Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field

Abstract

This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two $2d$ Bloch eigenvalues which have a conical crossing. It turns out that in the presence of an almost constant weak magnetic field, the spectrum near the crossing develops gaps which remind of the Landau levels of an effective mass-less magnetic Dirac operator.

51 pages, 2 figures. Will appear in Trans. A.M.S

References in corpus (3)

• Room-Temperature Quantum Hall Effect in Graphene
• Algebras of distributions suitable for phase-space quantum mechanics. I
• Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra

Cited by in corpus (1)

• Sharp spectral stability for a class of singularly perturbed pseudo-differential operators