On the forbidden graphene’s ZO (out-of-plane optic) phononic band-analog vibrational modes in fullerenes

The study of nanostructures’ vibrational properties is at the core of nanoscience research. They are known to represent a fingerprint of the system as well as to hint the underlying nature of chemical bonds. In this work, we focus on addressing how the vibrational density of states (VDOS) of the carbon fullerene family (Cn: n = 20 → 720 atoms) evolves from the molecular to the bulk material (graphene) behavior using density functional theory. We find that the fullerene’s VDOS smoothly converges to the graphene characteristic line-shape, with the only noticeable discrepancy in the frequency range of the out-of-plane optic (ZO) phonon band. From a comparison of both systems we obtain as main results that: (1) The pentagonal faces in the fullerenes impede the existence of the analog of the high frequency graphene’s ZO phonons, (2) which in the context of phonons could be interpreted as a compression (by 43%) of the ZO phonon band by decreasing its maximum allowed radial-optic vibration frequency. And 3) as a result, the deviation of fullerene’s VDOS relative to graphene may hold important thermodynamical implications, such as larger heat capacities compared to graphene at room-temperature. These results provide insights that can be extrapolated to other nanostructures containing pentagonal rings or pentagonal defects.

Electronic exchange-correlation, many-body effect issues on first-principles calculations of bulk SiC polytypes

The first-principles Projector-Augmented Wave method (PAW) is used to investigate the electronic, phonon band structure and dielectric properties of four bulk silicon carbide (SiC) polytypes. We employ PAW pseudopotential density functional theory with Perdew, Burke and Ernzerhof (PBE) and hybrid HSE06 approximations of the exchange-correlation functional. Many-body effects are incorporated using the GW approximation of the self-interaction to study SiC properties. GW method in its single-shot variant, which is based on the many-body perturbation theory (MBPT), is used to calculate the quasi-particle (QP) energies of the band structure and the dielectric properties for different polytypes. The electronic band structure determination within GW method uses the Wannier procedure where a basis set of maximally localized Wannier function (MLWF) is constructed to interpolate the QP energies of few regular mesh k-points to the high-symmetry lines in Brillouin zone. As a consequence of QP correction to the Kohn–Sham energies, bandgap is increased by upto 3 eV in case of 4H–SiC, as compared to PBE bandgap. GW results are comparable to those of hybrid functionals and are in good agreement with the experimental results. The optical properties are then studied within PBE, HSE06 and include many-body effects. In addition, the phonon band structure has been investigated within HSE06 and compared to previous PBE results. We found good agreement with the previous theoretical results and the experimental available data.