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

HORIA D. CORNEAN; BERNARD HELFFER; RADU PURICE

doi:10.1090/tran/8402

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

HORIA D. CORNEAN, BERNARD HELFFER, RADU PURICE

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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.

Original language	English
Journal	Transactions of the American Mathematical Society
Volume	374
Issue number	10
Pages (from-to)	7041-7104
Number of pages	64
ISSN	0002-9947
DOIs	https://doi.org/10.1090/tran/8402
Publication status	Published - Oct 2021

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© 2021 American Mathematical Society. All rights reserved.

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https://arxiv.org/pdf/2005.08699.pdf

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

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