The electron-phonon matrix element in the Dirac point of graphene
Abstract
The chief aim of this paper is to derive the matrix element of electron-phonon interaction in graphene as a function of phonon wave vector. The tight binding model, harmonic crystal approximation, and deformation potential approximation were employed for obtaining the matrix element. Required microscopic parameters are available in the current literature. This technique allows the most precise derivation of the electronphonon matrix element in graphene based on the semiempirical models. Scattering of electrons from the Dirac point is considered as most important. The 2D plots of the e-ph matrix element absolute value as a function of the phonon wave vector for in-plane modes are given as a result. These plots show the high anisotropy of the e-ph matrix element and singularities in high symmetry points. The results are in agreement with the long-wavelength approximation.
Supporting agencies: We would like to thank A. Ya. Vul’ and A. T. Dideykin for their attention. This work was supported by the Dynasty foundation Grant for PhD students and by the St. Petersburg government grant for PhD students. The work was partly supported by programs of the Presidium of the Russian Academy of Sciences “Fundamental Foundations of the Technologies of Nanostructures and Nanomaterials” and “Quantum Mesoscopic and Unordered Systems”.
About the Authors
S. V. Koniakhin
Ioffe Physical-Technical Institute of the Russian Academy of Sciences; St. Petersburg Academic University - Nanotechnology Research and Education Centre of the Russian Academy of Sciences
Russian Federation
Russian Federation
194021, St. Petersburg
E. D. Eidelman
Ioffe Physical-Technical Institute of the Russian Academy of Sciences; St. Petersburg Academic University - Nanotechnology Research and Education Centre of the Russian Academy of Sciences; St. Petersburg Chemical Pharmaceutical Academy
Russian Federation
Russian Federation
194021, St. Petersburg; 194021 St. Petersburg; 197022 St. Petersburg
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Review
For citations:
Koniakhin S.V., Eidelman E.D. The electron-phonon matrix element in the Dirac point of graphene. Nanosystems: Physics, Chemistry, Mathematics. 2014;5(1):142-147.
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