Supersolid helium at high pressure

Frustration-induced supersolid phases of extended Bose-Hubbard model in the hard-core limit

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.

Saga of Superfluid Solids

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.

Activated nucleation of vortices in a dipole-blockaded supersolid condensate

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.

Glass anomaly in the shear modulus of solid 4He

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).

Quantum dislocations: the fate of multiple vacancies in two-dimensional solid 4He

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.

Nonlinear elastic response in solid helium: critical velocity or strain?

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.

Pair-supersolid phase in a bilayer system of dipolar lattice bosons

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.

Hydrodynamics of superfluids confined in blocked rings and wedges

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.

Binding of a 3He impurity to a screw dislocation in solid 4He

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.

Finite-size Berezinskii-Kosterlitz-Thouless transition at grain boundaries in solid 4He and the role of 3He impurities

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.

Ac vortex-dependent torsional oscillation response and onset temperature T0 in solid 4He

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.

Observation of unusual mass transport in solid hcp (4)He

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.

Effect of 3He impurities on the nonclassical response to oscillation of solid 4He

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.

Nonclassical rotational inertia in helium crystals

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.

Nonclassical rotational inertia of a supersolid

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.

Oscillation frequency dependence of nonclassical rotation inertia of solid 4He

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.

Metastable states of a gas of dipolar bosons in a 2D optical lattice

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.

Bose-Einstein condensation in solid 4He

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.

Coexistence of ordinary elasticity and superfluidity in a model of a defect-free supersolid

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.

Measurement of the kinetic energy and lattice constant in hcp solid helium at temperatures 0.07-0.4 K

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.

Search for superfluidity in solid hydrogen

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.

Observation of classical rotational inertia and nonclassical supersolid signals in solid 4He below 250 mK

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.

Melting curve of 4He: no sign of a supersolid transition down to 10 mK

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.