Symmetry-dependent transport properties and bipolar spin filtering in zigzag alpha-graphyne nanoribbons

First-principles calculations are performed to investigate the transport properties of zigzag $\ensuremath{\alpha}$-graphyne nanoribbons (Z$\ensuremath{\alpha}$GNRs). It is found that asymmetric Z$\ensuremath{\alpha}$GNRs behave as conductors with linear current-voltage relationships, whereas symmetric Z$\ensuremath{\alpha}$GNRs have very small currents under finite bias voltages, similar to those of zigzag graphene nanoribbons. The symmetry-dependent transport properties arise from different coupling rules between the $\ensuremath{\pi}$ and ${\ensuremath{\pi}}^{*}$ subbands around the Fermi level, which are dependent on the wave-function symmetry of the two subbands. Based on the coupling rules, we further demonstrate the bipolar spin-filtering effect in the symmetric Z$\ensuremath{\alpha}$GNRs. It is shown that nearly 100$%$ spin-polarized current can be produced and modulated by the direction of bias voltage and/or magnetization configuration of the electrodes. Moreover, the magnetoresistance effect with the order larger than $500\phantom{\rule{0.16em}{0ex}}000%$ is also predicted. Our calculations suggest Z$\ensuremath{\alpha}$GNRs as a promising candidate material for spintronics.