Highly Polarized and Long Range Dissipationless Spin Transport Due to Counterflowing Electron and Hole Edge Channels

Abstract

The presence of edge channels in the quantum Hall regime leads to dissipationless charge transport over long distances. When graphene is interfaced with a magnetic material, the exchange interaction lifts the Landau levels spin degeneracy. This causes the presence of counterflowing edge channels with opposite spin polarization. We show theoretically that the spin-flip scattering between these edge channels enables a dissipationless spin transport with larger than 100% spin polarization of the charge current. It also allows the transport of spin over macroscopically long distances, even in the absence of an applied charge current.

Figures (3)

• Figure 1: Schematics of the electron spin-flip scattering between counterflowing spin up (red) and down (blue) channels at one edge of a magnetic graphene ribbon in the QHE regime. An electron can cross the section represented by the dashed line with opposite spins while propagating in opposite direction, effectively contributing to more than one spin passage to the spin current.
• Figure 2: (a) Energy dispersion of the spin-split Landau levels in magnetized graphene. The spin up electron (hole) Landau levels are plotted in light blue (red) and the spin down electron (hole) Landau levels are in dark blue (pink). They produce electron and hole like spin polarized counterflowing edge channels. When the Fermi energy $E_F$ is between the spin up and down zero Landau levels, the spin up and down carriers flow in opposite directions. (b) Spin polarization $\beta$ of the charge current as a function of the Fermi energy for the non-equilibrated (black) and fully equilibrated (green) case. Edge transport for the non-equilibration (c) and full equilibration (d) of the counterflowing edge channels. In (c), the dashed (solid) channel electrochemical potential is $\mu_1$ ($\mu_2$). In (d), the dashed (solid) channels are at electrochemical potentials $\mu_b$ ($\mu_t$).
• Figure 3: Schematics of the device under consideration, with $N^\uparrow=3$ and $N^\downarrow=2$ when an electrochemical potential bias $\mu$ is applied between the contacts (a), or a spin accumulation bias $\mu_s$ is applied at contact 2 (b). (c) Spatial dependence of the edge channels electrochemical potentials in (a). The x-position is measured in units of $\lambda_0$. See inset in (d) for the legend. (d) Edge channels electrochemical potential for (b). (e) Spatial dependence of the spin polarization of the charge current flowing at the top edge (solid black lines), bottom edge (black dashed) and of the total spin current (green) for (a). (f) Spin current induced by the application of the spin accumulation bias in (b).