Landau levels and edge states in graphene with strong spin-orbit coupling

We investigate the electronic properties of graphene in a magnetic and a strain-induced pseudo-magnetic field in the presence of strong spin-orbit interactions (SOI). For a homogeneous field we provide analytical results for the Landau level eigenstates for arbitrary intrinsic and Rashba SOI, including also the effect of a Zeeman field. We then study the edge states in a semi-infinite geometry in the absence of the Rashba term. We find that, for a critical value of the magnetic field, a quantum phase transition occurs, which separates two phases both with spin-filtered helical edge states but with opposite direction of the spin current. Finally,we discuss magnetic waveguides with inhomogeneous field profiles that allow for chiral snake orbits. Such waveguides are practically immune to disorder-induced backscattering, and the SOI provides non-trivial spin texture to these modes.