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arXiv:cond-mat/0406124

Supersolid Phase in Helium-4

Tiwari, Mukesh, Datta, Animesh

Published Jun 4, 2004• 0 citations
arXivHTMLPDF

Abstract

The probable observation of a supersolid helium phase was recently reported by Kim {\it et al}. In this article, we confirm their speculation. Based on a theoretical model for solid helium-4, we show that the emergence of such a phase is inevitable. This is the first instance of Bose-Einstein condensation (BEC) in a solid. We calculate the BEC transition temperature ($T_c$) and the Landau critical velocity ($v_c$) from the model, which respectively are 215 mK and $251 μ\rm{ms^{-1}}$. They are in excellent agreement with the experimental results; $T_c=$175 mK and $v_c \leq 300 μ\rm{ms^{-1}}$. We also prove that our model possesses the necessary and sufficient condition for the emergence of supersolidity. We briefly comment about similar behaviour in $^3$He.

DOI
10.48550/arxiv.cond-mat/0406124

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The probable observation of a supersolid helium phase was recently reported by Kim {\it et al}. In this article, we confirm their speculation. Based on a theoretical model for solid helium-4, we show that the emergence of such a phase is inevitable. This is the first instance of Bose-Einstein condensation (BEC) in a solid. We calculate the BEC transition temperature (TcT_cTc​) and the Landau critical velocity (vcv_cvc​) from the model, which respectively are 215 mK and 251μms−1251 μ\rm{ms^{-1}}251μms−1. They are in excellent agreement with the experimental results; Tc=T_c=Tc​=175 mK and vc≤300μms−1v_c \leq 300 μ\rm{ms^{-1}}vc​≤300μms−1. We also prove that our model possesses the necessary and sufficient condition for the emergence of supersolidity. We briefly comment about similar behaviour in 3^33He.
We present neutron scattering measurements of the atomic momentum distribution n(k)n(\mathbf{k})n(k) in solid helium under a pressure p=41 barp=41\text{ }\mathrm{bar}p=41 bar (molar volume ${V}_{m}=20.01\ifmmode\pm\else\textpm\fi{}0.02\text{ }\text{ }{\mathrm{cm}}^{3}/\mathrm{mol}$) and at temperatures between 80 and 500 mK. The aim is to determine whether there is Bose-Einstein condensation (BEC) below the critical temperature, Tc=200  mK{T}_{c}=200\text{ }\text{ }\mathrm{mK}Tc​=200  mK, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the k=0k=0k=0 state below Tc{T}_{c}Tc​, we find a condensate fraction of ${n}_{0}=(\ensuremath{-}0.10\ifmmode\pm\else\textpm\fi{}1.20)%$ at T=80  mKT=80\text{ }\text{ }\mathrm{mK}T=80  mK and ${n}_{0}=(0.08\ifmmode\pm\else\textpm\fi{}0.78)%$ at T=120  mKT=120\text{ }\text{ }\mathrm{mK}T=120  mK, consistent with zero. The shape of n(k)n(\mathbf{k})n(k) also does not change on crossing Tc{T}_{c}Tc​ within measurement precision.
Abstract Supersolid states simultaneously feature properties typically associated with a solid and with a superfluid. Like a solid, they possess crystalline order, manifesting as a periodic modulation of the particle density; but unlike a typical solid, they also have superfluid properties, resulting from coherent particle delocalization across the system. Such states were initially envisioned in the context of bulk solid helium, as a possible answer to the question of whether a solid could have superfluid properties1–5. Although supersolidity has not been observed in solid helium (despite much effort)6, ultracold atomic gases provide an alternative approach, recently enabling the observation and study of supersolids with dipolar atoms7–16. However, unlike the proposed phenomena in helium, these gaseous systems have so far only shown supersolidity along a single direction. Here we demonstrate the extension of supersolid properties into two dimensions by preparing a supersolid quantum gas of dysprosium atoms on both sides of a structural phase transition similar to those occurring in ionic chains17–20, quantum wires21, 22 and theoretically in chains of individual dipolar particles23, 24. This opens the possibility of studying rich excitation properties25–28, including vortex formation29–31, and ground-state phases with varied geometrical structure7, 32 in a highly flexible and controllable system.
The basic assumption of this paper is that in the presence of Bose-Einstein condensation (BEC) in liquid 4He^{4}\mathrm{He}4He, the wave functions of occupied many particle states are the superposition of two components; a phase coherent component, proportional to the ground state wave function and a phase incoherent component. It is shown that this assumption satisfies necessary conditions imposed by the presence of BEC and that the wave functions of the ideal Bose gas and wave functions of the Bijl-Feynman type are of this form. It is shown that this single assumption provides simple microscopic explanations of essentially all the exotic properties of helium II; why BEC implies two fluid behavior, how the superfluid and condensate fractions are linked, how Landau theory is linked to the presence of BEC, why the superfluid exhibits flow without viscosity and macroscopic quantum effects while the normal fluid does not, how the anomalous expansion and loss of spatial order, observed in helium II as it is cooled, is linked to BEC, and how the presence of sharp peaks observed in the dynamic structure factor are linked with BEC. The theory provides predictions that are in quantitative agreement with a wide range of presently unexplained experimental data on helium II.
This is the first book devoted to Bose–Einstein condensation (BEC) as an interdisciplinary subject, covering atomic and molecular physics, laser physics, low temperature physics and astrophysics. It contains 18 authoritative review articles on experimental and theoretical research in BEC and associated phenomena. Bose–Einstein condensation is a phase transition in which a macroscopic number of particles all go into the same quantum state. It has been known for some time that this phenomenon gives rise to superfluidity in liquid helium but recent research has focused on the search for BEC in other condensed matter systems, such as excitons, spin-polarised hydrogen, laser-cooled atoms, high-temperature superconductors and subatomic matter. This unique book gives an in-depth report on progress in this field and suggests promising research topics for the future. It will be of interest to graduate students and research workers in condensed matter, low temperature, atomic and laser physics.
Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K.