Numerical experiments on phonon properties of isotope and vacancy-type disordered graphene

Abstract

We have studied phonon properties of graphene theoretically with different concentrations of 13C isotope and vacancy-type defects. The forced vibrational method, which is based on the mechanical resonance to extract the pure vibrational eigenmodes by numerical simulation, has been employed to compute the phonon density of states (PDOSs) and mode pattern of isotope-disordered graphene as well as a combined isotope and vacancy-type defective graphene structure. We observe a linear reduction of the E2g mode frequencies with an increase in 13C concentration due to the reduced mass variation of the isotope mixture. We find a downshift of the E2g mode of 65cm−1, which is a very good agreement with the experimental results, and the phonon frequencies described by the simple harmonic oscillator model. The vacancy-type defects break down the phonon degeneracy at the Г point of the LO and TO modes, distort and shift down the phonon density of states significantly. The PDOS peaks for the combined isotope and vacancy-type defects show the remarkable increase in the low-frequency region induced by their defect formations. Due to phonon scattering by 13C isotope or vacancies, some graphene phonon wave functions become localized in the real space. Our numerical experiments reveal that the lattice vibrations in the defective graphene show the remarkably different properties such as spatial localization of lattice vibrations due to their random structures from those in the perfect graphene. The calculated typical mode patterns for in-plane K point optical phonon modes indicate that the features of strongly localized state depend on the defect density, and the phonon is localized strongly within a region of several nanometers in the random percolation network structures. In particular, for in-plane K point optical phonon modes, a typical localization length is on the order of ≈7nm for isotope impurities, ≈5nm for vacancy-type defects and ≈6nm for mixed-type defects at high defect concentrations of 30%. Our findings can be useful for the interpretation of experiments on infrared, Raman, and neutron-diffraction spectra of defective graphene, as well as in the study of a wide variety of other physical properties such as thermal conductivity, specific heat capacity, and electron–phonon interaction.