Fig. 2: Multislice electron ptychography characterisation of the coloured K_xWO₃ nanosheets.

a–c Enlarged and identical phase images of the coloured K_xWO₃ nanosheets with a thickness of 15 nm at 1 nm, 7 nm, and 15 nm in depth (slice 1 is defined as 1 nm in thickness from the top surface), showing that K⁺ ions are inserted into the A position of pseudo-K_xWO₃ perovskite, as boxed by red circles. d The mean phase intensity of the K⁺ intensity distribution from slices 1 to 15. e The Pearson correlation coefficients of the interplanar spacing of the {200 and {020} facets from slices 1 to 15 as a function of the intensity of K⁺ ions, showcasing that the more K⁺ ions, the more obvious lattice distortion. f The statistical box diagrams of the changed W-O-W chemical bonds at every slice in coloured K_xWO₃ nanosheets in 3 replicates, showing that the bond angle rises with area proximity to the surface along [200] and [020] zone axes, respectively. g Schematic view of the three-dimensional distribution of the colour centres in K_xWO₃ nanosheets, showcasing that the monoclinic structure (yellow atoms) gradually transforms into tetragonal (light blue atoms) and ultimately cubic structures (dark blue atoms) from the bulk to the surface, driven by embedded K⁺ ions along the [001] direction, thereby exhibiting pronounced depth-dependent lattice distortion.