Spontaneous decay of long-wavelength acoustic phonons

Berke, Andrew E.; Mayer, A P; Wehner, R.K.

doi:10.1088/0022-3719/21/12/014

Cited by 33 publications

(22 citation statements)

References 22 publications

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“…The intrinsic phonon lifetime (due to p − p interaction) is thus dominated by spontaneous down-conversion decay towards lower energy phonons (Fig.2.1-d). In the case of a normal phonon dispersion, it has been discussed that four-phonon interaction is the lowest order decay process [23]. Three-phonon decay processes are kinematically not allowed.…”

Section: The Phonon-phonon Interactionmentioning

confidence: 99%

“…Structures at about 40 − 46 and 58 − 63 meV and possibly at 23 − 29 and 75 − 85 meV are observed (Fig.4.12-b), suggesting that there is coupling to bosons at these energies. The multiple features show marked difference from the magnetic excitation The four shaded areas correspond to energies of (23)(24)(25)(26)(27)(28)(29), (40)(41)(42)(43)(44)(45)(46), (58)(59)(60)(61)(62)(63) and (75)(76)(77)(78)(79)(80)(81)(82)(83)(84)(85) meV where the fine features fall in. (c) The phonon density of states for LSCO measured from neutron scattering.…”

Section: Importance Of the Electron-phonon Interaction In Htscmentioning

confidence: 99%

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Electron-Phonon Interaction in Conventional and Unconventional Superconductors

Aynajian

2011

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Asking most scientists if it is worth to have a closer look at the phonon spectra of conventional superconductors like niobium and lead using inelastic neutron scattering, the answers would be quite discouraging. First of all, there exists the famous microscopic theory of Bardeen, Cooper, and Schrieffer (1957) known as the BCS theory, which explains nearly all aspects of conventional superconductivity. Second, the worldwide interest is oriented towards high temperature superconductivity in cuprates and heavy fermion systems. Thus the first experiments of this thesis, which addressed the phonon linewidths of superconducting niobium and lead, were only intended as a short testbed of the resolution properties of a new high-resolution neutron spectrometer at the research reactor FRM II. This new generation spectrometer, TRISP (triple axis spin echo), allows us to measure phonon linewidths over large parts of the momentum space, with a resolution in the sub-μeV range, i.e., two orders of magnitude better than what is achieved by conventional triple-axis neutron spectrometers.It was pointed out by Philip Allen that the phonon linewidth is proportional to the electron-phonon coupling parameter λ, which is an essential parameter describing the formation of Cooper pairs in phonon mediated superconductors. The superconducting energy gap, whose magnitude, symmetry, and temperature dependence are intimately related to Cooper pairing, can also be directly determined in phonon linewidth measurements. The opening of the gap results in a redistribution of electronic states and excitations in the immediate vicinity of the Fermi surface. Electron-phonon scattering is suppressed for phonon energies below the gap 2Δ(T ) due to the stability of the Cooper pairs below T c . Discontinuities in the phonon linewidths are thus expected when the phonon energy exceeds 2Δ(T ). Consequently, the gap and its momentum dependent anisotropy (and also the pairing symmetry) can be accurately resolved from a map of these discontinuities in different crystallographic directions. While phonon energies are highly sensitive to the superconducting energy gap, their momenta can serve as a similarly comprehensive probe of the geometry of the Fermi surface, which also leaves an imprint on the phonon linewidth. Phonons which connect nearly parallel segments of the Fermi surface exhibit an enhanced electron-phonon scattering probability, and thus linewidth extrema (termed Kohn anomalies) are expected. A full image of the underlying Fermi surface is contained in a map of these Kohn anomalies.The phonon-linewidth spectra of these long-known superconductors presented in this thesis showed new and unexpected features that were not visible in previous low resolution experiments. Anomalies were observed at phonon energies corresponding to the magnitude of the superconducting gap, 2Δ, in the electron spectrum. These features were not only visible, as expected, below the superconducting transition temperature T c , but persist to much higher temperatures. A...

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Section: The Phonon-phonon Interactionmentioning

confidence: 99%

Section: Importance Of the Electron-phonon Interaction In Htscmentioning

confidence: 99%

Electron-Phonon Interaction in Conventional and Unconventional Superconductors

Aynajian

2011

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“…[4][5][6] The propagation in the regime where the latter two effects are dominant is called quasidiffusion. [7][8][9][10] Because of a highlyfrequency-dependent decay rate of phonons A Ϫ1 ϭA 5 (A is a constant depending on phonon polarization and is the frequency͒, there exists a characteristic frequency (t) at an elapsed time t determined by A ( )ϭt.…”

Section: ͓S0163-1829͑97͒01645-7͔mentioning

confidence: 99%

Numerical evidence for the bottleneck frequency of quasidiffusive acoustic phonons

Tamura

1997

Phys. Rev. B

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A kinetic equation on quasidiffusion of phonons was recently analyzed by Esipov and he predicted the existence of a bottleneck frequency ( BN ) which separates the phonons decaying from those diffusing to a detector. We have solved numerically the kinetic equation and obtained the temporal evolution of phonon concentration excited at the center of a spherical sample. We have also performed Monte Carlo simulations of phonon propagation in the same geometry. At a time much later than the ballistic arrival time of phonons, both sets of results exhibit a sharp peak in the phonon concentration around the predicted BN . With Monte Carlo simulations we have also confirmed the same relaxation rate for the phonons of frequencies Ͻ BN . ͓S0163-1829͑97͒01645-7͔Propagation of high-frequency acoustic phonons in nonmetallic crystals at low temperatures is governed by the ͑1͒ focusing effect due to the anisotropy of the lattice, 1,2 ͑2͒ elastic scattering due to foreign and isotopic impurities, 3 and ͑3͒ anharmonic decay via three-phonon interaction. [4][5][6] The propagation in the regime where the latter two effects are dominant is called quasidiffusion. 7-10 Because of a highlyfrequency-dependent decay rate of phonons A Ϫ1 ϭA 5 (A is a constant depending on phonon polarization and is the frequency͒, there exists a characteristic frequency (t) at an elapsed time t determined by A ( )ϭt. This frequency gives the length l of space expansion at a time t as lϳv͓ A ( ) I ( )͔ 1/2 ϳt 9/10 , where v is the Debye velocity and I Ϫ1 ϭB 4 (B is a constant͒ is the elastic scattering rate. 7,8 Thus the average phonon distribution in a sample spreads more slowly than in ballistic propagation but faster than in normal diffusion. More recent observations show that the characteristic behavior of quasidiffusive phonons appears in the time trace of the detected phonon signal as an exponentially decaying tail at a time much later than the ballistic time of flight t b through the sample. [11][12][13] Experimentally, this exponential behavior has been observed for several semiconducting samples of slab geometry such as silicon, germanium, and GaAs with a photoexcitation technique at a low input power level. 13 It is critical for observing the exponential tails to remove liquid helium from the surface where the phonons are excited. Otherwise, the high-frequency phonons excited at the sample surface are lost into the helium bath and the quasidiffusive tail originating from these phonons is hardly observed. The quasidiffusion is also important in analyzing the phonon signal produced by high-energy particles in a crystal. [14][15][16][17][18] The applicability of a quasidiffusive model is seen by comparing the experimental heat pulses with Monte Carlo simulations. [19][20][21] Originally a simple one-branch model was proposed, where three-phonon polarizations were approximated by a single mode with the Debye velocity. 19 The Monte Carlo simulations based on this model can reproduce the exponential tail in the time-of-flight spectrum of phonons arrivi...

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“…These second-generation phonons are typically acoustic and in turn decay into even lower energy vibrations, eventually reaching equilibrium with the thermal bath. As a consequence of the reduced density of available decay channels and of the vanishing behaviour of the anharmonic matrix elements in the long-wavelength limit [5], the decay rates of the second-generation acoustic modes are usually much slower than those of first generation phonons, particularly when the latter belong to the optic branches [6]. It can be seen from this scenario that a slow phonon decay rate with respect to the phonon generation rate can potentially induce non-thermal phonon populations.…”

Section: Introductionmentioning

confidence: 99%

“…They range from truly 3D crystals (diamond), to quasi-or truly two-dimensional (2D) systems (graphite, graphene), to one-dimensional (1D) structures (SWNTs); in addition, their vibrational modes have been studied extensively and reliably with first-principles simulations [6]. In this paper we discuss recent advances in our understanding of ph-ph interactions in low-dimensional carbon systems.…”

Section: Introductionmentioning

confidence: 99%

Lattice anharmonicity in low‐dimensional carbon systems

Bonini

Rao

et al. 2008

Physica Status Solidi (b)

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The anharmonic properties of low‐dimensional carbon crystal lattices are reviewed. The energy and crystal momentum conservation rules in two‐ and one‐dimensional crystals lead to a drastic reduction of the phase space available for anharmonic phonon decay. This is illustrated with first principles calculations of the anharmonic properties of graphite and graphene. Experimental Raman linewidth data for the Radial Breathing Mode (RBM) in suspended single‐walled carbon nanotubes are also interpreted in terms of a simple model in which a phonon decay bottleneck induced by the low dimensionality leads to a population time dependence in which a fast initial decay is followed by a slow decay determined by the decay rate of a large population of secondary phonons. These results are key to understanding the combined dynamics of electrons and phonons that determines the electrical transport properties in low‐dimensional carbon nanostructures. In the case of the RBM in carbon nanotubes, they raise the intriguing possibility of using the linewidth of the Raman peak to determine the chirality of the nanotube. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Spontaneous decay of long-wavelength acoustic phonons

Cited by 33 publications

References 22 publications

Electron-Phonon Interaction in Conventional and Unconventional Superconductors

Electron-Phonon Interaction in Conventional and Unconventional Superconductors

Numerical evidence for the bottleneck frequency of quasidiffusive acoustic phonons

Lattice anharmonicity in low‐dimensional carbon systems

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