Size effect in Landau diamagnetism

The effect of the surface potential on the energy spectrum and magnetization of electrons in a metallic film in parrallel magnetic fields is investigated for rH ≫a and L ≫a (rH is the Larmor radius, a is the range of variation of the surface potential, and L is the film thickness). Relations are obtained for the energy levels and quantum magnetization oscillations in terms of the phase shift of the electron wave function upon reflection from the film surface. The size effect due to electrons with orbits tangent to the film surface is found to be independent of the phase shift.

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