Liquid-to-gas phase transitions in two-dimensional quantum systems at zero temperature

Miller, Michael David; Nosanow, L. H.

doi:10.1007/bf00116910

Cited by 73 publications

(70 citation statements)

References 12 publications

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“…i) 2D clusters with N particles [9,10,12] are predicted to become unbound when the mass m reaches a critical value m (N ) * [7]. This critical mass is predicted to be universal, i.e., m (N ) * = m * [10], and to be the same for the corresponding homogeneous system [8,19]. ii) For a given system size, the ground state energies E N near threshold are predicted to change exponentially as the atomic mass m decreases [7,11].…”

Section: Pacs Numbersmentioning

confidence: 99%

Threshold behavior of bosonic two-dimensional few-body systems

Blume

2005

Phys. Rev. B

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Bosonic two-dimensional self-bound clusters consisting of N atoms interacting through additive van der Waals potentials become unbound at a critical mass m (N) * ; m (N) * has been predicted to be independent of the size of the system. Furthermore, it has been predicted that the ground state energy EN of the N -atom system varies exponentially as the atomic mass approaches m * . This paper reports accurate numerical many-body calculations that allow these predictions to be tested. We confirm the existence of a universal critical mass m * , and show that the near-threshold behavior can only be described properly if a previously neglected term is included. We comment on the universality of the energy ratio EN+1/EN near threshold. PACS numbers:Restricting the motion of particles to one or two dimensions can lead to properties that differ dramatically from those in three dimensions. The most prominent two-dimensional (2D) system is the surface of bulk matter. Another example are one-or two-atom layer thin films, e.g., atomic or molecular hydrogen films [1,2], grown on substrates. Neglecting the adatom-substrate interaction, many properties of such systems can be understood within a truly 2D framework. In addition to homogeneous 2D systems, it is interesting to consider 2D clusters (see, e.g., Refs. [3,4]). What happens when a finite number of atoms is restricted to 2D space? Inhomogeneous 2D systems can potentially be studied by placing a few atoms on the surface of a substrate or by confining atoms by external potentials. Effectively 2D atom traps have been realized recently [5,6]; extension to optical lattices with only a few atoms per lattice site is possible with today's technology. These systems are particularly interesting since Feshbach resonances allow the interaction strengths to be tuned through application of magnetic fields.Bosonic 2D systems interacting through short-range two-body potentials that support one zero angular momentum bound state are predicted to exhibit intriguing universal, that is, model-independent, behaviors [7,8,9,10,11,12,13,14,15,16,17,18]. i) 2D clusters with N particles [9,10,12] are predicted to become unbound when the mass m reaches a critical value m (N ) * [7]. This critical mass is predicted to be universal, i.e., m (N ) * = m * [10], and to be the same for the corresponding homogeneous system [8,19]. ii) For a given system size, the ground state energies E N near threshold are predicted to change exponentially as the atomic mass m decreases [7,11]. Similarly, for a given atomic mass, the ground state energies near threshold are predicted to change exponentially with varying system size [17]. iii) The ratio between the ground state energies of a 2D system with N +1 atoms and those of a system with N atoms reaches, in the limit of zero-range interactions, a constant. This constant has been determined analytically for small 2D systems: E δ 3 /E δ 2 = 16.52 [9,16] and E δ 4 /E δ 3 = 11.94 [18]. For large systems, the ratio E δ N +1 /E δ N has been predicted to approach 8.57 [17]...

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Section: Pacs Numbersmentioning

confidence: 99%

Threshold behavior of bosonic two-dimensional few-body systems

Blume

2005

Phys. Rev. B

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“…It was argued by Miller and Nosanow [21] that pure two-dimensional 3 He should be a gas down to absolute zero. In the 4 He medium, however, the OREP provides a mechanism by which the 3 He subsystem could undergo a gas to liquid transition.…”

Section: Resultsmentioning

confidence: 97%

THE PROPERTIES OF THIN ^{3}He-^{4}He SUPERFLUID FILMS

Anderson¹,

Miller²

2001

Condens. Matter Phys.

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Thin3 He-4 He physisorbed films are examples of strongly interacting, quasi two-dimensional, fermion-boson mixture systems. The properties of the mixture systems can be tuned by changing the substrate or the 4 He film thickness. In this paper, we discuss the ground-state and magnetic groundstate of the 3 He subsystem and also the interactions between the excitations of the 4 He superfluid film with the single-particle excitations of the adsorbed 3 He. The ground-state of the 3 He system is calculated using a model for the 3 He-3 He effective interaction in the static 4 He film which explicitly includes the effective interaction due to exchange of virtual film excitations (ripplons). This latter effective interaction is evaluated in the random phase approximation and is shown not to be capable of causing the 3 He system to be self-bound. We discuss the evidence from magnetization, third sound and heat capacity measurements that the 3 He first transverse excited state is being occupied prior to monolayer completion.

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“…Recently, Sato et al [11] found the G-L transition with ρ c0 ≈ 1 nm −2 in the heat-capacity measurements on the third layer of 3 He on graphite down to T = 1 mK. This was inferred from a linear ρ−dependence of γ, the coefficient of the leading T -linear term of C in the degenerate region, as well as a kink at γ ≈ γ ideal .…”

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confidence: 97%

“…Most previous theories based on the variational calculations [2][3][4], the diffusion Monte Carlo calculation [5] and the Fermi hypernetted chain method [6] support the absence of self-binding of 3 He in 2D. Indeed, no signature of the gas-liquid (G-L) transition was experimentally observed in the first and second layer 3 He on graphite down to T ≈ 3 mK and to areal density ρ = 1 nm −2 [7]. This is in sharp contrast to monolayer 4 He with smaller quantum parameter on graphite.…”

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Observation of Self-Binding in MonolayerHe3

et al. 2012

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We report clear experimental signatures of the theoretically unexpected gas-liquid transition in the first three monolayers of 3 He adsorbed on graphite. The transition is inferred from the linear density dependence of the γ-coefficient of the heat capacity measured in the degenerate region (2 ≤ T ≤80 mK) below a critical liquid density (ρc0). Surprisingly, the measured ρc0 values (0.6∼0.9 nm −2 ) are nearly the same for all these monolayers in spite of their quite different environments. We conclude that the ground-state of 3 He in strict two dimensions is not a dilute quantum gas but a self-bound quantum liquid with the lowest density ever found. PACS numbers: 67.30.hr, 67.30.ej, 67.10.Db, 67.30.ef Matter can in principle be in either gas or a liquid phase at absolute zero if the quantum parameter, the zero-point kinetic energy divided by the potential energy, is large enough. The two-dimensional (2D) helium-3 ( 3 He) system has long been thought as the only material which stays gaseous at the ground state [1]. This system is experimentally realized in 3 He monolayers adsorbed on an atomically flat and strongly attractive graphite surface. Most previous theories based on the variational calculations [2-4], the diffusion Monte Carlo calculation [5] and the Fermi hypernetted chain method [6] support the absence of self-binding of 3 He in 2D. Indeed, no signature of the gas-liquid (G-L) transition was experimentally observed in the first and second layer 3 He on graphite down to T ≈ 3 mK and to areal density ρ = 1 nm −2 [7]. This is in sharp contrast to monolayer 4 He with smaller quantum parameter on graphite. It is well established experimentally [8] and theoretically [9] that in this system the G-L transition takes place at temperatures below 1 K and the self-bound liquid density at T = 0 (ρ c0 ) is 4 nm −2 .The first experimental address to this problem was made by Bhattacharyya and Gasparini [10], who found a kink or small discontinuity near 100 mK in the heat capacity (C) of submonolayer 3 He floated on a thin superfluid 4 He film adsorbed on a Nuclepore substrate. They attributed this to a puddle formation of 3 He in 2D. It is to be noted, however, that in this system the indirect 3 He-3 He interaction mediated by ripplons in the underlying 4 He film, which is not considered in most theoretical works, might be important. In addition, Nuclepore is believed to be a much less uniform substrate than graphite.Recently, Sato et al. [11] found the G-L transition with ρ c0 ≈ 1 nm −2 in the heat-capacity measurements on the third layer of 3 He on graphite down to T = 1 mK. This was inferred from a linear ρ−dependence of γ, the coefficient of the leading T -linear term of C in the degenerate region, as well as a kink at γ ≈ γ ideal . Here2 ) is the γ value of an ideal Fermi gas spreading over the whole surface area (A) of the substrate, and m is the bare mass of 3 He. Note that γ depends only on A and m not on the number of particles in the 2D case. One possible explanation for their result, which contradicts exi...

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Liquid-to-gas phase transitions in two-dimensional quantum systems at zero temperature

Cited by 73 publications

References 12 publications

Threshold behavior of bosonic two-dimensional few-body systems

Threshold behavior of bosonic two-dimensional few-body systems

THE PROPERTIES OF THIN ^{3}He-^{4}He SUPERFLUID FILMS

Observation of Self-Binding in MonolayerHe3

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