Reflectionless transport of surface Dirac fermions on topological insulators with induced ferromagnetic domain walls

The properties of surface Dirac fermions on a three-dimensional topological insulator in proximity to a magnetic insulator with spatially textured magnetization are considered. We present an exact analytical treatment of the domain-wall resistance and the spectrum for an extended generic domain wall with in-plane and out-of-plane magnetizations. In the latter case, we find oscillations in the domain-wall resistance as a function of the wall width and for certain widths a complete absence of reflections for all incoming momenta. The surprising occurrence of oscillations and the reflectionless potentials can be related to a supersymmetry of the surface Dirac Hamiltonian combined with the domain-wall profile.

Figure 1

The experimental setup for studying ballistic transport through a DW. Two leads with external voltage bias $V$ are attached to the structure of topological insulator coated with a isolating ferromagnetic layer that contains an in-plane tail-to-tail DW or out-of-plane DW.

Figure 2

Energy spectrum of the system with IP (a) and OOP DW (b) including the bound states for $Mw=3.9\hslash v$. The spectrum is symmetric with respect to positive and negative energies in both cases. The continuum of scattering states (yellow area) has an energy gap $2M$ in both cases. Continuum states that exist only on either side of the DW [red and green areas in (a)] are decaying into the potential step posed by the DW. The inset illustrates various momenta relevant for the scattering states.

Figure 3

Relative decrease in the conductance $\delta G$ due to the presence of the DW for IP and OOP DWs. In the case of an IP DW, we see that the values are rather large even for wider walls and decrease monotonically towards the asymptotic value $\delta G_{\mathrm{M}}$ as the wall width increases. To the contrary, for OOP DWs it decreases significantly when the wall width becomes of the order of the magnetic length $l_M=\hslash v/M$. The approximate formula (10) is drawn as black thin lines and shows very good agreement with the exact integration.