Distribution of the Kondo Temperature in Mesoscopic Disordered Metals

A local magnetic impurity is known to change the ground state of a Fermi liquid due to correlations created by the exchange interaction between its localised spin and the delocalised electrons. As a result, the magnetic impurity spin is screened at zero temperature by the formation of the Kondo singlet with the conduction electrons. Disorder is affecting the formation of the Kondo singlet in various ways. The distribution of exchange couplings, due to random positioning of the magnetic impurity in the host lattice, directly results in a corresponding distribution of the Kondo temperature 1,2. However, the distribution of LDOS in disordered metals is related nontrivially through an integral equation with the Kondo temperature. In a previous work the distribution of the Kondo temperature (DKT) has been related directly to the distribution of the LDOS at the Fermi energy 3,4. This could have some justification in open systems 5. Here we rather consider a magnetic impurity in a closed, phase coherent metal particle, where the energy levels El are discrete, a Kondo box 6,7. Then, the self consistent equation, determining the Kondo temperature of a magnetic impurity at position r is 8