Valley-polarized pumping current in zigzag graphene nanoribbons with different spatial symmetries

We numerically investigate the valley-polarized current in symmetric and asymmetric zigzag graphene nanoribbons (ZGNRs) by the adiabatic pump, and the effect of spatial symmetry is considered by introducing different pumping regions. It is found that pumping potentials with the symmetry V_p(x,y)=V_p(-x,y) can generate the largest valley-polarized current. The valley-polarized currents I₁₃^L with the pumping potential symmetry V_p(x,y)=V_p(x,-y) and I₁₄^L with V_p(x,y)=V_p(-x,-y) of symmetric ZGNRs are much smaller than those of asymmetric ZGNRs. We also find I₁₃^L and I₁₄^L of symmetric ZGNRs decrease and increase with the increasing pumping amplitude, respectively. Moreover, the dephasing effect from the electron-phonon coupling within the Buttiker dephasing scheme is introduced. The valley-polarized current of the symmetric ZGNRs with V_p(x,y)=V_p(x,-y) increases with the increase of the dephasing strength while that with V_p(x,y)=V_p(-x,-y) decreases as the dephasing strength increases.