Second Sound in Solid Helium

Ackerman, Christian; Bertman, B.; Fairbank, H. A. T.; Guyer, R. A.

doi:10.1103/physrevlett.16.789

Cited by 372 publications

(158 citation statements)

References 10 publications

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“…The group velocity, which largely depends on phonon frequency, can cause a significant broadening in a ballistic heat pulse. To take account of this effect, we suppose an experiment for observing second sound, similar to the past experiments for threedimensional materials 4,9,45,47 . Suppose we have a rectangular shape graphene sheet with a point heat source at the left edge and a point thermal sensor at the right edge, as illustrated in the inset of Fig.…”

Section: Methodsmentioning

confidence: 99%

“…In the macroscopic transport equation like equation (4), the scattering rate is averaged using the displaced state,|1i.…”

Section: Methodsmentioning

confidence: 99%

“…1c,d. The pulse in the hydrodynamic regime is transmitted by many N-scatterings 4,9,44,45 , whereas the pulse in the diffusive regime is largely damped by R-scattering and cannot propagate. The transmission of a heat pulse can also be observed in ballistic transport, but the sample size is limited to below phonon mean free path.…”

Section: Displaced Distribution Functionmentioning

confidence: 99%

“…Regimes where Fourier's law breaks down, such as ballistic 1 and hydrodynamic 2 phonon transport, were discovered in bulk materials more than 50 years ago, but these phenomena were observed only at extremely low temperatures [3][4][5] . Recent studies of low-dimensional materials, however, have highlighted the practical importance of ballistic phonon transport in applications such as thermoelectric materials 6 and electronic devices 7,8 .…”

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confidence: 99%

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Hydrodynamic phonon transport in suspended graphene

et al. 2015

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Recent studies of thermal transport in nanomaterials have demonstrated the breakdown of Fourier's law through observations of ballistic transport. Despite its unique features, another instance of the breakdown of Fourier's law, hydrodynamic phonon transport, has drawn less attention because it has been observed only at extremely low temperatures and narrow temperature ranges in bulk materials. Here, we predict on the basis of first-principles calculations that the hydrodynamic phonon transport can occur in suspended graphene at significantly higher temperatures and wider temperature ranges than in bulk materials. The hydrodynamic transport is demonstrated through drift motion of phonons, phonon Poiseuille flow and second sound. The significant hydrodynamic phonon transport in graphene is associated with graphene's two-dimensional features. This work opens a new avenue for understanding and manipulating heat flow in two-dimensional materials.

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Section: Methodsmentioning

confidence: 99%

“…In the macroscopic transport equation like equation (4), the scattering rate is averaged using the displaced state,|1i.…”

Section: Methodsmentioning

confidence: 99%

Section: Displaced Distribution Functionmentioning

confidence: 99%

mentioning

confidence: 99%

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Hydrodynamic phonon transport in suspended graphene

et al. 2015

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“…Many of the mentioned properties are only meaningful for perfect monocrystals of solid helium. Using the technique to grow large monocrystals of solid helium, developed by Shalnikov [5], Mezhov-Deglin has observed not only ballistic transport of thermal phonons but also hydrodynamics of the phonon gas [6], which, for instance, was a pre-requisite for observations of such a spectacular effect as the second sound (heat propagating as a wave) in solid helium [7].…”

Section: Solid Heliummentioning

confidence: 99%

Thermal conductivity and torsional oscillations of solid 4He

Brazhnikov

Zmeev

Golov

2012

Low Temperature Physics

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Polycrystalline samples of hcp 4 He of molar volume V m = 19.5 cm 3 with small amount of 3 He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of 3 He, x 3 , were studied: isotopically purified 4 He with the estimated x 3 < 10 -10 , commercial 'well-grade' helium with x 3 ~ 3⋅10 -7 and a mixture with x 3 = 2.5⋅10 -6. Torsional oscillations at two frequencies, 132.5 and 853.6 Hz, and thermal conductivity were investigated before and after annealing. The solid helium under investigation was located not only in the annular container but also in the axial fill line inside two torsion rods and dummy bob of the doublefrequency torsional oscillator. The analysis of the frequency shifts upon loading with helium and changing temperatures of different parts of the oscillator suggests that the three techniques probe the properties of solid helium in three different locations: the two different torsion modes respond to the changes of the shear modulus of solid helium in either of the two torsion rods while the thermal conductivity probes the phonon mean free path in solid helium inside the annular container. The temperature and width of the torsional anomaly increase with increasing frequency and x 3 . The phonon mean free path increases with increasing x 3 . Annealing typically resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them. PACS: 67.80.bd Superfluidity in solid 4 He, supersolid 4 He; 65.40.-b Thermal properties of crystalline solids.

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Construction of Propagators for Quantum Crystals

Yukalov

1981

Annalen der Physik

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We present here a mathematical basis of the iterative procedure developed earlier by the author for strongly anharmonic crystals. We generalize the approach to the case of any strongly nonideal nonuniform system. The cofivergence of this procedure is defied as convergence in the mean with respect to averages of observable-quantity operators. The definitions yield self-consistent conditions for a zero-order iteration in a natural way. Divergences in high-order iterations are considered and two ways to eliminate them are proposed. The method is applied to a stmnglyanisotropic strongly-anharmonic quantum crystal. Konstruktion von Propaqatoren in der Quantentheorie der KristalleInhaltsubersicht. Im folgenden wird die mathematische Grundlage fiir das vom Autor schon friiher entwickelte iterative Verfahren zur Beschreibung stark anharmonischer Kristalle dargestellt. Wir verallgemeinern die Methode auf den Fall beliebiger stark nichtidealer und niohteinheitlicher Systeme. Die Konvergenz dieses Verfahrens ist definiert als eine Konvergenz im Nittel beziiglich der Mittelwverte von Operatoren beobachtbarer GroBen. Diese Definition fiihrt auf natiirlichem Wege zu in sich widerspruchsfreien Bedingungen bei einer Iteration Nullter Ordnung. Divergenzen bei der Iteration in hoherer Ordnung werden ebenfalls betrachtet und 2 Wege zu ihrer Eliminierung vorgeschlagen. Die Methode wird angewandt auf die Quantentheorie stark anisotropischer nnd anharmonischer Kristalle.

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Second Sound in Solid Helium

Cited by 372 publications

References 10 publications

Hydrodynamic phonon transport in suspended graphene

Hydrodynamic phonon transport in suspended graphene

Thermal conductivity and torsional oscillations of solid 4He

Construction of Propagators for Quantum Crystals

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