Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond and
Edgardo Stockmeyer
Vol. 5 (2023), No. 3, 643–727
DOI: 10.2140/paa.2023.5.643
Abstract
We study Dirac operators on two-dimensional domains coupled to a magnetic field
perpendicular to the plane. We focus on the infinite-mass boundary condition (also
called MIT bag condition). In the case of bounded domains, we establish the
asymptotic behavior of the low-lying (positive and negative) energies in
the limit of strong magnetic field. Moreover, for a constant magnetic field
, we study the
problem on the half-plane and find that the Dirac operator has continuous spectrum except for
a gap of size
,
where
is a universal constant. Remarkably, this constant characterizes certain energies of
the system in a bounded domain as well. Our findings give a fairly complete
description of the eigenvalue asymptotics of magnetic two-dimensional Dirac
operators under general boundary conditions.