Extended Data Fig. 4: Simulated phonon dispersion and PDOS.
From: Imaging of isotope diffusion using atomic-scale vibrational spectroscopy
The phonon dispersion (left) and PDOS (right) of 12C and 13C graphene obtained by DFPT calculations in Quantum Espresso. The energy difference between 12C and 13C graphene is 7.7 meV at the highest energy peak in PDOS corresponding to the LO mode and 6.7 meV at the second highest energy peak which is mainly contributed from the LO/TO mode. The interatomic force constants calculated from DFPT is, for instance, 52.4 eV Å−2 for the in-plane direction at Γ. This calculation was performed to estimate the energy shift of the PDOS of 12C and 13C with the simple model. To reproduce the experimental spectra, full calculation considering the charge modulation in the higher-order Brillouin Zone is necessary, although such calculation is beyond the scope of this study and is not addressed here.
