Fig. 1. (a) Schematic structure of of germanene spin filter. The blue regions on the left and right side are left and right lead. The area surrounded by red solid line is the central device. The regions shown in gray and yellow are exerted to the Z-direction exchange field and electric field. (b) Side view of germanene spin filter. Red and yellow spheres represent atoms in the top and bottom buckled-layer of germanene. (a)单层锗烯自旋过滤器件结构示意图(左、右两侧蓝色区域为左、右电极区域; 中间红色实线包围区域内为中心器件区; 灰色和黄色分别表示Z轴方向交换场和电场的施加区域); (b)单层锗烯自旋过滤器件侧视图(红色和蓝色小球分别代表锗烯翘曲层顶部和底部的锗原子)

Fig. 2. Relationship between the conductance G and electron Fermi energy when applying different values of local exchange field M: (a) Spin-dependent conductance with M = 0.01t, 0.03t, 0.05t, 0.07t;　(b) spin-dependent conductance with M = 0.09t. The red solid line represents spin-up electrons and the blue dash line represents spin-down electrons. 施加不同强度的局域交换场M时, 电导G与电子费米能量 之间的关系(红色实线表示自旋向上的电子, 蓝色虚线表示自旋向下的电子)　(a) M = 0.01t, 0.03t, 0.05t, 0.07t时的自旋相关电导; (b)　 M = 0.09t时的自旋相关电导

Fig. 3. (a) Energy-band diagram of germanene without external field; (b) energy-band diagram of germanene with local exchange field ; the solid (hollow) triangle represents the upper (lower) edge state, the dot represents the energy band, the red (blue) colour corresponds to the spin-up (spin-down) electron; (c) the spin-dependent conductance as a function of electronic energy when . (a)无外场时锗烯的电子能带结构; (b)交换场强度为 时的电子能带结构; 其中实心(空心)三角表示上(下)边缘态, 圆点表示体能带, 红色(蓝色)对应自旋向上(向下)的电子; (c)交换场强度为 时自旋相关电导随着电子能量的变化

Fig. 4. (a) The spin-dependent conductance as a function of electron Fermi energy when and ; (b) the spin-dependent conductance vs electron Fermi energy when ; (c) energy-band diagram of germanene with local exchange field and electric field . The solid (hollow) triangle represents the upper (lower) edge state, the dot represents the energy band, the red (blue) colour corresponds to the spin-up (spin-down) electron. (a)局域交换场和电场强度为 和 时自旋相关电导随着电子费米能量 的变化; (b)交换场和电场强度为 时自旋相关电导随着电子费米能量 的变化; (c)交换场和电场强度为 时的电子能带结构; 其中实心(空心)三角表示上(下)边缘态, 圆点表示体能带, 红色(蓝色)对应自旋向上(向下)的电子