Quantum Phase Transition of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow><mml:mi>e</mml:mi></mml:math>in Aerogel at a Nonzero Pressure [Phys. Rev. Lett. 79, 253 (1997)]

Matsumoto, K.; Porto, J. V.; Pollack, Lois; Smith, Emily M.; Ho, Tin-Lun; Parpia, J. M.

doi:10.1103/physrevlett.79.2922

Cited by 34 publications

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“…A crucial parameter, the coherence length ξ 0 , can easily be varied within a factor 5 by varying the pressure. The torsional oscillator experiments [2,3] and NMR experiments [4] measure directly such basic quantities as the superfluid density, the pairing amplitude and the spin susceptibility.In this letter we give theoretical explanations for some of the experimental observations on superfluid 3 He in aerogel. As a first attempt we study a model, where the aerogel is assumed as a homogeneous scatterer of the quasiparticles of 3 He.…”

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confidence: 99%

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confidence: 99%

“…However, both the experimental and theoretical studies are difficult because of the complicated structure of these substances. Recently, a new possibility was opened for studying impurity effects on unconventional pairing states: superfluid 3 He in very porous aerogel. This system has many advantages.…”

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Models for SuperfluidH3ein Aerogel

Thuneberg¹,

et al. 1998

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Several recent experiments find evidence of superfluidity of 3 He in 98%-porous aerogel. The primary effect of the aerogel is that it scatters the quasiparticles of 3 He. We find that many experimental findings are quantitatively understood by a relatively simple model that takes into account strong inhomogeneity of the scattering on a length scale of 100 nm. PACS: 74.25.Fy, 74.70.Tx, 72.15.Eb The discovery of unconventional paring states in hightemperature superconductors has generated a lot of interest in impurity scattering in these materials. In particular, the inhomogeneity of the scattering has been considered recently [1]. However, both the experimental and theoretical studies are difficult because of the complicated structure of these substances. Recently, a new possibility was opened for studying impurity effects on unconventional pairing states: superfluid 3 He in very porous aerogel. This system has many advantages. For example, the pure state of superfluid 3 He is absolutely pure in experiments, and it is theoretically very well understood. A crucial parameter, the coherence length ξ 0 , can easily be varied within a factor 5 by varying the pressure. The torsional oscillator experiments [2,3] and NMR experiments [4] measure directly such basic quantities as the superfluid density, the pairing amplitude and the spin susceptibility.In this letter we give theoretical explanations for some of the experimental observations on superfluid 3 He in aerogel. As a first attempt we study a model, where the aerogel is assumed as a homogeneous scatterer of the quasiparticles of 3 He. This model gives predictions with a correct tendency, but it is insufficient quantitatively. A "slab model" gives a clue that the inhomogeneity of the scattering is crucial for understanding the discrepancy. Based on that we construct a relatively simple model of inhomogeneous scattering that quantitatively can explain both the transition temperature and the pairing amplitude, and predicts an inhomogeneity length scale of 100 nm. We also consider the upper limit for anisotropic scattering set by the NMR measurements.In the experiments the aerogel fills only 2% of the total volume (V = 0.02), and its surface to volume ratio is A = 260, 000 cm −1 [5]. Assuming naively that the material consists of a network of one-dimensional strands, we can from these numbers alone estimate the strand diameter 4V /A = 3 nm. The distance between strands is √ 4πV /A = 20 nm. The mean free path for straight line trajectories is estimated as ℓ = 4/A = 150 nm. This is also the mean free path for quasiparticles of 3 He when the aerogel is filled with 3 He at millikelvin temperatures. Quasiclassical theory.-Because the volume fraction of the aerogel strands (including an inert layer of 3 He atoms on the strands) is small, we neglect all effects that are linear in the volume fraction. In particular, we assume that the density, the Landau Fermi-liquid parameters, the coupling constant of the pairing interaction, and the dipole-dipole interaction constant are...

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Models for SuperfluidH3ein Aerogel

Thuneberg¹,

et al. 1998

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“…Torsional oscillator 1 , NMR 2,3 , and specific heat experiments 4 performed on 3 He in aerogel show substantial suppression of the transition temperature and order parameter. Thuneberg et al 5 describe a model for such a system in the framework of the Ginzburg-Landau theory, where the free energy of various superfluid 3 He phases is expressed with different combinations of the β coefficients 6 .…”

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Specific Heat of Disordered 3He

Choi¹,

Davis²,

Pollanen³

et al. 2006

AIP Conference Proceedings

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Abstract. Porous aerogel is a source of elastic scattering in superfluid 3 He and modifies the properties of the superfluid, suppressing the transition temperature and order parameter. The specific heat jumps for the B-phase of superfluid 3 He in aerogel have been measured as a function of pressure and interpreted using the homogeneous and inhomogeneous isotropic scattering models. The specific heat jumps for other p-wave states are estimated for comparison.

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“…The cell was filled to 14 bar, then cooled to 0.3 mK. The pressure of the 3 He was slowly reduced, and the temperature held fixed by demagnetization of the nuclear cooling stage as necessary [18]. At this temperature there is no superfluid 3 He at pressures below 6.2 bar.…”

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Dissipation Mechanisms near the SuperfluidHe3Transition in Aerogel

et al. 2004

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We have investigated the dissipation (Q ÿ1 ) using the torsion pendulum technique for pure 3 He and 3 He mixtures in silica aerogel near the 3 He superfluid transition (T c ) in aerogel. With pure 3 He the Q ÿ1 decreases at the onset of superfluidity. When phase separated 3 He mixtures are introduced into the aerogel, the Q ÿ1 does not decrease as rapidly and eventually increases for the highest 4 He content. We provide a model for the related attenuation of transverse sound that takes into account elastic and inelastic scattering processes and exhibits a decrease in at T c . DOI: 10.1103/PhysRevLett.92.195301 PACS numbers: 67.40.Pm, 67.57.Pq The superfluid phases of liquid 3 He are characterized by unconventional pairing correlations, reminiscent of those in the unconventionally paired heavy fermion superconductors, hole doped high-T c cuprate superconductors, the Ruddlesden-Popper system Sr 2 RuO 4 , and others. This unconventionality is defined through the vanishing Fermi surface average of the pair potential (gap) h p i FS 0, and is manifested by the sensitivity of thermodynamic, response and transport properties to even small concentrations of nonmagnetic impurities. Low density aerogels, dilute correlated aggregates of silica whose constituents' size is of near atomic scale (1.5 nm mean diameter) provide the opportunity to study the effects of disorder on the superfluidity of 3 He, by itself the purest material known at low temperature.We explore quasiparticle dissipation effects in superfluid 3 He-B in aerogel and provide the first model for the shear viscosity of superfluid 3 He-B in the presence of impurities. The shear viscosity, together with a Drude contribution govern the attenuation of transverse sound which is closely related to the decrease in dissipation seen in the experiment below T c . We interpret this decrease as the first experimental evidence for an impurity-limited viscosity aside from metallic superconductivity.At temperatures below 100 mK, bulk 3 He behaves like a Fermi liquid and the transport mean free path (mfp) is determined by inelastic quasiparticle-quasiparticle scattering. Because of the restricted phase space accessible to quasiparticles as the temperature is lowered, the time between collisions, , and the mfp both increase as T ÿ2 . The scattering rate is manifested in transport (viscosity, thermal conductivity, spin diffusion). At the bulk superfluid transition temperature T c0 a rapid decrease in the viscosity is observed [1][2][3]. The aerogel strands provide an additional mechanism for elastic scattering of quasiparticles and since the strand diameter is much smaller than the 3 He coherence length, aerogels can be considered as an impurity added to bulk 3 He [4]. The geometrical mfp in aerogel whose porosity (in the context of superfluid 3 He is typically in excess of 97%) varies from 100 nm in 97% open to 400 nm in the 99:5% open aerogel.Confining 3 He to silica aerogel affects the hydrodynamics of the system. The aerogel is compressible and the 3 He liquid motion ...

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Quantum Phase Transition ofH3ein Aerogel at a Nonzero Pressure [Phys. Rev. Lett. 79, 253 (1997)]

Cited by 34 publications

References 0 publications

Models for SuperfluidH3ein Aerogel

Models for SuperfluidH3ein Aerogel

Specific Heat of Disordered 3He

Dissipation Mechanisms near the SuperfluidHe3Transition in Aerogel

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