Fig. 2: Atomically quantitative analysis of ZO modes at h-¹⁰BN/h-¹¹BN interface.

a HAADF image of h-¹⁰BN/h-¹¹BN interface. b The corresponding experimental EELS obtained at the same region of a, and the corresponding first-principles calculation results with the same experimental parameters. See analysis details in methods. c Spatial distribution of typical phonon modes around the h-¹⁰BN/h-¹¹BN interface. The arrows are eigenvectors extracted from DFT calculations corresponding to the Brillouin Zone center (q = Γ, ω = 102.5 meV) and Brillouin Zone boundary (q = K, ω = 71.2 meV & ω = 74.7 meV), denoting the two out-of-plane vibrations in b. d Quantitative energy variation of the ZO modes. The black dots are fitted phonon energy of each spectrum, and the error bars are standard deviation shown as the red and cyan shades. The orange and cyan solid lines are fitting of black dots by the Logistic function, presenting the transition width of ZO_{low q} (Brillouin Zone center) and ZO_{high q} (Brillion Zone boundary) is 3.44 nm and 1.66 nm respectively. See analysis details in methods. e Schematic of phonon-induced vibration dipole and accumulated bound charge at interface caused by the discontinuity of atom displacement. Detailed spatial distribution of the charge density refer to supplementary fig. 9.