Fig. 1. Top view and side views of relaxed structures of five isomers of GeSe monolayer (in the figures, a and b denote the lattice constants, respectively): (a) α-GeSe; (b) β-GeSe; (c) γ-GeSe; (d) δ-GeSe; (e) ε-GeSe. 单层GeSe的5种同分异构弛豫后结构的俯视图和侧视图(图中a和b表示晶格常数)　(a) α-GeSe; (b) β-GeSe; (c) γ-GeSe; (d) δ-GeSe; (e) ε-GeSe

Fig. 1. Band structures of α-GeSe monolayer under applied strains: (a) σ = 0; (b) σ_x = 2%; (c) σ_x = 7%; (d) σ_y = –8%; (e) σ_y = –1%; (f) σ_y = 8%; (g) σ_xy = –1%; (h) σ_xy = –6%; (i) σ_xy = 8%. 单层α-GeSe在应变调控下能带结构　(a) σ = 0; (b) σ_x = 2%; (c) σ_x = 7%; (d) σ_y = –8%; (e) σ_y = –1%; (f) σ_y = 8%; (g) σ_xy = –1%; (h) σ_xy = –6%; (i) σ_xy = 8%

Fig. 2. Absorption coefficients for five isomers in GeSe monolayer.5种GeSe单层同分异构体的吸收系数

Fig. 2. Optimized structures of ε-GeSe monolayer under 20% tensile strain, respectively: (a) Armchair direction; (b) zigzag direction; (c) biaxial direction.ε-GeSe单层施加20%拉伸应变下优化后的结构　(a) 扶手椅方向; (b) 锯齿形方向; (c) 双轴方向

Fig. 3. Variation of band gap along with the applied in-plane strain (The square represents the strain along armchair (σ_x) direction, while the circle represents the strain along zigzag (σ_y) direction, the triangle represents the bi-axial (σ_xy) strain, the solid and hollow symbols denote the indirect and direct band gap, respectively) 带隙随平面内应变的变化图(方块表示沿扶手椅(σ_x)方向的应变, 圆圈表示沿锯齿形(σ_y)方向的应变, 三角形代表双轴(σ_xy)应变, 实心和空心符号分别表示间接和直接带隙)

Fig. 4. Band structures of ε-GeSe monolayer under applied strains (σ_x, σ_y, σ_xy represent the strains along the armchair, zigzag and biaxial directions, respectively. The arrow represents the direction from the conduction band minimum (CBM) to the valence band maximum (VBM)): (a) σ= 0 (in the figure, arepresents the conduction band minimum of ε-GeSe, b represents the valence band point corresponding to the same path point of a, c is the valence band maximum of ε-GeSe, d is the conduction band point corresponding to the same path point of c); (b) σ_x = 10%; (c) σ_x = 20%; (d) σ_y = 10%; (e) σ_y = 20%; (f) σ_xy = 10%; (g) σ_xy = 20%. 应变调控下ε-GeSe单层的能带结构 (σ_x, σ_y和σ_xy分别表示沿扶手椅形、锯齿形和双轴方向的应变箭头表示导带最小值 (CBM)指向价带最大值 (VBM)的方向)　(a) σ = 0 (图中a表示ε-GeSe的导带最小值, b表示与a相同路径点的价带点, c是ε-GeSe的价带最大值, d是与c的相同路径点的导带点); (b) σ_x = 10%; (c) σ_x = 20%; (d) σ_y = 10%; (e) σ_y = 20%; (f) σ_xy = 10%; (g) σ_xy = 20%

Fig. 5. Isosurfaces of partial charge densities of monolayer ε-GeSe ((a), (b), (c), (d) are corresponding points to a, b,c andd in Fig. 4(a), respectively). 单层ε-GeSe部分电荷密度的等值面 ((a), (b), (c), (d)分别对应于图4(a)中a, b, c和d所标注的点)

Table 1. Relaxed structural parameters of five isomers of GeSe monolayer (aandb are the lattice constants, respectively.h is the buckling height of GeSe; E_b is the bind energy per atom; E_g is the fundamental band gap).

Table 2. Calculated results of vibration frequencies of five isomers of GeSe (E₀ represents zero energy, E_f/i represents virtual frequency, E_f/i/E₀ denotes virtual frequency occupies the proportion of zero energy).

Table 3. Summary of the optimized geometric structures and energy gaps for ε-GeSe under in-plane strains along the armchair (σ_x), zigzag (σ_y) and biaxial (σ_xy) directions (Negative values of strain denote compress strains, while positive values denote tensile strains. d₁, d₂ and d₃ (as shown in Fig. 1(e)) represent the distance between Ge and Se atoms, respectively. θ₁ represents the θ(Ge-Se-Ge) bond angle. θ₂ represents the θ(Se-Ge-Se) bond angle. E_g(eV) is the band gap under the corresponding strain，（ind.）is the indirect band gap, (dir.) is the direct band gap)