Valley-polarized pumping current in zigzag graphene nanoribbons with different spatial symmetries<xref rid="cpb_27_12_127203fn1" ref-type="fn">*</xref> <fn id="cpb_27_12_127203fn1"> <label>*</label> <p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11704190, 11874221, and 11504240) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20171030).</p> </fn>

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

Project supported by the National Natural Science Foundation of China (Grant Nos. 11704190, 11874221, and 11504240) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20171030).

Yu Zhizhou^{1, †}, Xu Fuming²

(color online) (a) Schematic diagram of ZGNRs with two semi-infinite leads (orange shadow). Four pumping regions are represented by blue and green shadows in the central region. The origin of the axis is set to be the center of ZGNRs. (b) Band structure of ZGNRs with a width of 4.1 nm. The first subbands are highlighted with orange color and the arrows for different valley indices K and K′ denote the moving directions of electrons.