On the low lying spectrum of the magnetic Schrödinger operator with kagome periodicity

Philippe Kerdelhué (1) , Jimena Royo-Letelier (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]

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

Mots clés: Spectral analysis; Schrödinger operator

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Kerdelhué, Jimena Royo-Letelier. On the low lying spectrum of the magnetic Schrödinger operator with kagome periodicity. 2014. ⟨hal-00969569⟩