Structure of Superconductors with Dilute Magnetic Impurities

  • Reiner Kümmel


We consider a superconductor with magnetic impurities so dilute that they can be regarded as being completely isolated. Then it is sufficient to discuss a system with one impurity at the origin. The Hamiltonian of this system can be diagonalized by defining new wave field operators Ψp(r, t) and Ψ p (r, t) for particles with a new quantum number p from the ordinary electron field operators Ψ(r, t) and Ψ(r, t):
$${{\psi }_{1,2}}\left( r,t \right)={{\left( {{C}_{1,2}}-{{C}_{2,1}} \right)}^{-1/2}}\left( {{\psi }_{\uparrow }}+{{C}_{1,2}}{{\psi }_{\downarrow }} \right)$$
$$\psi _{1,2}^{\dagger }\left( r,t \right)={{\left( {{C}_{1,2}}-{{C}_{2,1}} \right)}^{-1/2}}\left( \psi _{\downarrow }^{\dagger }-{{C}_{2,1}}\psi _{\uparrow }^{\dagger } \right)$$
$${{C}_{1,2}}={{\left( {{S}_{x}}+i{{S}_{Y}} \right)}^{-1}}\left( -{{S}_{z}}\pm \sqrt{{{S}^{2}}} \right)$$
p is called the “paraspin” and has the values 1 and 2. S = (S x , S y , S z ) is the impurity spin, the operator character of which is neglected.


Fermi Surface Pair Potential Vortex Line Magnetic Impurity Impurity Spin 
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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • Reiner Kümmel
    • 1
  1. 1.Departamento de FísicaUniversidad del ValleCaliColombia

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