CRITICAL SIZE OF SMALL PARTICLES FOR THE DEVELOPMENT OF RESONANCES

It has been often claimed that the formation of a Kondo ground state requires a minimum particle radius of r >> zeta-R = HBAR v(F)/DELTA, where DELTA = k(B)T(K) is the width of the Kondo resonance. We suggest that this minimum size is an artifact of the high symmetry of the sphere for which these calculations have been performed. A similar argument applies to other resonances. This question of minimal size is investigated for a Friedel resonance in two geometries, a sphere and a parallelepiped with a noninteger ratio of its edge lengths. A numerical calculation shows that the minimum linear size of the sample can be much smaller than zeta-R.