On a magnetic Lieb–Thirring-type estimate and the stability of bipolarons in graphene

Abstract

Two-dimensional Weyl–Dirac relativistic fermions have attracted tremendous interest in condensed matter as they mimic relativistic high-energy physics. This paper concerns two-dimensional Weyl–Dirac operators in the presence of magnetic fields, in addition to a short-range scalar electric potential of the Bessel–Macdonald-type, restricted to its positive spectral subspace. This operator emerges from the action of a pristine graphene-like QED3 model recently proposed by De Lima, Del Cima, and Miranda, “On the electron–polaron–electron–polaron scattering and Landau levels in pristine graphene-like quantum electrodynamics,” Eur. Phys. J. B93, 187 (2020). A magnetic Lieb–Thirring-type inequality à la Shen is derived for the sum of the negative eigenvalues of the magnetic Weyl–Dirac operators restricted to their positive spectral subspace. An application to the stability of bipolarons in graphene in the presence of magnetic fields is given.