1
|
Tu WL, Wu HK, Suzuki T. Frustration-induced supersolid phases of extended Bose-Hubbard model in the hard-core limit. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:455401. [PMID: 32634790 DOI: 10.1088/1361-648x/aba383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 07/07/2020] [Indexed: 06/11/2023]
Abstract
We investigate exotic supersolid phases in the extended Bose-Hubbard model with infinite projected entangled-pair state, numerical exact diagonalization, and mean-field theory. We demonstrate that many different supersolid phases can be generated by changing signs of hopping terms, and the interactions along with the frustration of hopping terms are important to stabilize those supersolid states. We argue the effect of frustration introduced by the competition of hopping terms in the supersolid phases from the mean-field point of view. This helps to give a clearer picture of the background mechanism for underlying superfluid/supersolid states to be formed. With this knowledge, we predict and realize thed-wave superfluid, which shares the same pairing symmetry with high-Tcmaterials, and its extended phases. We believe that our results contribute to preliminary understanding for desired target phases in the real-world experimental systems.
Collapse
Affiliation(s)
- Wei-Lin Tu
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Huan-Kuang Wu
- Department of Physics, Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, MD 20742, United States of America
| | - Takafumi Suzuki
- Graduate School of Engineering, University of Hyogo, Hyogo, Himeji 670-2280, Japan
| |
Collapse
|
2
|
Abstract
The article presents the state of the art and reviews the literature on the long-standing problem of the possibility for a sample to be at the same time solid and superfluid. Theoretical models, numerical simulations, and experimental results are discussed.
Collapse
|
3
|
Mason P, Josserand C, Rica S. Activated nucleation of vortices in a dipole-blockaded supersolid condensate. PHYSICAL REVIEW LETTERS 2012; 109:045301. [PMID: 23006094 DOI: 10.1103/physrevlett.109.045301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2012] [Indexed: 06/01/2023]
Abstract
We investigate theoretically and numerically a model of a supersolid in a dipole-blockaded Bose-Einstein condensate. The dependence of the superfluid fraction with an imposed thermal bath and a uniform boost velocity on the condensate is considered. Specifically, we observe a critical velocity for the nucleation of vortices in our system that is strongly linked to a steplike decrease in the superfluid fraction. We are able to use a scaling argument based on the energy required to activate a vortex, relating the critical temperature to the critical velocity, and find that this relationship is in good agreement with the numerical simulations carried out on the nonlocal Gross-Pitaevskii equation.
Collapse
Affiliation(s)
- Peter Mason
- Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | | | | |
Collapse
|
4
|
Choi H, Takahashi D, Kono K, Kim E. Evidence of Supersolidity in Rotating Solid Helium. Science 2010; 330:1512-5. [DOI: 10.1126/science.1196409] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- H. Choi
- Department of Physics and Center for Supersolid and Quantum Matter Research, KAIST, Daejeon 305-701, Republic of Korea
| | - D. Takahashi
- Low Temperature Physics Laboratory, RIKEN, Wako-shi, Saitama 351-0198, Japan
| | - K. Kono
- Low Temperature Physics Laboratory, RIKEN, Wako-shi, Saitama 351-0198, Japan
| | - E. Kim
- Department of Physics and Center for Supersolid and Quantum Matter Research, KAIST, Daejeon 305-701, Republic of Korea
| |
Collapse
|
5
|
Su JJ, Graf MJ, Balatsky AV. Glass anomaly in the shear modulus of solid 4He. PHYSICAL REVIEW LETTERS 2010; 105:045302. [PMID: 20867856 DOI: 10.1103/physrevlett.105.045302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2010] [Revised: 04/27/2010] [Indexed: 05/29/2023]
Abstract
The shear modulus of solid H{4}e exhibits an anomalous increase at low temperatures that behaves qualitatively similar to the frequency change in torsional oscillator experiments. We propose that this stiffening of the shear modulus with decreasing temperature can be described with a glass susceptibility assuming a temperature-dependent relaxation time τ(T). Below a characteristic crossover temperature T{X}, where ωτ(T{X})∼1, a significant slowing down of dynamics leads to an increase in the shear modulus. We predict that the maximum change of the amplitude of the shear modulus and the height of the dissipation peak are independent of the applied frequency ω. Our calculations also show a qualitative difference in behavior of the shear modulus depending on the temperature dependence of τ(T).
Collapse
Affiliation(s)
- Jung-Jung Su
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | |
Collapse
|
6
|
Rossi M, Vitali E, Galli DE, Reatto L. Quantum dislocations: the fate of multiple vacancies in two-dimensional solid 4He. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:145401. [PMID: 21389528 DOI: 10.1088/0953-8984/22/14/145401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Defects are believed to play a fundamental role in the supersolid state of (4)He. We have studied solid (4)He in two dimensions (2D) as a function of the number of vacancies n(v), up to 30, inserted in the initial configuration at ρ=0.0765 Å( - 2), close to the melting density, with the exact zero-temperature shadow path integral ground state method. The crystalline order is found to be stable also in the presence of many vacancies and we observe two completely different regimes. For small n(v), up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At larger n(v), the formation energy of an extra vacancy at fixed density decreases by one order of magnitude to about 0.6 K. It is no longer possible to recognize vacancies in the equilibrated state because they mainly transform into quantum dislocations and crystalline order is found almost independently of how many vacancies have been inserted in the initial configuration. The one-body density matrix in this latter regime shows a non-decaying large distance tail: dislocations, that in 2D are point defects, turn out to be mobile, their number is fluctuating, and they are able to induce exchanges of particles across the system mainly triggered by the dislocation cores. These results indicate that the notion of the incommensurate versus the commensurate state loses meaning for solid (4)He in 2D, because the number of lattice sites becomes ill defined when the system is not commensurate. Crystalline order is found to be stable also in 3D in the presence of up to 100 vacancies.
Collapse
Affiliation(s)
- M Rossi
- Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy.
| | | | | | | |
Collapse
|
7
|
Day J, Syshchenko O, Beamish J. Nonlinear elastic response in solid helium: critical velocity or strain? PHYSICAL REVIEW LETTERS 2010; 104:075302. [PMID: 20366894 DOI: 10.1103/physrevlett.104.075302] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2009] [Revised: 01/24/2010] [Indexed: 05/29/2023]
Abstract
Torsional oscillator experiments show evidence of mass decoupling in solid 4He. This decoupling is amplitude dependent, suggesting a critical velocity for supersolidity. We observe similar behavior in the elastic shear modulus. By measuring the shear modulus over a wide frequency range, we can distinguish between an amplitude dependence which depends on velocity and one which depends on some other parameter such as displacement. In contrast with the torsional oscillator behavior, the modulus depends on the magnitude of stress, not velocity. We interpret our results in terms of the motion of dislocations which are weakly pinned by 3He impurities but which break away when large stresses are applied.
Collapse
Affiliation(s)
- James Day
- Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2G7, Canada
| | | | | |
Collapse
|
8
|
Trefzger C, Menotti C, Lewenstein M. Pair-supersolid phase in a bilayer system of dipolar lattice bosons. PHYSICAL REVIEW LETTERS 2009; 103:035304. [PMID: 19659292 DOI: 10.1103/physrevlett.103.035304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2009] [Revised: 05/19/2009] [Indexed: 05/28/2023]
Abstract
The competition between tunneling and interactions in bosonic lattice models generates a whole variety of different quantum phases. While, in the presence of a single species interacting via on site interaction, the phase diagram presents only superfluid or Mott insulating phases, for long-range interactions or multiple species, exotic phases such as supersolid or pair-superfluid appear. In this Letter, we show for the first time that the coexistence of effective multiple species and long-range interactions leads to the formation of a novel pair-supersolid phase, namely, a supersolid of composites. We propose a possible implementation with dipolar bosons in a bilayer two-dimensional optical lattice.
Collapse
Affiliation(s)
- C Trefzger
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
| | | | | |
Collapse
|
9
|
|
10
|
Dasgupta C, Valls OT. Hydrodynamics of superfluids confined in blocked rings and wedges. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:016303. [PMID: 19257135 DOI: 10.1103/physreve.79.016303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2008] [Indexed: 05/27/2023]
Abstract
Motivated by many recent experimental studies of nonclassical rotational inertia (NCRI) in superfluid and supersolid samples, we present a study of the hydrodynamics of a superfluid confined in the two-dimensional region (equivalent to a long cylinder) between two concentric arcs of radii b and a (b<a) subtending an angle beta , with 0< or =beta< or =2pi . The case beta=2pi corresponds to a blocked ring. We discuss the methodology to compute the NCRI effects and calculate these effects both for small angular velocities, when no vortices are present, and in the presence of a vortex. We find that, for a blocked ring, the NCRI effect is small and that therefore there will be a large discontinuity in the moment of inertia associated with blocking or unblocking circular paths. For blocked wedges (b=0) with beta>pi , we find an unexpected divergence of the velocity at the origin, which implies the presence of either a region of normal fluid or a vortex for any nonzero value of the angular velocity. Implications of our results for experiments on "supersolid" behavior in solid 4He are discussed. A number of mathematical issues are pointed out and resolved.
Collapse
Affiliation(s)
- Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
| | | |
Collapse
|
11
|
Corboz P, Pollet L, Prokof'ev NV, Troyer M. Binding of a 3He impurity to a screw dislocation in solid 4He. PHYSICAL REVIEW LETTERS 2008; 101:155302. [PMID: 18999608 DOI: 10.1103/physrevlett.101.155302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2008] [Indexed: 05/27/2023]
Abstract
Using first-principles simulations for the probability density of finding a 3He atom in the vicinity of the screw dislocation in solid 4He, we determine the binding energy to the dislocation nucleus E(B)=0.8+/-0.1 K and the density of localized states at larger distances. The specific heat due to 3He features a peak similar to the one observed in recent experiments, and our model can also account for the observed increase in shear modulus at low temperature. We further discuss the role of 3He in the picture of superfluid defects.
Collapse
Affiliation(s)
- P Corboz
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
| | | | | | | |
Collapse
|
12
|
Gaudio S, Cappelluti E, Rastelli G, Pietronero L. Finite-size Berezinskii-Kosterlitz-Thouless transition at grain boundaries in solid 4He and the role of 3He impurities. PHYSICAL REVIEW LETTERS 2008; 101:075301. [PMID: 18764549 DOI: 10.1103/physrevlett.101.075301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2008] [Indexed: 05/26/2023]
Abstract
We analyze the complex phenomenology of the nonclassical rotational inertia (NCRI) observed at low temperature in solid 4He within the context of a two-dimensional Berezinskii-Kosterlitz-Thouless transition in a premelted 4He film at the grain boundaries. We show that both the temperature and 3He doping dependence of the NCRI fraction (NCRIF) can be ascribed to finite size effects induced by the finite grain size. We give an estimate of the average size of the grains which we argue to be limited by the isotopic 3He impurities and we provide a simple power-law relation between the NCRIF and the 3He concentration.
Collapse
Affiliation(s)
- Sergio Gaudio
- Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Rome, Italy
| | | | | | | |
Collapse
|
13
|
Penzev A, Yasuta Y, Kubota M. Ac vortex-dependent torsional oscillation response and onset temperature T0 in solid 4He. PHYSICAL REVIEW LETTERS 2008; 101:065301. [PMID: 18764467 DOI: 10.1103/physrevlett.101.065301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2007] [Indexed: 05/26/2023]
Abstract
Detailed studies of ac velocity V_{ac} and T dependence of torsional oscillator responses of solid 4He are reported. A characteristic onset temperature T_{0} approximately 0.5 K is found, below which a significant V_{ac}-dependent change occurs in the energy dissipation for the samples at approximately 32 bar and for one at 49 bar. A V_{ac} dependence of the so-called "nonclassical rotational inertia" fraction also appears below approximately T_{0}. The log(V_{ac}) linear dependence, which suggests involvement of quantized vorticies, was examined in the nonclassical rotational inertia fraction. We find a common 1/T;{2} dependence for this linear slope change in all of the samples for 30<V_{ac}<300 microm/s. We discuss that our observation is consistent with nonlinear rotational susceptibility of the vortex fluid, proposed by Anderson above T_{c} below T0.
Collapse
Affiliation(s)
- Andrey Penzev
- Institute for Solid State Physics (ISSP), University of Tokyo, Kashiwanoha 5-1-5, Kashiwa 277-8581, Japan
| | | | | |
Collapse
|
14
|
Ray MW, Hallock RB. Observation of unusual mass transport in solid hcp (4)He. PHYSICAL REVIEW LETTERS 2008; 100:235301. [PMID: 18643513 DOI: 10.1103/physrevlett.100.235301] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2008] [Revised: 04/16/2008] [Indexed: 05/26/2023]
Abstract
Solid (4)He has been created off the melting curve by growth at a nearly constant mass via the "blocked capillary" technique and growth from the (4)He superfluid at constant temperature. The experimental apparatus allows injection of (4)He atoms from superfluid directly into the solid. Evidence for the superfluidlike transport of mass through a sample cell filled with hcp solid (4)He off the melting curve is found. This mass flux depends on temperature and pressure.
Collapse
Affiliation(s)
- M W Ray
- Laboratory for Low Temperature Physics, Department of Physics, University of Massachusetts, Amherst, MA 01003, USA
| | | |
Collapse
|
15
|
Kim E, Xia JS, West JT, Lin X, Clark AC, Chan MHW. Effect of 3He impurities on the nonclassical response to oscillation of solid 4He. PHYSICAL REVIEW LETTERS 2008; 100:065301. [PMID: 18352487 DOI: 10.1103/physrevlett.100.065301] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2007] [Indexed: 05/26/2023]
Abstract
We have investigated the influence of impurities on the possible supersolid transition in 4He by systematically enriching isotopically pure samples with 3He. The addition of 3He broadens the onset of nonclassical rotational inertia and shifts it to higher temperature, suggesting that the phenomenon is correlated with the condensation of 3He atoms onto the dislocation network in solid 4He.
Collapse
Affiliation(s)
- E Kim
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | | | | | | | | | | |
Collapse
|
16
|
Clark AC, West JT, Chan MHW. Nonclassical rotational inertia in helium crystals. PHYSICAL REVIEW LETTERS 2007; 99:135302. [PMID: 17930606 DOI: 10.1103/physrevlett.99.135302] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2007] [Indexed: 05/25/2023]
Abstract
It has been proposed that the observed nonclassical rotational inertia (NCRI) in solid helium results from the superflow of thin liquid films along interconnected grain boundaries within the sample. We have observed NCRI in large (4)He crystals grown at constant temperature and pressure, demonstrating that the superfluid grain boundary model cannot explain the phenomenon.
Collapse
Affiliation(s)
- A C Clark
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
| | | | | |
Collapse
|
17
|
Aftalion A, Blanc X, Jerrard RL. Nonclassical rotational inertia of a supersolid. PHYSICAL REVIEW LETTERS 2007; 99:135301. [PMID: 17930605 DOI: 10.1103/physrevlett.99.135301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2007] [Revised: 07/16/2007] [Indexed: 05/25/2023]
Abstract
As proposed by Leggett [Phys. Rev. Lett. 25, 1543 (1970)10.1103/PhysRevLett.25.1543], the supersolidity of a crystal is characterized by the nonclassicalical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau, and Rica [Phys. Rev. Lett. 72, 2426 (1994)10.1103/PhysRevLett.72.2426], we prove that NCRI occurs. This is done by analyzing the ground state of the aforementioned model, which is related to a sphere packing problem, and then deriving a theoretical formula for the moment of inertia. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity.
Collapse
Affiliation(s)
- Amandine Aftalion
- Université Pierre et Marie Curie-Paris 6, CNRS-UMR 7598, Laboratoire Jacques-Louis Lions, 175 rue du Chevaleret, Paris, F-75013, France.
| | | | | |
Collapse
|
18
|
Aoki Y, Graves JC, Kojima H. Oscillation frequency dependence of nonclassical rotation inertia of solid 4He. PHYSICAL REVIEW LETTERS 2007; 99:015301. [PMID: 17678161 DOI: 10.1103/physrevlett.99.015301] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2007] [Indexed: 05/16/2023]
Abstract
The nonclassical rotational inertia fraction of the identical cylindrical solid 4He below 300 mK is studied at 496 and 1173 Hz by a double resonance torsional oscillator. Below 35 mK, the fractions are the same at sufficiently low rim velocities. Above 35 mK, the fraction is greater for the higher than the lower mode. The dissipation peak of the lower mode occurs at a temperature approximately 4 mK lower than that of the higher mode. The drive dependence of the two modes shows that the reduction of the fraction is characterized by critical velocity, not amplitude or acceleration.
Collapse
Affiliation(s)
- Y Aoki
- Serin Physics Laboratory, Rutgers University, Piscataway, New Jersey 08854, USA
| | | | | |
Collapse
|
19
|
Menotti C, Trefzger C, Lewenstein M. Metastable states of a gas of dipolar bosons in a 2D optical lattice. PHYSICAL REVIEW LETTERS 2007; 98:235301. [PMID: 17677913 DOI: 10.1103/physrevlett.98.235301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2006] [Revised: 04/04/2007] [Indexed: 05/16/2023]
Abstract
We investigate the physics of dipolar bosons in a two-dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this Letter, we consider the properties of the system beyond its ground state, finding that it is characterized by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and opens possibilities of using them as quantum memories.
Collapse
Affiliation(s)
- C Menotti
- ICFO - Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | | | | |
Collapse
|
20
|
Affiliation(s)
- Philip Phillips
- Loomis Laboratory of Physics, University of Illinois, Urbana, IL 61801, USA.
| | | |
Collapse
|
21
|
Diallo SO, Pearce JV, Azuah RT, Kirichek O, Taylor JW, Glyde HR. Bose-Einstein condensation in solid 4He. PHYSICAL REVIEW LETTERS 2007; 98:205301. [PMID: 17677706 DOI: 10.1103/physrevlett.98.205301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2007] [Indexed: 05/16/2023]
Abstract
We present neutron scattering measurements of the atomic momentum distribution n(k) in solid helium under a pressure p=41 bar (molar volume Vm=20.01+/-0.02 cm3/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, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the k=0 state below Tc, we find a condensate fraction of n0=(-0.10+/-1.20)% at T=80 mK and n0=(0.08+/-0.78)% at T=120 mK, consistent with zero. The shape of n(k) also does not change on crossing Tc within measurement precision.
Collapse
Affiliation(s)
- S O Diallo
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716-2593, USA
| | | | | | | | | | | |
Collapse
|
22
|
Josserand C, Pomeau Y, Rica S. Coexistence of ordinary elasticity and superfluidity in a model of a defect-free supersolid. PHYSICAL REVIEW LETTERS 2007; 98:195301. [PMID: 17677624 DOI: 10.1103/physrevlett.98.195301] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2006] [Indexed: 05/16/2023]
Abstract
The mechanical behavior of a supersolid is studied in the framework of a fully explicit model derived from the Gross-Pitaevskii equation without assuming any defect or vacancy. A set of coupled nonlinear partial differential equations plus boundary conditions is derived. The conditions of mechanical equilibrium are studied under external constraints such as steady rotation and external stress. Our model explains the experimentally observed paradoxical behavior: a nonclassical rotational inertia fraction in the limit of small rotation speed but a solidlike elastic response to small stress or an external force field.
Collapse
Affiliation(s)
- Christophe Josserand
- Institut Jean Le Rond D'Alembert, CNRS UMR 7190, Case 162, 4 place Jussieu, 75005 Paris, France
| | | | | |
Collapse
|
23
|
Adams MA, Mayers J, Kirichek O, Down RBE. Measurement of the kinetic energy and lattice constant in hcp solid helium at temperatures 0.07-0.4 K. PHYSICAL REVIEW LETTERS 2007; 98:085301. [PMID: 17359107 DOI: 10.1103/physrevlett.98.085301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2006] [Indexed: 05/14/2023]
Abstract
The single atom kinetic energy kappa of high purity solid hcp 4He has been measured by neutron Compton scattering, at temperatures between 0.07 and 0.4 K and a pressure of 40 bar. Within statistical error of approximately 2% no change in kappa was observed. The values of kappa at approximately 0.07 K were the same in a single crystal and a polycrystalline sample and were also unaffected (within statistical error) by the addition of 10 ppm of 3He. The lattice constant was also found to be independent of temperature to within 1 part in 2000. These results suggest that the supersolid transition in 4He has a different microscopic origin to the superfluid transition in the liquid.
Collapse
Affiliation(s)
- M A Adams
- ISIS Facility, Rutherford Appleton Laboratory, Chilton OX11 0QX, United Kingdom
| | | | | | | |
Collapse
|
24
|
Clark AC, Lin X, Chan MHW. Search for superfluidity in solid hydrogen. PHYSICAL REVIEW LETTERS 2006; 97:245301. [PMID: 17280295 DOI: 10.1103/physrevlett.97.245301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2006] [Indexed: 05/13/2023]
Abstract
A torsional oscillator study of solid para-hydrogen has been carried out down to 20 mK in a search for evidence of superfluidity. We found evidence of a possible phase transition, marked by an abrupt increase in the resonant period of oscillation and onset of extremely long relaxation times as the temperature was raised above 60 mK. In contrast to solid 4He, the change in the period for para-hydrogen is not a consequence of irrotational superflow. The long relaxation times observed suggest the effect is related to the motion of residual ortho-hydrogen molecules in the solid.
Collapse
Affiliation(s)
- A C Clark
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
| | | | | |
Collapse
|
25
|
|
26
|
Rittner ASC, Reppy JD. Observation of classical rotational inertia and nonclassical supersolid signals in solid 4He below 250 mK. PHYSICAL REVIEW LETTERS 2006; 97:165301. [PMID: 17155406 DOI: 10.1103/physrevlett.97.165301] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2006] [Revised: 08/15/2006] [Indexed: 05/12/2023]
Abstract
We have confirmed the existence, as first reported by Kim and Chan, of a supersolid state in solid 4He at temperatures below 250 mK. We have employed a torsional oscillator cell with a square cross section to insure a locking of the solid to the oscillating cell. We find that the nonclassical rotational inertia signal is not a universal property of solid 4He but can be eliminated through an annealing of the solid helium sample. This result has important implications for our understanding of the supersolid state.
Collapse
Affiliation(s)
- Ann Sophie C Rittner
- Laboratory of Atomic and Solid State Physics and the Cornell Center for Materials Research, Cornell University, Ithaca, NY 14853-2501, USA
| | | |
Collapse
|
27
|
Todoshchenko IA, Alles H, Bueno J, Junes HJ, Parshin AY, Tsepelin V. Melting curve of 4He: no sign of a supersolid transition down to 10 mK. PHYSICAL REVIEW LETTERS 2006; 97:165302. [PMID: 17155407 DOI: 10.1103/physrevlett.97.165302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2006] [Indexed: 05/12/2023]
Abstract
We have measured the melting curve of 4He in the temperature range from 10 to 400 mK with the accuracy of about 0.5 micro bar. Crystals of different quality show the expected T4 dependence in the range from 80 to 400 mK without any sign of the supersolid transition, and the coefficient is in excellent agreement with available data on the sound velocity in liquid 4He and on the Debye temperature of solid 4He. Below 80 mK, we have observed a small deviation from T4 dependence, which, however, cannot be attributed to the supersolid transition, because instead of decrease the entropy of the solid rather remains constant, about 2.5 x 10(-6) R.
Collapse
Affiliation(s)
- I A Todoshchenko
- Low Temperature Laboratory, Helsinki University of Technology, FIN-02015 HUT, Finland.
| | | | | | | | | | | |
Collapse
|