Edge modes generated by intersection between 3 energy bands

In this contribution, we investigate 2-dimensional model problems of three coupled equations. We assume that the underlying Hamiltonian presents a symmetric intersection between three eigenvalues of Dirac's type with a mass function that vanish along a curve. We investigate the existence of edge modes for these models: such functions are solutions of the semiclassical associated evolution problem that are asymptotic to a coherent state with zero energy and break the correspondence principle by propagating inside the crossing set and not along a classical trajectory.