Orbital-Selective Engineering of Strain-Tunable Chern Insulators in Momentum Space

Abstract

Unlike conventional approaches where topological order is statically fixed post-synthesis, we demonstrate that a single external knob-strain-can independently modulate topological order and functional responses in the Tc-adsorbed penta-hexa silicene (Tc_PH-Si) monolayer, with both properties governed by a single microscopic mechanism: momentum-space orbital-selective engineering of Tc-dxz_Si-px hybridization. Combining first-principles calculations and tight-binding models, we show that biaxial strain drives a complete topological pathway: C=1 (0) to C=0 (-2) to C = -1 (-3 to -4) to C = 0 metallic state (-6). This is exemplified by two pivotal states: a topologically critical point yet functionally optimal state at -2 strain (C=0) hosting a direct bandgap (0.17 eV) and d11 = 8.34 pm_V, and a topologically nontrivial but equally optimal state at -4 strain (C = -1) with d11 = 11.01 pm_V-three times that of MoS2. Berry curvature analysis reveals that functionality arises from local orbital hybridization strength, while topology originates from its global phase distribution. This establishes a new paradigm for materials design, transforming static functional materials into dynamically tunable quantum platforms.

Figures (5)

• Figure 1: (a) , (b) Top and side view od the Tc@PH-Si. (c) The evolution of the band gap and the Chern Numbers with the strain. The yellow rectangles marked in the figure denote the direct band gap regions.
• Figure 2: Surface-projected band structures of the Tc-adsorbed PH-silicene nanoribbon under different strains: (a) 0% strain, (b) -3% and (c) -4%. Electronic structures of Tc@PH-Si under different strains with and without SOC (d) 0% strain, (e) -3% and (f) -4%.
• Figure 3: $d$-orbital projected band structures of the Tc in the monolayer Tc@PH-Si under different strains: (a) 0%, (c) -3% and (e) -4%; $p$-orbital projected band structures of the Si in the Tc@PH-Si under different strains: (b) 0%, (d) -3% and (f) -4%. The sizes of the circles indicate the weight of different orbitals.
• Figure 4: (a) Strain dependence of ICOHP for various orbital pairs in Tc-adsorbed PH-silicene, in which $S_{1}$ ($S_{2}$) means spin up (down), respectively. (b)Projected COHP (pCOHP) for Tc-$d_{xz}$/Si-$p_{x}$ (red) and Tc-$5s$/Si-$3s$ (blue) orbital pairs in Tc adsorbed PH-silicene at (left) -4% strain (C = -1) and (right) 0% strain (C = 1).
• Figure 5: (a)Magnetic anisotropy energy (MAE = $E_{out}$ - $E_{in}$) for all 3d and 4d transition metals adsorbed on PH-silicene. Negative (positive) values indicate an out-of-plane (in-plane) easy axis; (b)Strain dependence of the magnetic anisotropy energy (MAE) for Tc@PH-Si, with the easy axis along the out-of-plane direction; (c) Strain dependence of the Chern number (red triangles) and piezoelectric coefficients $d_{11}$ (blue squares) and $d_{31}$ (cyan circles) in Tc@PH-Si; (d) and (e) Berry curvature at 0% and -4% strain.