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Phonon Spectroscopy of the Electron-Hole-Liquid W PHONON SPECTROSCOPY OF THE ELECTRON-HOLE-LIQUID W. Dietsche, S. Kirch, J. Wolfe To cite this version: W. Dietsche, S. Kirch, J. Wolfe. PHONON SPECTROSCOPY OF THE ELECTRON- HOLE-LIQUID. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-447-C6-449. 10.1051/jphyscol:19816129. jpa-00221192 HAL Id: jpa-00221192 https://hal.archives-ouvertes.fr/jpa-00221192 Submitted on 1 Jan 1981 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAI, DE PHYSIQUE CoZZoque C6, suppZe'ment au nOl2, Tome 42, de'cembre 1981 page C6-447 PHONON SPECTROSCOPY OF THE ELECTRON-HOLE-LIQUID W. ~ietschejS.J. Kirch and J.P. Wolfe Physics Department and Materials Research ihboratory, University of IZZinois at Urbana-Champaign, Urbana, IL. 61 801, U. S. A. Abstract.-We have observed the 2kF cut-off in the phonon absorption of electron-hole droplets in Ge and measured the deformation potential. Photoexcited carriers in Ge at low temperatures condense into metallic drop- lets of electron-hole liquid (EHL).' These droplets provide a unique, tailorable system for studying the electron-phonon interaction in a Fermi liquid. The inter- 2 action of phonons with EHL was considered theoretically by Keldysh and has been studied experimentally using heat In contrast, we have employed mono- chromatic phonons5 to examine the frequency dependence of the absorption over the range of 150 - 500 GHz. The conservation of momentum and energy in the electron- phonon scattering process implies that only phonons with wave vectors up to twice the Fermi wave vector are absorbed leading to a 2k cut-off. One unique feature -- F of the electron-hole liquid is that k can be changed by applying crystal stress, a F feature which we have exploited. The inset in Fig. 1 shows our experimental set-up. Two superconducting tunnel junctions, a PbBi generator (G) and an A1 detector (D),were placed on opposite faces of the ultra-pure Ge crystal near one edge. A cloud of EHL droplets was created at that face using a cw Nd: YALG laser (A = 1.06um). The position, size, and shape 6 of the cloud was determined by directly imaging its recombination luminescence. We studied phonons propagating in the [Ill] direction, and found a measurable absorption only for longitudinal phonons (LA). In the [Ill] direction, phonon absorption is expected to be dominated by the single [lll] valley, because all the other valleys (and the holes) have much smaller cut-off frequencies. Application of stress along the [lli] direction gradually depopulates the [Ill] valley. This leads to a reduction of k along [Ill] and thus to a reduction in the cut-off F frequency of the phonons. Two LA phonon spectra taken at zero stress are shown in Fig. 1. The frequency is varied by sweeping the generator bias voltage, while the monochromatic signal is provided by an additional pulse modulation. Time of flight separation allowed resolution of the different modes. Two features were typical of all the data: a rise in intensity which begins at 150 Qiz (Fl) due to the detector threshold and a decrease which ends at 530 GHz (F2) due to isotope scattering. "Present address : Physik Department, TU Miinchen, F.R.G. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816129 JOURNAL DE PHYSIQUE PHONON ENERGY (mrV) Fig. 1: Phonon signal vs. frequency, zero stress. L I I I 1 0 200 400 600 PHONON FREQUENCY IGHr) Between F1 and F2, the signal consists of a monochromatic part and a background. This background is a common feature in tunnel-junction spectroscopy and is attributed to 2A-phonons and inelastic decay products. Below F1 and above F2 only background phonons are detected. Between F1 and F2 the background will lie 5 between the interpolations (1) and (2) as inferred from earlier spectroscopic work. The actual cloud-on and cloud-off phonon intensities can now be compared. Assuming a phonon absorption of the form I = I exp (-d/l), where d is the effective EHL thickness and 1 is the absorption length, the resulting d/l are plotted in Fig. 2a. The ends of the error bars indicate the results obtained by using the two alter- native backgrounds. A similar procedure led to the plots in Fig. 2 (b) and (c) for two moderate stresses. PHONON ENERGY (msVI Fig. 2: d(ef f . EHL thickness)/l (absorption length) vs. frequency PHONON FREQUENCY ($Hz) The dashed lines in Fig. 2 are fits to deformation potential scattering theory following the procedure of on well.^ The theoretical cut-of f s are rather broad because the sound velocity is comparable to the Fermivelocity in the EHL. The frequency dependence of our data agrees remarkably well with the theory. At zero stress the experimental cut-off was obscured by the isotope scattering. At increasing stress the cut-off is observed to move through the experimental frequency range. An effective thickness, d zllym, was determined from an analysis of the imaging data. This value is sufficiently larger than a typical droplet radius of about 2um. With this value of d, the absorption data of Fig. 2 yield the defor- 2 mation potential Z = ( + Z )' = (15 f?)eV independent of stress. u d Our value of the phonon deformation potential is close to the static deformation 2 potential,8 49 eV for single electrons in Ge. In contrast, a recent theoretical 2 prediction9 for the screened electrons in the EHL yielded 149 eV . In summary, by using the method of phonon spectroscopy we have obtained the first experimental measurement of the phonon deformation potential of EHL in Ge and demonstrated a fundamental property of this Fermi liquid -- the 2kF cut-off. This work was supported by NSF under the ?lRL Grant PMR-77-23999. REFERENCES 1. T. M. Rice and J. C. Hensel, T. G. Phillips, and G. A. Thomas, Solid State Physics 32 (1977). 2. L. V. Keldysh, Pis'ma Zh. Eksp. Teor. Fiz. 2, 100 (1976) [JETP Lett. 3,86 (197 6) 1 . 3. V. S. Bagaev, L. V.Keldysh, M. N. Sibeldin, and V. A. Tsvetkov, Zh. Eksp. Teor Fiz. 2,702 (1976) [Sov. Phys. JETP 43, 362 (1976)l. 4. J. C. Hensel and R. C. Dynes, Phys. Rev. Lett. 2, 969 (1977). 5. H. Kinder, 2. Phys. 262, 295 (1973); H. Kinder and W. Dietsche in Phonon Scattering in Solids (L. T. Challis, V. W. Rampton and A. F. G. Wyatt, eds. 1976), p. 199. 6. M. Greenstein and J. P. Wolfe, Phys. Rev. Lett. 41, 715 (1978). 7. E. M. Conwell, Sol. State Phys. Suppl. 2 (Academic, N.Y., 1967). 8. K. Kurase, K. Enjouji, and E. Otsuka, J. Phys. Soc. Jpn. 2, 1248 (1970). 9. R. S. Markiewicz, Phys. Stat. Sol. Bg, 659 (1977). .
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