Perimeter corrections to the Landau diamagnetism

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Abstract
If the free electron gas is enclosed in a box of finite volume the Dirichlet boundary condition imposed on the wavefunction modifies the density of states (it increases the energy levels). This is also true in presence of a uniform magnetic field and gives rise to the perimeter corrections chi ' to the Landau diamagnetic susceptibility chi 0. The author analyses the effect for the zero-field susceptibility by a Green function approach rather than by enumerating the energy levels. The perimeter contribution chi ' to the susceptibility is always positive (paramagnetic). The relative correction chi '/ chi 0 is given by (apart from a constant of order unity) l*surface area/volume, where l is a characteristic length and is equal to the thermal de Broglie wavelength at high temperatures and to the Fermi wavelength in another extreme of complete degeneracy. Thus the effect may be observable in small metallic particles of size 10-100 AA, in particular if the electron effective mass is small such as, e.g., in bismuth.

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