Quantum oscillations of Kondo screening phases in strong magnetic fields*

We generalize the method of numerical renormalization group to analyze the Kondo effect in strong magnetic fields, where the density of states for itinerary electrons at the chemical potential varies discontinuously as the magnetic field changes. We first examine phases of many-body ground states in the presence of single impurity. By investigating change of $z$-component of total spin, $Delta S_z$, and spin-spin correlation between the impurity and conduction electrons, we find that there are three states competing for the ground state when Zeeman splitting is present. One of the states is doublet in which the impurity spin is unscreened. The other two states are Kondo screening states with $Delta S_z=1/2$ and $Delta S_z=1$, in which the impurity spin is partially screened and completely screened respectively. For Kondo systems with two-impurities in strong magnetic fields, we find that the interplay between the Kondo screening effect, RKKY interaction, and quantum oscillations due to Landau levels determines the ground state of the system. Combination of these three factors results in different screening scenarios for different phases in which spins of two impurities can form spin-0 or spin-1 states, while impurity spins in these phases can be either screened, partially screened, or unscreened by conduction electrons. The emergence of these competing states as the ground state oscillates with the change of magnetic field, chemical potential or inter-impurity distance. This leads to quantum oscillations in magnetization and conductivity. In particular, we find extra peak structures in longitudinal conductivity that reflect changes of Kondo screening phases and are important features to be observed in experiments. Our results provide a complete characterization of phases for Kondo effect in strong magnetic fields.