MIT OpenCourseWare http ocw mit edu 8 512 Theory of Solids II Spring 2009 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 1 Lecture 20 Local Moments in Metals Friedel Sum Rule We ask the question under what condition a given impurity in a metal carries a localized spin A useful result for the discussion of the e ect of an impurity potential on the electronic state is the Friedel sum rule Assuming spherical symmetry the electronic waveunctions are described by the phase shift for angular momentum channel Friedel s sum rule states that the number of electrons added to the system by the impurity Z is given by Z 2 2 1 kF Reading Ziman Theory of Solids Chapter 5 5 Lecture 21 Anderson Model and the Kondo Problem We next consider the situation where the electronic state introduced by the impurity lies inside the conduction band The localized state now becomes a resonance due to the hybridization with the conduction electron This is called the Friedel resonance Ander son introduced a model where the localized state hybridizes with the conduction electron but in addition has an energy cost U for double occupation The model is solved by the Hartree Fock approximation leading to a criteria for the formation of a local moment The interaction of the local moment with the conduction electrons leads to the Kondo problem Reading Kittel Quantum Theory of Solids Chapter 18 p 353
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