Fig. 2. Nano-FTIR spectra and phonon polariton dispersion of encapsulated TBG heterostructure.

a Optical microscope image of the twisted bilayer graphene (red solid and dash) encapsulated with 8 nm (16 nm at folded region), top h-BN (yellow solid) and 20 nm bottom h-BN. Scale bar: 10 μm. b Nano-FTIR spectra taken at AB/BA domain (blue solid line) and on the domain wall (DW) (red solid line). Inset: domain walls imaged through phonon polariton in h-BN. The blue and red dots indicate the tip locations where nano-FTIR spectra were taken at AB/BA and domain wall, respectively. Data were normalized to the signal of SiO₂/Si substrate. c FDTD simulated spectra calculated for AB/BA domain (blue solid line) and along the domain wall (red solid line). d Tight-binding model calculated frequency dependence of the real part (top) and imaginary part (bottom) of the local conductivity σ_xx for the center of the soliton regions (red solid line), and the uniform regions (blue solid line). The soliton width is 10 nm and E_F = 50 meV. e Near-field amplitude image of the h-BN/graphene/h-BN at frequency ω = 1430 cm⁻¹ (top) and ω =  1530 cm⁻¹ (bottom). The green dashed lines indicate the edges of the heterostructure. f Line profiles taken along blue and red dashed lines in e. Double arrows indicate λ_p/2. g Measured dispersion relation of the phonon polariton in the heterostructure (blue circles). Black solid line is the theoretic prediction.