  We prove the existence of infinitely many non square-integrable stationary
solutions for a family of massless Dirac equations in 2D. They appear as
effective equations in two dimensional honeycomb structures. We give a direct
existence proof thanks to a particular radial ansatz, which also allows to
provide the exact asymptotic behavior of spinor components. Moreover, those
solutions admit a variational characterization. We also indicate how the
content of the present paper allows to extend our previous results for the
massive case [5] to more general nonlinearities.
