TIGHT-BINDING AND NEARLY-FREE-ELECTRON APPROACH TO LATTICE ELECTRONS IN EXTERNAL MAGNETIC FIELDS

The energy structure for lattice electrons in an external magnetic field is treated by extension of either the tight-binding or the nearly-free-electron method. The secular problems resulting from both methods are identical, if the coupling integrals and the real lattice characterizing the tight-binding method are interchanged with the Fourier integrals and the orbit lattice characterizing the nearly-free-electron method. A Bloch-type transformation reducing these essentially two-dimensional secular problems to one dimension is performed, following the procedure introduced in a preceding paper. For rational fluxes 2πNM per lattice cell, an even finite secular determinant is left, yielding a splitting of each zero-field band into M subbands. Total agreement between the level structures resulting from the two approaches is found. The relation of these structures to the de Haas-van Alphen periods in the case of magnetic breakdown is discussed. © 1969 The American Physical Society.