Effects of electron-phonon coupling on Landau levels in graphene

Abstract

We calculate the density of states (DOS) in graphene for electrons coupled to a phonon in an external magnetic field. We find that coupling to an Einstein mode of frequency ${\omega }_E$ not only shifts and broadens the Landau levels (LLs), but radically alters the DOS by introducing a new set of peaks at energies $E_n\pm {\omega }_E$, where $E_n$ is the energy of the $n$th LL. If one of these new peaks lies sufficiently close to a LL, it causes the LL to split in two; if the system contains an energy gap, a LL may be split in three. The new peaks occur outside the interval $(-{\omega }_E,{\omega }_E)$, leaving the LLs in that interval largely unaffected. If the chemical potential is greater than the phonon frequency, the zeroth LL lies outside the interval and can be split, eliminating its association with a single Dirac point. We find that coupling to an extended phonon distribution such as a Lorentzian or Debye spectrum does not qualitatively alter these results.

16 pages, 17 figures, 1 table. Accepted for publication in PRB

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• Magneto-optical conductivity in graphene including electron-phonon coupling
• Magneto-optics of general pseudospin-s two-dimensional Dirac-Weyl fermions
• Electron-phonon bound states in graphene in a perpendicular magnetic field
• Observation of Giant Quantized Phonon Modes in Graphene via Tunneling Spectra
• Electron-phonon correlations on spin texture of gapped helical Dirac Fermions