Graphene Valley Filter Using a Line Defect

With its two degenerate valleys at the Fermi level, the band structure of graphene provides the opportunity to develop unconventional electronic applications. Herein, we show that electron and hole quasiparticles in graphene can be filtered according to which valley they occupy without the need to introduce confinement. The proposed valley filter is based on scattering off a recently observed line defect in graphene. Quantum transport calculations show that the line defect is semitransparent and that quasiparticles arriving at the line defect with a high angle of incidence are transmitted with a valley polarization near 100%.

Figure 1

Extended line defect in graphene. (a) Arrangement of the carbon atoms around the line defect highlighted in gray. The structure exhibits translational symmetry along the defect with a primitive cell shown in beige. The two sublattices in graphene indicated by blue and green atoms reverse upon reflection at the line defect, as can be seen in the enlarged overlay. (b) Scanning tunneling microscope image of the line defect in graphene (image adapted from Ref. 5).

Figure 2

Valley states scattering off the line defect. (a) Energies close to the Fermi level in graphene have dark contours and are located in the corners of the first Brillouin zone contained within the gold hexagon. The two valleys, $K$ and $K^{\prime }$, are identified as the two disjoint low-energy regions in the reciprocal primitive cell enclosed by the blue rectangle. (b) An incident quasiparticle state is defined by the valley index $\tau$ and wave vector $\overrightarrow{q}$, where the latter points in the direction $\widehat{q}$ given by the angle of incidence $\alpha$. (c) Owing to energy and momentum conservation along the line defect, there are only two nonevanescent scattered states allowed. (d) The sublattice symmetric $|+⟩$ and antisymmetric $|-⟩$ components of the incident state $|{\Phi }_{\tau }⟩$ are transmitted and reflected, respectively. The thickness of each arrow indicates the probability the quasiparticle will follow the respective path.

Figure 3

The probability that an incident quasiparticle at the Fermi level with valley index $\tau$ and angle of incidence $\alpha$ will transmit through the line defect.

Figure 4

Transmission probability for a quasiparticle with finite energy. (a) The transmission probability for a quasiparticle approaching the line defect at an angle of incidence $\alpha$ is indicated by the brightness, ranging from 0 to 1 in increments of 0.05. For the angle $\alpha$ shown, the transmission is near one if the quasiparticle has valley index $\tau =+1$, as illustrated on the right, where the filled (open) circle represents an electron (hole) quasiparticle. (b) The transmission probability for the corresponding quasiparticle with valley index $\tau =-1$.