Critical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities

It is well known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature, these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power-law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo screening is strongly suppressed. When the exchange coupling $J$ is smaller than a certain value $J^{*}$, the metal-insulator transition point extends to a critical region in the disorder strength parameter and to a band of critical states.

Figure 1

The fraction of free magnetic moments $P_{\mathrm{FM}}$ [Eq. (12)] in a three-dimensional disordered electron system as a function of the exchange coupling $J$ (in units of band width $D$) and the disorder strength $W$ (in units of the critical value $W_c^O$). Dashed line: $J_c^A(W)$, Eq. (5), the critical exchange coupling caused by local spectral gaps due to Anderson localization. For $J<J^{*}\approx 0.3D$, there is a critical metal region for $W_c^O<W<W_c(J)$, Eq. (13). Insets: temperature dependence of the local magnetic susceptibility $\chi$ of a single magnetic impurity in the metallic and in the insulating phase, showing Kondo screening and free moment behavior, respectively.