Comment on "Missing 2k(F) response for composite fermions in phonon drag".

In a recent Letter Zelakiewicz et al. report on the mysterious absence of a Kohn anomaly in the phonon mediated drag of composite fermions (CFs) in double layer electron systems [1]. In particular the temperature dependence and the magnitude of the drag transresistivity when moving away from ν = 1/2 are claimed to be inconsistent with current expectations for CFs. Here we show that all the results in [1] can be simply explained by phonon drag of free electrons in the lowest Landau level [2]. In this model the electron-phonon interaction follows a universal behavior when plotted as a function of lB/λp where λp = h̄v/kBT is the typical phonon wave length for acoustic phonons with a sound velocity v and lB = (h̄/eB) 1/2 is the magnetic length. This universality entails a scaling of the phonon mediated drag ρD(T,B) = ρs(ν)f(lB/λp) with a filling factor dependent normalization factor ρs(ν) and a scaling function f(lB/λp). In Fig. 1 the results of such an analysis are shown. The drag transresistivity ρD as presented in [1], arbitrarily normalized to its value ρs at TB −1/2 = 0.6 TK, is plotted as a function of TB(∝ lB/λp). Indeed, as indicated by the lines, all the drag data presented in [1] scale to a single function in particular around the position where a maximum occurs in ρD/T . The identical dependence of ρs on B and the inverse electron concentration 1/n (insets in Fig. 1) show that ρs indeed only depends on ν = hn/eB supplying an additional indication for the validity of a free electron model for all the data presented in [1]. It was indicated in [1] that such a simple rescaling does not seem to work for data at ν = 1/4, where a 10% lower position of the ‘Kohn-anomaly maximum’ was observed. We note, however, that these data are taken at a considerably lower electron concentration. On the other hand, when extrapolating the data from Fig. 2a of [1] to lower fields, the maximum for ν = 3/4 definitely occurs at much lower T than that for ν = 1/2. Therefore it seems that the data obtained on the 1/4-3/4 CF-family are far from being conclusive to discriminate between a CF model and a free electron picture. Moreover, it is worthwhile mentioning that experiments on the direct phonon drag of CFs measured by thermopower (TEP) showed that any CF signature disappears as soon as the related minima in ρxx at odd denominator filling factors start to weaken [3]. At the high temperatures as used in [1] the phonon drag TEP is well described by the model of non-interacting Landauquantized electrons [4]. Of course it can not be excluded that CFs still exist at these high temperatures. However, no specific property which can not be simply related to free electrons is observed in phonon drag and a CF interpretation becomes meaningless. The fact that even the ν = 1/3 and ν = 2/3 minima (inset of Fig. 2a in [1]) are merely visible in ρD and very weakly developed in ρxx strongly proposes that it is sufficient to use a model as in [4] for a proper analysis of the data in [1]. In conclusion we have shown that all the data on the phonon mediated drag in coupled two-dimensional electron systems in high magnetic fields presented in [1] can be straightforwardly explained in a framework of electrons in the lowest Landau level without the need to use any new CF models.