Effects of electron-electron interactions on the electronic Raman scattering of graphite in high magnetic fields

Abstract

We report the observation of strongly temperature ($T$)-dependent spectral lines in electronic Raman-scattering spectra of graphite in a high magnetic field up to 45 T applied along the $c$ axis. The magnetic field quantizes the in-plane motion, while the out-of-plane motion remains free, effectively reducing the system dimension from 3 to 1. Optically created electron-hole pairs interact with, or shake up, the one-dimensional Fermi sea in the lowest Landau subbands. Based on the Tomonaga-Luttinger liquid theory, we show that interaction effects modify the spectral line shape from ${(\ensuremath{\omega}\ensuremath{-}\ensuremath{\Delta})}^{\ensuremath{-}1/2}$ to ${(\ensuremath{\omega}\ensuremath{-}\ensuremath{\Delta})}^{2\ensuremath{\alpha}\ensuremath{-}1/2}$ at $T$ = 0. At finite $T$, we predict a thermal broadening factor that increases linearly with $T$. Our model reproduces the observed $T$-dependent line shape, determining the electron-electron interaction parameter $\ensuremath{\alpha}$ to be $\ensuremath{\sim}$0.05 at 40 T.