On the absence of bound states for a planar massless Brown-Ravenhall-type operator

We address the question of the existence of bound states for a suitably projected two-dimensional massless Dirac operator in the presence of a Bessel-Macdonald potential (also known as $K_0$-potential potential), raised by De Lima, Del Cima and Miranda, in Eur.Phys.J. B (2020) 93, 187. Based on Relativistic Hardy Inequality, we prove that this operator has no bound states if $\gamma \leqslant \gamma_{\rm crit}$ (subcritical region), where $\gamma$ is a coupling constant.