Chiral fermion dynamics in 2d magnetic vortices: Manifestation of momentum-spin-locking

Abstract

The electronic surface-states of a topological insulator in the presence of an in-plane magnetization vortex M(ϕ)=M(cos(Φ+νϕ), sin(Φ+νϕ)) are investigated theoretically. For a general angle of magnetization Φ∈[0,2π) and topological charge ν = 1, the modifications to the zero-mass single Dirac cone dispersion are treated exactly and the spectrum of bound eigenstates which forms in the energy window ±M cos(Φ) is derived. The space-time resolved dynamics of Dirac fermions in the presence of such vortices is studied numerically using a single-cone (2 + 1)D finite-difference scheme. In the continuous spectral region, Φ-dependent scattering of Dirac fermions at the vortex is observed. Depending on the type of vortex (Φ, ν) and the impact parameter, the propagation direction of the Dirac fermion is changed: the magnetization of the vortex exerts a torque onto the fermion spin which, by momentum-spin locking associated with the helical Dirac states, results in an in-plane rotation of the propagation direction of the scattered Dirac fermion. In head-on collisions of a Gaussian wave-packet with ν = 1 vortices a Φ-dependent lensing effect is seen in our simulations. Depending on the direction of incidence, the vortex Φ=−π/2, ν = 2 is identified as a coherent particle-beam splitter or “condenser” in head-on collisions.