Fig. 4: Electron–optical–phonon and electron–phason coupling in TBG.

a, Inset, measured inelastic conductance step, versus θ, corresponding to the intervalley (near the K point in the phonon BZ) optical modes (TO and LO), normalized following equation (1) using the measured tip area and DOS (we divided the measured step by 2 to obtain the average contribution of the TO and LO modes). Solid lines are theoretically calculated in-layer (green) and interlayer (yellow) contributions. Visibly, for optical phonons, the dominant EPC mechanism is the in-layer one (Methods section ‘Theory model for inelastic tunnelling through phonon emission and the two mechanisms of EPC’). Main, the intervalley average optical modes EPC, \({g}_{{\rm{optical}}}=\sqrt{({g}_{{\rm{TO}}}^{2}+{g}_{{\rm{LO}}}^{2})/2}\), determined from the measurements in the inset. Error bars are obtained from differences between measurements at positive and negative bias and all other experimental uncertainties. b, Intervalley TO phonon energy as a function of θ extracted from Fig. 2e. c, Inset, measured inelastic conductance step, versus θ, corresponding to the acoustic TA mode, normalized following equation (1) using the measured tip area and DOS. Solid lines are the theoretically calculated in-layer (green) and interlayer (yellow) contributions. In contrast to optical phonons, the EPC of the acoustic phonons is dominated by the interlayer coupling mechanism, which is the layer-antisymmetric phason mode. Main panel, the electron–phason coupling, g_phason, determined from the measurements in the inset. Error bars are obtained from differences between measurements at positive and negative bias and all other experimental uncertainties. d, TA mode energy as a function of θ extracted from Fig. 2e.