The wave function of a Bloch electron in a magnetic field
1966; IOP Publishing; Volume: 89; Issue: 3 Linguagem: Inglês
10.1088/0370-1328/89/3/325
ISSN1747-3810
Autores Tópico(s)Quantum optics and atomic interactions
ResumoIt is shown that the wave function of an electron moving through a periodic lattice in a magnetic field can be written as the product of a phase factor and a series of terms of the form Fm(r)uk, m(r), where uk, m(r) is the periodic part of the zero-field Bloch function for state k in band m, and Fm(r) is a smooth envelope function. The wave vector k is allowed to vary with r, and a coupled set of equations is derived for the functions Fm(r), the coefficients of which depend on the form of k(r). In the absence of magnetic breakdown, one envelope function Fl(r) is much larger than the others, and the coupled set reduces to a single equation for Fl. If k(r) is suitably chosen, Fl(r) is localized around a quantum reference orbit Q, which itself lies very close to the semi-classical orbit in the lth band. The difference in areas between the two orbits yields the value of the phase correction term γ in the Onsager quantization rule, and it is found that, if field-dependent correction terms are neglected, γ = ½ for all orbits. The effect of lattice imperfections on orbit quantization is discussed, and it is shown that this problem can be treated semi-classically.
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