On the Dirac bag model in strong magnetic fields

Abstract

In this work 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 $B$, we study the problem on the half-plane and find that the Dirac operator has continuous spectrum except for a gap of size $a\_0\sqrt{B}$, where $a\_0\in (0,\sqrt{2})$ is a universal constant. Remarkably, this constant characterizes certain energies of the system in a bounded domain as well. We discuss how these findings, together with our previous work, give a fairly complete description of the eigenvalue asymptotics of magnetic two-dimensional Dirac operators under general boundary conditions.