Observation of Magnetophonon Resonance of Dirac Fermions in Graphite

Coherent coupling of Dirac fermion magnetoexcitons with an optical phonon is observed in graphite as marked magnetic-field dependent splittings and anticrossing behavior of the two coupled modes. The sharp magnetophonon resonance occurs in regions of the graphite sample with properties of superior single-layer graphene having enhanced lifetimes of Dirac fermions. The greatly reduced carrier broadening to values below the graphene electron-phonon coupling constant explains the appearance of sharp resonances that reveal a fundamental interaction of Dirac fermions.

Figure 1

(a) Schematic visualizations of the phonon and magnetoexciton modes involved in the magnetophonon resonance (MPR). The graphene layer is illustrated in the $x\mathrm{\text{−}}y$ plane. The magnetic-field direction in the experiment is tilted by $\theta =20°$ from the $z$ axis. (b) Energies of two coupled normal modes versus magnetic field close to the MPR at around $B=5\mathrm{T}$. (c) and (d) Raman spectra acquired at 4.55 and 5.6 T, respectively. The energies of the two coupled modes ${\omega }_{-}$ and ${\omega }_{+}$ are indicated by the two dots in panel (b). The origin of the additional peak ${\omega }_I$ is discussed later in the text.

Figure 2

(a) and (b) Magnetic-field dependence of the $E_{2g}$ phonon spectra taken at two representative regions of the sample. One region displays significant MPR effect while the other does not. The smooth curves are Lorentzian fits to the data. (c) Mode energy evolution extracted from the spectra displayed in (a).

Figure 3

Detailed Raman spectra of the main MPR observed for magnetic fields ranging from 4.2 to 6.4 T. The theoretical calculation of the anticrossing associated to the magnetophonon resonance (MPR) at 5 T (see text) is indicated by dotted lines. The spectral component that corresponds to the two coupled modes is highlighted. The spectra are shifted vertically so that each component taken at a given magnetic field has its peak aligned at that magnetic field.

Figure 4

MPR induced anticrossing behavior of the coupled modes. The two upper and lower lines in (a) are the theoretical fits of the energy of the two branches while the line in the middle is the Landau level transition $-1\to 2$ or $-2\to 1$. The two lines in (b) correspond to the full-width-at-half-maximum (FWHM) of the coupled modes. The triangles are the experimental data. The inset reports the magnetic-field evolution of the ${\omega }_I$ mode.