Comment on “Fr¨ohlich Mass in GaAs-Based Structures” S. N. Klimin and J. T. Devreese Theoretische Fysica van de Vaste Stoffen (TFVS), Universiteit Antwerpen, B-2610 Antwerpen, Belgium (Dated: January 24, 2006) 6 0 0 InarecentLetter[1],Faugerasetal. investigatethecyclotronresonance(CR)spectraofdopedGaAsquantumwell 2 structures. FromananalysisoftheirdatatheseauthorsquestionthevalidityoftheconceptoftheFr¨ohlichinteraction n andthepolaronmassinarealsystem. ItisstatedinRef. [1],thatFr¨ohlich’spolarontheorywouldpredictaresonant a J magnetopolaroncoupling nearthe longitudinalopticalphononfrequency ωLO. Becauseofthe absenceofanticrossing 6 at ω ≈ωLO in the experimental data [1] for a GaAs/AlAs quantum well, they conclude that the CR spectra “do not 2 showanysignofinteractionrelatedtothe Fr¨ohlichcoupling”,andtherefore,that“the conceptofthe polaronicmass, relatedtothis interaction,isno longereffective”(Ref. [1], p. 4). The experimentalevidence forthe interactionofthe l] electronswithsomemodeswithfrequenciesclosetothetransverseopticalphononfrequencyωTO isattributedinRef. l a [1] to the deformationpotential. However,the deformationpotential, induced by the opticalphonons near the center h of the Brillouin zone in cubic semiconductors, has only off-diagonal matrix elements involving the heavy and light s- holestates[3]. Sincetheopticalconductivityintheexperiment[1]isduetobandelectrons,theanticrossingnearωTO e cannot be interpreted in terms of the deformation electron-phonon interaction. Furthermore, the phenomenological m dielectric model of Ref. [1] does not predict the anticrossing near ωTO. . In contrast to the statement that “there is no quantum mechanical treatment of the hybrid modes” ([1], p. 1), t a such a treatment has been performed in Ref. [4]. In that paper we demonstrated [4] that in a quantum well with m sufficiently high electrondensity, mixing ofbulk-like andinterface polaropticalphonons with intrasubbandplasmons - leadstotheappearanceofhybridmagnetoplasmon-phononmodes,whichinteractwiththeelectrons. Thisinteraction d n is the renormalized Fr¨ohlich interaction. One of the frequencies of the hybrid modes, which is close to ωTO in GaAs, o provides a dominant contribution to the CR spectrum. The resulting peak positions, the frequencies of the hybrid c magnetoplasmon-phonon modes as well as the magnitude of the splitting of the CR peaks calculated in Ref. [4] are [ in good agreement with the experimental data [2]. 1 The resonant magnetopolaron coupling also appears in the recent measurements of the CR spectra for a 13 nm v wide GaAs quantum well [1]. Owing to this magnetopolaron effect, the CR peaks split near ωTO and also change 2 their positions with respect to those obtained without electron-phonon interaction. These splitting and shift of the 2 CRpeaksnearthe TO-phononfrequency predictedinRef. [4]onthe basisofthe Fr¨ohlichinteractionareclearlyseen 6 in Fig. 1. The theoretical peak positions of the CR spectra calculated within the many-polaronapproach of Ref. [4] 1 0 compare well with the experimental data [1], as distinct from the CR energies calculated without electron-phonon 6 interaction, which show no particular features in the region of the optical-phonon frequencies. 0 In conclusion, in contrast to the statement of Ref. [1] that the concept of the Fr¨ohlich polaron mass has to be / t reexamined in a real material, we conclude that this concept is valid and even necessary to interpret the CR spectra a of quantum wells, e. g., those studied in Ref. [1]. m TheauthorsacknowledgediscussionswithV.M.FominandF.Brosens. ThisworkhasbeensupportedbytheGOA - d BOF UA 2000, IUAP, FWO-V projects G.0274.01N, G.0435.03, the WOG WO.025.99 (Belgium) and the European n Commission GROWTH Programme,NANOMAT project, contract No. G5RD-CT-2001-00545. o c : v i X [1] C. Faugeras, G. Martinez, A.Riedel, R. Hey,K.J. Friedland, and Yu.Bychkov,Phys. Rev.Lett. 92, 107403 (2004). r [2] A. J. L. Poulter, J. Zeman, D. K. Maude, M. Potemski, G. Martinez, A. Riedel, R. Hey, and K. J. Friedland, Phys. Rev. a Lett. 86, 336 (2001). [3] G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, NewYork, 1975). [4] S. N.Klimin and J. T. Devreese, Phys.Rev.B 68, 245303 (2003). 2 Fig. 1. (Color online) Experimental [1] (squares) and theoretical (solid curves) CR energies of a 13 nm width GaAs/AlAs quantum well with the electron density n0 = 7×1011 cm−2 in a perpendicular magnetic field. The dashed curve represents CR energies calculated without electron-phonon interaction.