# Effect of a magnetic field on the two-phonon Raman scattering in graphene 

$^{3}$Laboratoire de Physique et Mod´ elisation des Milieux Condens´ es, Universit´ e Joseph Fourier and CNRS, 25 rue des Martyrs, 38042 Grenoble, France 

$^{5}$School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA 

C. Faugeras, 1 P. Kossacki, 1, 2 D. M. Basko, 3 M. Amado, 1, 4 

M. Sprinkle, 5 C. Berger, 5, 6 W.A. de Heer, 5 and M. Potemski 1 

$^{1}$LNCMI-CNRS, BP 166, 38042 Grenoble, France 

$^{2}$Institute of Experimental Physics, University of Warsaw, Poland 

$^{4}$QNS-GISC, Departamento de F´ısica de Materiales, Universidad Complutense, E-28040 Madrid, Spain 

$^{6}$CNRS-Institut N ´ e el, BP 166, 38042 Grenoble Cedex 9, France. 

We have studied, both experimentally and theoretically, the change of the so-called 2 D band of the Raman scattering spectrum of graphene (the two-phonon peak near 2700 cm − $^{1}$) in an external magnetic field applied perpendicular to the graphene crystal plane at liquid helium temperature. A shift to lower frequency and broadening of this band is observed as the magnetic field is increased from 0 to 33 T. At fields up to 5–10 T the changes are quadratic in the field while they become linear at higher magnetic fields. This effect is explained by the curving of the quasiclassical trajectories of the photo-excited electrons and holes in the magnetic field, which enables us (i) to extract the electron inelastic scattering rate, and (ii) to conclude that electronic scattering accounts for about half of the measured width of the 2 D peak. 

Graphene, a two-dimensional plane of carbon atoms arranged in a honeycomb lattice, has stimulated many experimental and theoretical efforts to study and un- derstand its exotic electronic and optical properties $^{1}$. Graphene can be produced by mechanical exfoliation of bulk graphite $^{2}$, by the decomposition of a SiC substrate at high temperatures, 3 or by epitaxial growth on differ- ent metal surfaces $^{4}$. Graphene on SiC is well adapted for optical measurements as samples are of macroscopic size and lie on a substrate which can be insulating, and hence, transparent in a wide, from far-infrared to visible spectral range. 

Raman scattering is a key element to graphene studies as it is a reliable and non-destructive technique to estab- lish the monolayer character of a graphene specimen 5,6 or the negligeable interlayer coupling in multilayer epitaxial graphene (MEG) samples $^{7}$. This relies on the analysis of the shape of the observed 2 D band feature (the two- phonon peak around 2700 cm − $^{1}$, also referred as D ∗ or G $^{′}$) which is the second-order overtone of the D band. While defects (in a general meaning – impurities, inter- face roughness, etc.) are needed for the D band to be observed, the 2 D band is always seen and it even appears as the most pronounced feature in the Raman scattering spectrum of graphene. Because of the doubly-resonant nature of the D band 8,9 and the fully-resonant nature of the 2 D band, 10,11 they both show a dispersive behavior with the excitation energy, what allowed to tracing the phonon band structure of different carbon allotropes $^{12,13}$. In this paper, we show that a strong magnetic field ap- plied perpendicular to the plane of a graphene crystal significantly affects the 2 D band feature. Increasing the 

PACS numbers: 63.22.+m, 63.20.Kr, 78.30.Na, 78.67.-n 

## I. INTRODUCTION 

magnetic field up to 33 T, we observe a simultaneous red shift of the 2 D band energy and a strong broadening of the peak. 

In the following, we show that the evolution of the 2 D band in magnetic field can be understood and modelled quantitatively as a pure orbital effect of the magnetic field on the intermediate states of the Raman process, i. e., electrons and holes. The field induces circular orbits to the photo-generated electron-hole pairs, and this modifies the momenta of the optical phonons emitted during the Raman scattering process. This leads to a red shift and to a broadening of the 2 D band feature as the magnetic field is increased, an effect that we observe experimentally and describe theoretically below. We note that this effect is not specific to a graphene monolayer as the two essential ingredients are the fully-resonant nature of the 2 D peak, and the free motion of electrons in the plane. Thus, it should also be characteristic for the multilayer graphene and graphite. 

Raman scattering measurements were performed in the backscattering geometry at liquid helium temperature and in magnetic fields up to 33 T applied perpendicu- lar to the plane of the graphene crystal. A Ti:Saphire laser tuned at an accurately controlled wavelength of 720 nm (corresponding to the incident photon energy ℏ ω$_{in}$ = 1 . 722 eV) was used for excitation. Optical fibers, both with a core diameter of 200 µ m, were used for exci- tation and for collection. The resulting laser spot on the sample had a diameter of ∼ 600 µ m with a typical power of ∼ 100 mW. 

## II. SAMPLES AND EXPERIMENT 

