Fig. 1: Atomic structures and simulated scanning tunneling microscope (STM) patterns of the pristine high-symmetry phase and chiral Star-of-David (c-SoD) charge density wave (CDW) phase of monolayer β-In₂Se₃.

a Schematic side view of the atomic structure of the pristine high-symmetry monolayer β-In₂Se₃ (β_c-In₂Se₃). b Top view of the lattice vectors of monolayer β_c-In₂Se₃ (black arrows) and the c-SoD reconstructed phase (orange arrows), the rotation angle between the two sets of lattices is R = 13.9°. c Schematic diagram of the displacement of the middle layer Se [Se(m)] atoms during the β_c-to-c-SoD CDW transition, where Se(m) atoms are marked as Se(m1), Se(m2), Se(m3) and Se(t) atoms are marked as Se(t1), Se(t2), Se(t3), Se(t4) according to their locations. The CDW transition can be named the left-handed (LH) mode and right-handed (RH) mode according to the clockwise or counterclockwise motions of Se(m2) atoms. Top view of the actual atomic structures of (d) β_c and (e) LH-c-SoD phases of monolayer In₂Se₃. The c-SoD configuration is formed by the atoms enclosed by the gray dotted line in Fig. 1d being twisted together according to the LH mode. f, g Diagram of the reciprocal lattice vectors extracted from the fast Fourier-transform mapping of the atomic structures of the β_c and c-SoD phases of monolayer In₂Se₃. White and orange arrows represent the reciprocal lattice vectors of β_c (\({{{{\boldsymbol{a}}}}}^{*}\) and \({{{{\boldsymbol{b}}}}}^{*}\)) and c-SoD (\({{{{\boldsymbol{a}}}}}_{{{{\rm{CDW}}}}}^{*}\) and \({{{{\boldsymbol{b}}}}}_{{{{\rm{CDW}}}}}^{*}\)) phase of 2D In₂Se₃, respectively. Density functional theory simulated STM images of the (h, i) empty and (j, k) filled states of β_c and LH-c-SoD phases, the simulated bias voltages are +2 V and −2 V, respectively.