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We study in a semiclassical regime a two-dimensional magnetic periodicSchr\"odinger operator. We first review some results for the square (Harper),triangular and hexagonal (case of the graphene) lattices. Then we study thecase considered by Hou when the periodicity is given by a kagome lattice. Wereduce the problem to the study of discrete and pseudodifferential operatorsand obtain pictures similar to Hofstadter's butterfly. We prove the existenceof flat bands, which do not occur in the three previous cases.

On the low lying spectrum of the magnetic Schr\"odinger operator with kagome periodicity