Peculiarities of the Landau level collapse in graphene ribbons in crossed magnetic and in-plane electric fields

Abstract: Employing the low-energy effective theory alongside a combination of analytical and numerical techniques, we explore the Landau level collapse phenomenon, uncovering previously undisclosed features. We consider both finite-width graphene ribbons and semi-infinite geometries subjected to a perpendicular magnetic field and an in-plane electric field, applied perpendicular to both zigzag and armchair edges. In the semi-infinite geometry the hole (electron)-like Landau levels collapse as the ratio of electric and magnetic fields reaches the critical value $ +(-) 1$. On the other hand, the energies of the electron (hole)-like levels remain distinct near the edge and deeply within the bulk approaching each other asymptotically for the same critical value. In the finite geometry, we show that the electron (hole)-like levels become denser and merge, forming a band.