate can be calculated from the inelastic cross section proportional to pi nu Im T- |pi nu T|^2, where T is the T-matrix which is evaluated numerically exactly using the numerical renormalization group.