A Controllable Valley Polarization In Graphene

Graphene was sucessfully made in2004by Geim et al. This new kind of carbonnanomaterial has attracted much attention. In room temperature, the electron with high edgemobility, so graphene is likely to replace silicon materals. We develop a tigh-binding theory tostudy the electronic transport through extended line defects in monolayer grapheme.Firstly, the valley polarized electronic transport through only one line defect ingraphene is studied. By means of the translational symmetry along the line defect, the TBHamiltonian can be projected into a subspace with a xed component of electronic Blochwavevector. By a further reducing, the original problem can be mapped into aquasi-one-dimensional TB “atomic” chain, which is analytically solvable. Based on such amodel, we can work out an analytical expression about the transmission probability in termsof the TB parameters. The feature of the transmission probability in low-energy limit isdiscussed. The TB expression can be transferred into the simple form obtained previously byDirac Fermion theory. We suggest that a strain along the line defect can be utilized tomodulate the incident angle of the valley polarized complete transmission. Thus, a valleyltering effect with an adjustable incident angle can be realized.Then, the electron transport of different conical valleys also is investigated in graphenewith extended line-defects. Importantly, the valley polarization changes with varying thedistance between the line-defects and the number of the line-defects. The valley polarizationcan reach to the maximum value of one, namely a100%polarization, at a small incident angle.Further numerical calculations manifest that100%polarization should be attributed to thebehavior of electron quantum interference, more precisely the phenomenon of the standingwave between the line-defects. The findings make us get rid of helplessness in the choose ofthe electron’s incident angle and provides a reliable way to realize a controllable valleypolarization in experiment. With the great advance in graphene related technologies, a valleypolarization resonator and also a detector of a valley polarization, being the key componentsin valleytronics, are promising to be realized in the system of the line-defect graphene.