Geodesic
Spectrum of the bloch electron in a magnetic field in a two-dimensional lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 3, pp. 461-472

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The Hamiltonian of an electron in a two-dimensional lattice of point potentials in a transverse magnetic field is considered. An expression is found for the Green's function of this Hamiltonian, and from it an equation that determines the dispersion laws $\text{E}_s(\mathbf k)$ is obtained in the case of rational magnetic flux. A detailed investigation of the spectrum is made for the case of integral flux. A criterion is obtained for the conditions under which the Landau levels enter the spectrum of the lattice Hamiltonian. 
@article{TMF_1984_58_3_a12,
     author = {V. A. Geiler and V. A. Margulis},
     title = {Spectrum of the bloch electron in a magnetic field in a two-dimensional lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {461--472},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_3_a12/}
}
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V. A. Geiler; V. A. Margulis. Spectrum of the bloch electron in a magnetic field in a two-dimensional lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 3, pp. 461-472. http://geodesic.mathdoc.fr/item/TMF_1984_58_3_a12/