Improvement of valley splitting and valley injection efficiency for graphene/ferromagnet heterostructure

Xu Longxiang¹, Lu Wengang^{2, 3, †}, Hu Chen⁴, Guo Qixun¹, Shang Shuai¹, Xu Xiulan¹, Yu Guanghua¹, Yan Yu⁵, Wang Lihua⁶, Teng Jiao^{1, ‡}

Structure model of the transport system and the (E, k_x)-resolved transmission coefficients. (a) Model of the Cu/graphene/Au/Ni heterostructure. The current direction is presented by a red arrow. (b)(d) The (E, k_x)-resolved transmission coefficients for M ∥ X and M ∥ Z, respectively. (c) Band structure of the left lead. The red and the blue dotted lines in (c) and (d) represent the regions where the valley splitting occurs.