Spin-Filtered Edge States and Quantum Hall Effect in Graphene

Electron edge states in graphene in the quantum Hall effect regime can carry both charge and spin. We show that spin splitting of the zeroth Landau level gives rise to counterpropagating modes with opposite spin polarization. These chiral spin modes lead to a rich variety of spin current states, depending on the spin-flip rate. A method to control the latter locally is proposed. We estimate Zeeman spin splitting enhanced by exchange, and obtain a spin gap of a few hundred Kelvin.

Figure 1

(a) Graphene energy spectrum near the armchair boundary obtained from Dirac model, Eq. (1). The boundary condition, Eq. (5), lifts the $K$, $K^{\prime }$ degeneracy. The odd integer numbers of edge modes lead to the half-integer QHE. (b) Spin-split graphene edge states: the blue (red) curves represent the spin up (spin down) states. These states propagate in opposite directions at zero energy.

Figure 2

Four-terminal device with chiral spin edge states (no backscattering). In response to charge current of $I^c=2i_V=4e^{2}V/h$ between reservoirs 1 and 2, pure spin current of $I^s=2i_V$ flows between 4 and 3, while Hall voltage is zero.

Figure 3

Same as in Fig. 2 with backscattering between edge states induced by altering local spin-flip rate. Strong backscattering gives rise to asymmetric current flow with the current between 1 and 2 fully spin polarized. Inset shows how Hall voltage probe can be used to detect spin current.