25 30 35 40 FWHM (cm -1 ) 25 30 35 40 0 10 20 30 2636 2638 2640 2642 2644 2646 2648 Raman shift (cm -1 ) B (T) 0 10 20 30 2666 2668 2670 2672 2674 2676 2678 B (T) a) d) b) c) FIG. 2: (Color online) a) FWHM and b) Raman shift of the low-energy component of the 2 D band as a function of the magnetic field. c) FWHM and d) Raman shift of the high- energy component of the 2 D band as a function of the mag- netic field. Solid red lines are calculated with our model (see text). bine radiativ ely producing a scattered photon. In the ab- sence of the magnetic field, the trajectories are straight lines, so tha t in order to meet at the same point with opposite mo menta and contribute to the Raman scatter- ing signal, th e electron and the hole must necessarily be scattered bac kwards during the phonon emission. 29 This fixes the pho non momentum ℏ q (measured from the K or K ′ point) as q = p + p $^{′}$, where ℏ p = ℏ ω$_{in}$/ (2 v ) and ℏ p ′ = ℏ ( ω$_{in}$ − 2 ω$_{ph}$ ) / (2 v ) are the electronic momenta (also measur ed from the Dirac points) before and af- ter the phon on emission, ω$_{in}$ is the excitation frequency, ω$_{ph}$ is the p honon frequency, and v is the electronic ve- locity (the s lope of the Dirac cones). A slight spread in the phon on momentum due to the quantum uncer- tainty, | q − p − p $^{′}$|  ∼ 2 γ/v (2 γ being the electron inelas- tic scattering rate), gives a contribution to the width of the 2 D peak , ∼ 2 γ ( v$_{ph}$/v ), where v$_{ph}$ = dω$_{ph}$/dq is the phonon grou p velocity. 29 In a magn etic field, the electron and hole trajectories are no longe r straight lines but, because of the Lorentz force that ac ts on charged particles in a magnetic field, they corresp ond to circular cyclotron orbits. As a result, one can see from Fig. 3 that (i) phonons with smaller momenta, q = p cos ϕ + p $^{′}$cos ϕ $^{′}$, can be emitted, and (ii) since eac h phonon can be emitted at an arbitrary in- stant in time, the length of the arc describing the electron trajectory is random [not exceeding the electron mean free path v/ ( 2 γ )], and so are the angles ϕ, ϕ $^{′}$. Note that the frequenc ies of the two emitted phonons remain equal even with an applied magnetic field due to the symmetry under C$_{2}$ ro tation around the axis perpendicular to the crystal plane. 40 Tuning the magnetic field is, in this sense, equivalent to changing the resonant conditions of the Ra- man scatter ing process at a fixed excitation wavelength and allows e xploring part of the phonon band structure closer to the K point. Fact (i) results in the overall red shift of the Raman peak, while fact (ii) introduces an additional spread in q , and contributes significantly to the broadening of the peak as observed through Raman scattering measurements. To produce the observed effects, the electron and the hole do not have to complete a full orbit. The probability of this latter event vanishes as e − 2 πR (2 γ/v $^{)}$, where R = p ( eB/ ℏ c ) − 1 is the cyclotron radius. This implies that the separation between the electronic Landau levels, ℏ ω$_{c}$ = ℏ v/R , may still be smaller than their broadening 2 ℏ γ and, in our experiment, this is still the case even at B = 30 T. In other words, even magnetic fields far from the quantization limit can give a noticeable effect. A closely related effect has been discussed in the context of density- density response of a degenerate electron gas in a non- quantizing magnetic field $^{30}$. To obtain some more quantitative information about the behavior of the 2 D peak in magnetic fields, we cal- culate the Raman matrix element M ( q ) for a given phonon wave vector q in a clean graphene monolayer. It is convenient to perform the calculation in the coor- dinate representation, analogously to the calculation for In the following, we show that our observations are due to the finite curvature of the trajectories of the photo- excited electrons and holes in the magnetic field. The main idea is illustrated in Fig. 3. In the semi-classical real-space picture of the Raman process, 29 the incident photon creates an electron and the hole with opposite momenta at an arbitrary location within the laser spot. They subsequently propagate along the classical trajec- tories, and emit phonons. If they meet at some other location, again with opposite momenta, they can recom- measured from the K point, is q ≈ 0 . 24 ˚ A − 1 at 1.7 eV excitation. Thus, q ≫ 1 /l$_{B}$ and the Kohn anomaly re- mains inaccessible for these phonons even at our highest fields. This is in striking contrast with the main first- order Raman feature, the so-called G band due to the doubly degenerate E$_{2}$$_{g}$ optical phonons at the Γ point of the phonon band structure. These phonons are directly in the region of the Kohn anomaly, and their frequency and lifetime are noticeably affected even by a moderate gate voltage. 25,26 In strong magnetic fields, the G band exhibits a pronounced magneto-phonon effect, 18 as the phonon state is modified by the coupling to electronic inter-Landau-level transitions. 27,28 3