Abstract
The derivation of one-band hamiltonians in a magnetic field is reconsidered and it is shown that only smooth solutions are consistent with their framework. Based on this result and on symmetry arguments a discussion is given for the splitting of a Bloch band into an integer number of subbands when a “rational” magnetic field is turned on. It is questioned whether this splitting which holds in a one-band effective hamiltonian approximation remains valid in an exact calculation.
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