Electric and Magnetic Moments of Small Metallic Particles in the Quantum Size Effect Regime

  • F. Meier
  • P. Wyder


For macroscopic metal samples of the size used in most experiments the periodic boundary conditions are the appropriate ones to use in calculating electronic properties. In a naive free-electron model the energy levels are given by ε n = h 2 π 2 n 2/(2m*L 2), where L is the linear dimension of the system, m* is the effective mass of the electron, and n 2 = n 2 x + n 2 + n 2 y + n 2 z , with the n i integers. The spacing between two neighboring levels at the Fermi energy εF is then given by Δdeg = (h 2π2 n F /m*L 2), with n F = p F Lh (p F is the Fermi momentum). However, if we consider the electron levels of sufficiently minute metallic particles, imperfections in the shape of such particles will remove the artificial degeneracy of the system due to the periodic boundary conditions. Then the average distance between two levels at the Fermi surface is Δ = Δdeg/(4πn 2 F/8), which is, of course, just the inverse of the density of states v at the Fermi surface. In a particle of volume V = L 3 containing N electrons we therefore have for spin degenerate levels
$$\Delta = {v^{ - 1}} = {\pi ^2}{h^3}/V{p_{\text{F}}}{m^*} = \tfrac{4}{3}{\varepsilon _{\text{F}}}/N$$


Periodic Boundary Condition Fermi Surface Fermi Momentum Average Magnetic Moment Small Gold Particle 
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Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • F. Meier
    • 1
  • P. Wyder
    • 1
  1. 1.Fysisch LaboratoriumKatholieke UniversiteitNijmegenThe Netherlands

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