Extended Data Fig. 2: Representative spectral profiles and images for two other rTBG samples.

a, c, The spectral Raman profiles evidence different frequency values for the \({G}_{{\rm{r}}}^{-}\) and \({G}_{{\rm{r}}}^{+}\) peaks observed in two different rTBG samples (black arrows link the profiles to the corresponding images in b and d). The vertical lines indicate the central frequencies for the observed \({G}_{{\rm{r}}}^{-}\), G and \({G}_{{\rm{r}}}^{+}\) peaks. b, d, The spectral images are based on the G′-band intensities (colour scale). The arrow in d indicates the where the specrum in c was taken. In Fig. 2f (rTBG with θ = 0.09°), the peaks are observed at \({\omega }_{{G}_{{\rm{r}}}^{-}}=1,522\,{{\rm{cm}}}^{-1}\) and \({\omega }_{{G}_{{\rm{r}}}^{+}}=1,612\,{{\rm{cm}}}^{-1}\). The frequency difference between the theoretically predicted \({G}_{{\rm{r}}}^{-}\) and \({G}_{{\rm{r}}}^{+}\) peaks is \(\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}=45\,{{\rm{cm}}}^{-1}\) (for θ = 0.987°; already reaching the limit of our computational capability). For the experimentally observed \({G}_{{\rm{r}}}^{-}\) and \({G}_{{\rm{r}}}^{+}\) peaks for θ = 0.09°, it is \(\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}=90\,{{\rm{cm}}}^{-1}\). Our ability to experimentally define the θ dependence of the splitting is also limited, by the TERS resolution. We cannot properly image a moiré pattern smaller than 40 nm (twice the TERS resolution), limiting the rTBG samples that we can image to those with θ < 0.3°. The \(\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}\) splitting is predicted to increase with decreasing twist angle⁶, consistent with experimental observations: for L_M ≈ 160 nm (θ ≈ 0.09°), we observed \({\omega }_{{G}_{{\rm{r}}}^{-}}=1,522\,{{\rm{cm}}}^{-1}\) and \({\omega }_{{G}_{{\rm{r}}}^{+}}=1,612\,{{\rm{cm}}}^{-1}\) (\(\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}=90\,{{\rm{cm}}}^{-1}\)); for L_M ≈ 210 nm (θ ≈ 0.07°), we observed \({\omega }_{{G}_{{\rm{r}}}^{-}}=1,517\,{{\rm{cm}}}^{-1}\) and \({\omega }_{{G}_{{\rm{r}}}^{+}}=1,616\,{{\rm{cm}}}^{-1}\) (\(\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}=99\,{{\rm{cm}}}^{-1}\)); for L_M > 1,000 nm (θ < 0.01), \({\omega }_{{G}_{{\rm{r}}}^{-}}\) was not observed, but \({\omega }_{{G}_{{\rm{r}}}^{+}}=1,619\,{{\rm{cm}}}^{-1}\) follows the trend.