Open Access

Peter Schwab

• In the presence of a magnetic field, a normal-metal ring carries an equilibrium current, usually called persistent current. In rings where the electron motion is diffusive, several mechanisms which produce a persistent current have been found: A persistent current exists, if the electrons can diffuse around the ring without loosing their phase coherence. However, none of the mechanisms known can explain the amplitude of the currents measured in the experiments. We study the effect of paramagnetic impurities on the persistent current. Magnetic impurities tend to destroy quantum coherence. In weak magnetic fields the persistent current is strongly reduced due to the impurity spin dynamics. Instead there are temporal current fluctuations following the actual spin configuration. By freezing out the spin dynamics in a magnetic field, the amplitude of the typical current, i.e. the current fluctuations, is of the same order as without magnetic impurities. However the mechanism of restoringIn the presence of a magnetic field, a normal-metal ring carries an equilibrium current, usually called persistent current. In rings where the electron motion is diffusive, several mechanisms which produce a persistent current have been found: A persistent current exists, if the electrons can diffuse around the ring without loosing their phase coherence. However, none of the mechanisms known can explain the amplitude of the currents measured in the experiments. We study the effect of paramagnetic impurities on the persistent current. Magnetic impurities tend to destroy quantum coherence. In weak magnetic fields the persistent current is strongly reduced due to the impurity spin dynamics. Instead there are temporal current fluctuations following the actual spin configuration. By freezing out the spin dynamics in a magnetic field, the amplitude of the typical current, i.e. the current fluctuations, is of the same order as without magnetic impurities. However the mechanism of restoring the persistent current works rather badly, and the maximum value for the current is only reached for magnetic fields with a Zeeman energy larger than the spin-flip scattering rate. We discuss the mean current in a model of non-interacting and for weakly interacting electrons, as well as the stochastic current fluctuations. We find qualitatively different behavior of the current as a function of the Zeeman energy in all these cases. For example, the interaction contribution to the mean current is strongly reduced in the presence of magnetic impurities, regardless of whether the impurity spins are polarized or not. If the Thouless energy $E_c$ and the temperature are below the Kondo temperature, the impurity spins are effectively screened, the magnetic impurities scatter like nonmagnetic impurities. None of these mechanisms ever lead to a persistent current which is larger than in the clean limit, i.e.\ without magnetic impurities. Although we cannot explain the large currents observed experimentally, our results for the current as a function of parameters like the impurity concentration, magnetic field and so on, may serve as a test for the applicability of the theoretical concepts (in comparison with future, systematic experiments). In addition we consider quantum corrections to the free energy of the magnetic impurities; due to these corrections we find a contribution to the persistent current which is -- for $1/\tau_s \sim E_ c$ and $T \le E_c$ -- larger than in a theory without magnetic impurities. The current as a function of temperature is of the order $I \sim (E_c^2/\phi_0 T) \cdot \exp( -T/3E_c )$. The current depends crucially on spin-orbit scattering: Without spin-orbit scattering, we find diamagnetic currents, and for strong spin-orbit scattering, we find paramagnetic currents.…