β Scribed by H.P Gail; J Schmid-Burgk
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The effects of a magnetic field on the self-shielding of an electron gas against small electrostatic perturbations V are studied by use of Bloch wave functions and by the random phase approximation.
V is taken to be periodic along the field lines. It is demonstrated that in the weak field limit, p&e V + 0, magnetic effects become negligible. For &I > eV such effects may be important only under limited physical conditions. Singularities discussed by Glasser and Kaplan [I] are replaced by peaks of finite amplitude and width, appearing with the frequency of neck orbit oscillations. Peak profiles and the Lindhard singularity are investigated for the case V # 0.
Glasser and Kaplan [I] have recently discussed the dielectric tensor for an electron gas embedded in a uniform magnetic field, following earlier work by Green et al. [2], Hebborn and March [3, 41, Stephen [5], and Horing [6]. Their work on the extent to which such a gas reacts by self-shielding to a spatially periodic electrostatic perturbation led to the interesting observation that the presence of the magnetic field, however weak, causes singularities to appear in the dielectric tensor. Such singularities lead to complete self-shielding against the externally applied wave. This effect may be of importance for the magnetic properties of crystals since some aspects of their Fermi surface structure depend on the effective lattice potential, the size of which is diminished when large self-shielding takes place.
Glasser and Kaplan use a random phase first order Born approximation propagator method to determine the spatially periodic component of the electron density. They allow arbitrary orientations of the perturbing wave vector q, with respect to B. the magnetic induction. Even for q parallel to B some singularities appear. To investigate more closely the nature of such singularities we propose here to treat this special case of q parallel to B by a somewhat different technique but retaining the random phase approximation. Assuming, for physical reasons, 303
π SIMILAR VOLUMES
Exact analysis is presented to derive the magnetic response functions and their singularities of free-electron gas in a uniform magnetic field of arbitrary strength at T = 0 'Ii. The newly defined functions, A,(s) = XVI (S -n)p of p =-= -$, 4, 8, are \_ \_ employed to obtain the Fermi energy, magnet
The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux tube, i.e., of zero width, is investigated. Since both a direct