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Fraass, Benedick A.; Granfors, Paul R.; Simmons, R. O.

doi:10.1103/physrevb.39.124

Cited by 72 publications

(66 citation statements)

References 43 publications

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“…Experimental evidence [13,14] points toward a commensurate hcp ground state in 4 He, as the measured vacancy activation energy is approximately 10 − 15 K, and appears to rule out thermally activated vacancies at the characteristic temperatures below 0.2 K of the KC experiment. X-ray measurements [13] on hcp 4 He put the tightest upper bound on the vacancy concentration n V (T → 0), disfavoring the ALC and DMZ/ABH scenarios, although ABH debate the interpretation of these measurements [6]. On the theoretical side, two of us have proven that a superfluid crystal must generically be incommensurate [15], a view which is supported by recent numerical simulations showing that ideal hcp crystals of 4 He are insulating [16,17,18].…”

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“…Measurements of pressure-driven flow have yielded a null result in hexagonal-close-packed (hcp) 4 He [11,12]. Experimental evidence [13,14] points toward a commensurate hcp ground state in 4 He, as the measured vacancy activation energy is approximately 10 − 15 K, and appears to rule out thermally activated vacancies at the characteristic temperatures below 0.2 K of the KC experiment. X-ray measurements [13] on hcp 4 He put the tightest upper bound on the vacancy concentration n V (T → 0), disfavoring the ALC and DMZ/ABH scenarios, although ABH debate the interpretation of these measurements [6].…”

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confidence: 99%

“…Measurements of pressure-driven flow have yielded a null result in hexagonal-close-packed (hcp) 4 He [11,12]. Experimental evidence [13,14] The physics of vacancies in solid Helium is an important open problem, even aside from its relevance to the experiment of KC, and has been studied for a long time. The majority of microscopic calculations have been variational [19,20,21], and focused on the properties of a single vacancy.…”

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Fate of Vacancy-Induced Supersolidity inHe4

et al. 2006

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The supersolid state of matter, exhibiting non-dissipative flow in solids, has been elusive for thirty five years. The recent discovery of a non-classical moment of inertia in solid 4 He by Kim and Chan provided the first experimental evidence, although the interpretation in terms of supersolidity of the ideal crystal phase remains subject to debate. Using quantum Monte Carlo methods we investigate the long-standing question of vacancy-induced superflow and find that vacancies in a 4 He crystal phase separate instead of forming a supersolid. On the other hand, non-equilibrium vacancies relaxing on defects of poly-crystalline samples could provide an explanation for the experimental observations.PACS numbers: 75.10. Jm, 05.30.Jp, 67.40.Kh, 74.25.Dw The observation of a non-classical moment of inertia in solid 4 He by Kim and Chan (KC) has provided the first experimental evidence of a possible supersolid phase of matter [1,2], which is characterized by crystalline order and frictionless flow. Early theories of supersolidity were based on the assumption that the low-temperature 4 He crystal may be incommensurate (the number of atoms is not an integer multiple of that of lattice sites). As a consequence of their quantum behavior, point defects such as vacancies and interstitials can Bose condense at low temperature, giving rise to superflow.In particular, the Andreev-Lifshitz-Chester (ALC) scenario [3,4] assumes that the gain in kinetic energy by delocalizing the vacancy can overcome the potential energy cost of creating it in a perfect crystal, such that a dilute gas of highly mobile vacancies can be stabilized. The energetics of this scenario is illustrated in the lower curve in Fig. 1. Similar supersolid ground states with a low density of strongly correlated vacancies were recently put forward by Dai, Ma and Zhang (DMZ) [5] and also by Anderson, Brinkman and Huse (ABH) [6]. Their scenarios are possible even when single-vacancy excitations in the perfect crystal are gapped, as indicated in Fig. 1. It was also recently suggested that the onset of supersolidity leads to anomalies in the elastic moduli [7].Although the initial experimental observation by KC has been confirmed by other groups [8,9,10], the interpretation in terms of superflow in the crystal phase is becoming increasingly questionable. Repeated cycles of annealing make the supersolid signal weaker to vanishing [8]. Measurements of pressure-driven flow have yielded a null result in hexagonal-close-packed (hcp) 4 He [11,12]. Experimental evidence [13,14] The physics of vacancies in solid Helium is an important open problem, even aside from its relevance to the experiment of KC, and has been studied for a long time. The majority of microscopic calculations have been variational [19,20,21], and focused on the properties of a single vacancy. Various estimates of the vacancy activation energy [19,20], including the one obtained by Ceperley and Bernu using Path Integral Monte Carlo simulations [16], are in quantitative agreement with experiment. However,...

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Fate of Vacancy-Induced Supersolidity inHe4

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“…For ǫ b → ∞, our model is reduced to the vacancy model proposed by Andreeve and Lifshitz [6]. Let z(= 12) be the number of the nearest neighbors in a hcp lattice, the onset of Bose condensation of vacancies (interstitials) is given exactly by ǫ a(b) − zt a(b) = 0 − , which coincides with having zero activation energy for a single defect, a condition that is not supported by experiments [10] and theoretical estimates [11,12] for 4 He. This is the quandary we stated in the introduction.…”

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“…The NMR experiments [8, 9] on solid 3 He rule out a non-negligible zero point vacancy concentration. The energy of a vacancy in solid 4 He was estimated to be about 10K by the x-ray scattering experiment [10] and to be 15K in a theoretical calculation [11]. The energy of a pure interstitial state has recently been calculated to be about 48 ± 5K [12].…”

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Theory for supersolidHe4: Vacancy condensation facilitated by a low-energy bound state of a vacancy and an interstitial

Dai

Zhang

2005

Phys. Rev. B

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Although both vacancies and interstitial have relatively high activation energies in the normal solid, we propose that a lower energy bound state of a vacancy and an interstitial may facilitate vacancy condensation to give supersolidity in 4 He . We use a phenomenological two-band boson lattice model to demonstrate this new mechanism and discuss the possible relevance to the recently observed superfluid-like, non-classical rotational inertial experiments of Kim and Chan in solid 4 He. Some of our results may also be applicable to trapped bosons in optical lattices. Prokofev and Svistunov [7]. Experiments and more sophisticated microscopic calculations have, however, provided constraints to any theory for supersolid in 4 He. The NMR experiments [8, 9] on solid 3 He rule out a non-negligible zero point vacancy concentration. The energy of a vacancy in solid 4 He was estimated to be about 10K by the x-ray scattering experiment [10] and to be 15K in a theoretical calculation [11]. The energy of a pure interstitial state has recently been calculated to be about 48 ± 5K [12]. Assuming that the observed supersolidity is a genuine bulk phenomenon, the quandary is thus how defects with such high activation energies can condense at low temperature.In this Letter, we propose a possible solution to this quandary. In addition to vacancies and interstitials, there is a third type of defects, with relatively low excitation energy, which corresponds to a bound state of a vacancy and an interstitial, henceforth called an "exciton". While such excitons do not carry mass and will not contribute to supersolid phenomena like those observed by Kim and Chan [1, 2], they can facilitate supersolidity by two mechanisms. First, vacancies can condense above a background of excitons easier than above the defect free (DF) normal state, so that the condensation energy can more than compensate for the exciton excitation energy. Second, in a background formed of a coherent mixture of the DF state and the exciton, the effective kinetic energy of vacancies and interstitials can be enhanced due to constructive interference between hopping processes involving the DF state and those involving the exciton.The essence of our theory is that while, consistent with all known experiments, the normal solid state is the DF state, the supersolid state results from condensation of vacancies and/or interstitials about a defect rich background of excitons. This physics is shown quantitatively using a phenomenological two-band lattice boson model to represent the defects in solid 4 He. Using mean field theory (MFT), we show that superfluidity in solid helium can exist in parameter regimes qualitatively consistent with all the known experiments and microscopic calculations. We will argue that the key results will hold beyond MFT, and indeed are rendered more robust by inclusion of quantum fluctuations. Because of the "vacuum switching" between the normal and supersolid states, the transition at zero temperature is generically first order.We start with the lattic...

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Scattering Studies of Condensed Helium Isotopes

Simmons

2003

Particle Scattering, X-Ray Diffraction, and Microstructure of Solids and Liquids

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X-ray measurements of thermal vacancies in hcpHe4

Cited by 72 publications

References 43 publications

Fate of Vacancy-Induced Supersolidity inHe4

Fate of Vacancy-Induced Supersolidity inHe4

Theory for supersolidHe4: Vacancy condensation facilitated by a low-energy bound state of a vacancy and an interstitial

Scattering Studies of Condensed Helium Isotopes

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