Phonon Dispersion Relations for hcp<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>at a Molar Volume of 16<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math

Reese, Randall; Sinha, Sunil K.; Brun, T. O.; Tilford, Charles R.

doi:10.1103/physreva.3.1688

Cited by 61 publications

(16 citation statements)

References 16 publications

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“…• a marked asymmetry in the intensity of the acoustic phonon with respect to +q and −q (where q is the reduced wavevector measured from the (1 0 0) Bragg point). This has been observed in previous studies of solid 4 He [17,18]. • a broad spectral feature that appears at about 2 meV, for wavevectors beyond the point of intersection mentioned above, and extends beyond the energy and wavevector range measured here.…”

Section: Resultssupporting

confidence: 56%

“…The measurements reveal portions of the spectrum that were not previously observable, were done at lower temperatures and provide higher resolution than in earlier experiments [17,18]. We find no evidence for a phase transition within the solid state but we do provide evidence for dispersive non-phonon excitations.…”

Section: Introductionmentioning

confidence: 50%

“…The intensities for the longitudinal branches were calculated from the inelastic structure factor based on this self-consistent phonon theory [18,20], and compare favourably to the data in figure 2 except at the intersection. In particular, the asymmetry in the intensity of the acoustic phonon branch phonons is well reproduced.…”

Section: Resultsmentioning

confidence: 99%

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Neutron scattering study of the excitation spectrum of solid helium at ultra-low temperatures

et al. 2008

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There has been a resurgence of interest in the properties of solid helium due to the recent discovery of non-classical rotational inertia (NCRI) in solid 4 He by Chan and coworkers below 200 mK which they have interpreted as a transition to a 'supersolid' phase. We have carried out a series of elastic and inelastic neutron scattering measurements on single crystals of hcp 4 He at temperatures down to 60 mK. While we have found no direct evidence of any change in the excitation spectrum at low temperatures, we have found that the excitation spectrum of solid 4 He shows several interesting features, including extra branches in addition to the phonon branches. We interpret these extra branches as single particle excitations due to propagating vacancy waves, which map on to the famous 'roton minimum' long known in the excitation spectrum of superfluid liquid 4 He. The results show that in fact solid 4 He shares several features in common with the superfluid.

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Section: Resultssupporting

confidence: 56%

Section: Introductionmentioning

confidence: 50%

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Neutron scattering study of the excitation spectrum of solid helium at ultra-low temperatures

et al. 2008

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“…Experimental data from Ref. 30. Frequencies calculated at discrete wave vectors are interpolated by cubic splines as a guide to the eyes.…”

Section: Transverse Modesmentioning

confidence: 99%

Zero-temperature dynamics of solidH4efrom quantum Monte Carlo simulations

2009

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The lattice dynamics of hcp crystalline 4 He is studied at zero temperature and for two different densities ͑near and far from melting͒, using a ground-state path-integral quantum Monte Carlo technique. The complete phonon dispersion is obtained, with particular attention to the separation of optic and acoustic branches and to the identification of transverse modes. Our study also sheds light on the residual coherence affecting quasiparticle excitations in the intermediate momentum region, in between the phonon and nearly free-particle regimes.The lattice dynamics of solid 4 He has long been considered a major challenge to ab initio calculations, due to the strong anharmonicity of this highly quantum solid. Many calculations have been performed within the self-consistent phonon ͑SCP͒ approximation, 1,2 which however may be rather unsatisfactory, due to the magnitude of anharmonic effects. A significant improvement has been made possible by the application of a variational quantum Monte Carlo ͑QMC͒ approach, based on the shadow wave function formalism, to bcc 3 He ͑Ref. 3͒ and to hcp 4 He. 4 The variational nature of this approach, however, makes it not fully suitable at high energy where optical or zone-boundary longitudinal excitations exhibit broad multiphonon features. In this spectral regime, the calculation of the full dynamic structure factor is therefore in order. QMC techniques based on path integrals allow quite naturally for the calculation of imaginarytime correlation functions from which various spectral functions, such as the dynamic structure factor, can be obtained upon analytical continuation. This technique has been successfully demonstrated for superfluid 4 He, 5,6 as well as for the bcc crystalline phases of 4 He ͑Refs. 7 and 8͒ and 3 He. 9 In the latter studies the spectrum of the transverse excitations has also been obtained, albeit in the one-phonon approximation only. 2 In this work we present an extensive study of the dynamical properties of hcp 4 He at zero temperature, performed by estimating the dynamic structure factor from ground-state path-integral simulations. 6,10,11 This technique allows us to parallel to some extent the procedure followed experimentally to map phonon dispersions from the measured neutron scattering. In the long-wavelength region-well approximated by a phonon picture of the collective density excitations-we thus obtain longitudinal as well as transverse modes for both acoustic and optical branches. For higher wave-vectors we analyze the dynamic structure factor in terms of corrections to the so-called impulse approximation, 12 finding a coherent response which is peculiar of both superfluid and solid helium.In Sec. I we give an introductory account of the phonon theory of long-wavelength excitations in solids. In Sec. II the reader is provided with an outline of the numerical methods adopted in this work. In Sec. III we report on the analysis of our QMC results both in the phonon regime and in the intermediate momentum region. Sec. IV is finally devoted to a few c...

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“…At two different laboratories, this has been done in fcc phase 13,14 and at similar and lower densities in the hcp phase. [15][16][17] Data analysis generally included the fitting of dispersion curves using a Born-von Kármán model. In several of the publications, the model force constants were used to obtain a one-phonon density of states g() from which values of ͗u Q 2 ͘ were inferred.…”

Section: ͑5͒mentioning

confidence: 99%

Atomic vibration amplitudes in fcc and hcp4Hethrough x-ray diffraction measurements

Venkataraman

Simmons

2003

Phys. Rev. B

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Atomic vibration amplitudes in dense fcc and hcp 4 He crystals have been measured using synchrotron x rays from the dependence of integrated Bragg intensities up to wave vectors of 91 nm Ϫ1 . Observed raw Bragg x-ray integrated intensities cover an extraordinary range, greater than 10 5 , due to the combined effect of the Debye-Waller factor and electronic form factor. From analysis of these intensities mean-square atomic vibration amplitudes ͗u Q 2 ͘ and Lindemann ratios are determined. Path-integral Monte Carlo ͑PIMC͒ computations of Draeger and Ceperley, extrapolated to the thermodynamic limit, provide excellent agreement with these experimental results. For both present measurements and the PIMC results, one finds both a predominantly Gaussian distribution in ͗u Q 2 ͘ and an extraordinarily large Lindemann ratio. In contrast, these directly measuredx-ray values are significantly larger than published values inferred from Born-von Kármán fitting to phonon dispersion measured by neutron scattering. Mildly anharmonic neon, which is fairly well described by selfconsistent phonon theories, is contrasted with present results on fcc 4 He at corresponding densities.

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Phonon Dispersion Relations for hcpHe4at a Molar Volume of 16cm3

Cited by 61 publications

References 16 publications

Neutron scattering study of the excitation spectrum of solid helium at ultra-low temperatures

Neutron scattering study of the excitation spectrum of solid helium at ultra-low temperatures

Zero-temperature dynamics of solidH4efrom quantum Monte Carlo simulations

Atomic vibration amplitudes in fcc and hcp4Hethrough x-ray diffraction measurements

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