Inserted: 12 oct 2020
Last Updated: 11 mar 2021
Journal: Commun. Contemp. Math.
In this paper we show the existence of infinitely many symmetric solutions for a cubic Dirac equation in two dimensions, which appears as effective model in systems related to honeycomb structures. Such equation is critical for the Sobolev embedding and solutions are found by variational methods. Moreover, we prove also prove smoothness and exponential decay at infinity.