Superfluidity of grain boundaries in solid 4He

Quantum polyamorphism in compressed distinguishable helium-4

We demonstrate that two amorphous solid states can exist in ⁴He consisting of distinguishable Boltzmann atoms under compressed conditions. The isothermal compression of normal or supercritical fluid ⁴He was conducted at 3-25 K using the isobaric-isothermal path integral centroid molecular dynamics simulation. The compression of fluid first produced the low-dispersion amorphous (LDA) state possessing modest extension of atomic necklaces. Further isothermal compression up to the order of 10 kbar to 1 Mbar or an isobaric cooling of LDA induced the transition to the high-dispersion amorphous (HDA) state. The HDA was characterized by long quantum wavelengths of atoms extended over several Angstroms and the promotion of atomic residual diffusion. They were related to the quantum tunneling of atoms bestriding the potential saddle points in this glass. The change in pressure or temperature induced the LDA-HDA transition reversibly with hysteresis, while it resembled the coil-globule transition of classical polymers. The HDA had lower kinetic and higher Gibbs free energies than the LDA at close temperature. The HDA was absent at T ≥ 13 K, while the LDA-HDA transition pressure significantly decreased with lowering temperature. The LDA and HDA correspond to the trapped and tunneling regimes proposed by Markland et al. [J. Chem. Phys. 136, 074511 (2012)], respectively. The same reentrant behavior as they found was observed for the expansion factor of the quantum wavelength as well as for atomic diffusivity.

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.

Dislocation Structure and Mobility in hcp ^{4}He

Using path-integral Monte Carlo simulations, we assess the core structure and mobility of the screw and edge basal-plane dislocations in hcp ^{4}He. Our findings provide key insights into recent interpretations of giant plasticity and mass flow junction experiments. First, both dislocations are dissociated into nonsuperfluid Shockley partial dislocations separated by ribbons of stacking fault, suggesting that they are unlikely to act as one-dimensional channels that may display Lüttinger-liquid-like behavior. Second, the centroid positions of the partial cores are found to fluctuate substantially, even in the absence of applied shear stresses. This implies that the lattice resistance to motion of the partial dislocations is negligible, consistent with the recent experimental observations of giant plasticity. Further results indicate that both the structure of the partial cores and the zero-point fluctuations play a role in this extreme mobility.

Compression-Driven Mass Flow in Bulk Solid ^{4}He

Mass flow has been observed in solid ^{4}He coexisting with superfluid confined in Vycor, but its physical mechanism remains an open question. Here we report observations of flow in experiments in which Vycor has been eliminated, allowing us to study the intrinsic flow in solid ^{4}He without the complications introduced by the presence of superfluid and the associated solid-liquid interfaces. By growing crystals with ^{3}He concentration as low as x_{3}=5×10^{-12}, we also avoided the low temperature flow suppression observed in previous experiments and found that the flow rate continued to increase down to at least 28 mK without saturation. In addition, ^{3}He concentrations of 120 ppb, which suppressed most of the low temperature flow in previous experiments, had no effect in our samples. The larger ^{3}He concentrations needed to block the bulk solid flow suggest that the mass flow involves a larger area, such as disordered liquid layer on solid surface and grain boundaries.

Search for supersolidity in solid 4He using multiple-mode torsional oscillators

In 2004, Kim and Chan (KC) reported a decrease in the period of torsional oscillators (TO) containing samples of solid (4)He, as the temperature was lowered below 0.2 K [Kim E, Chan MHW (2004) Science 305(5692):1941-1944]. These unexpected results constituted the first experimental evidence that the long-predicted supersolid state of solid (4)He may exist in nature. The KC results were quickly confirmed in a number of other laboratories and created great excitement in the low-temperature condensed-matter community. Since that time, however, it has become clear that the period shifts seen in the early experiments can in large part be explained by an increase in the shear modulus of the (4)He solid identified by Day and Beamish [Day J, Beamish J (2007) Nature 450(7171):853-856]. Using multiple-frequency torsional oscillators, we can separate frequency-dependent period shifts arising from changes in the elastic properties of the solid (4)He from possible supersolid signals, which are expected to be independent of frequency. We find in our measurements that as the temperature is lowered below 0.2 K, a clear frequency-dependent contribution to the period shift arising from changes in the (4)He elastic properties is always present. For all of the cells reported in this paper, however, there is always an additional small frequency-independent contribution to the total period shift, such as would be expected in the case of a transition to a supersolid state.

Topological quantum phases of 4He confined to nanoporous materials

The ground state of (4)He confined in a system with the topology of cylinder can display properties of solid, superfluid, and liquid crystal. This phase, which we call a compactified supersolid (CSS), originates from wrapping the basal planes of the bulk hcp solid into concentric cylindrical shells, with several central shells exhibiting superfluidity along the axial direction. Its main feature is the presence of a topological defect which can be viewed as a disclination with Frank index n = 1 observed in liquid crystals, and which, in addition, has a superfluid core. The CSS as well as its transition to an insulating compactified solid with a very wide hysteresis loop are found by ab initio Monte Carlo simulations. A simple analytical model captures qualitatively correctly the main property of the CSS--a gradual decrease of the superfluid response with increasing pressure.

Path-integral simulation of solids

The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.

Ideal shear strength of a quantum crystal

Using path-integral Monte Carlo simulations, we compute the ideal shear strength (ISS) on the basal plane of hcp (4)He. The failure mode upon reaching the ISS limit is characterized by the homogeneous nucleation of a stacking fault and it is found to be anisotropic, consistent with Schmid's law of resolved shear stress. Comparing the ISS of hcp (4)He to a large set of classical crystals shows that it closely fits the approximately universal modified Frenkel model of ideal strength. In addition to giving quantitative stress levels for the homogeneous nucleation of extended defects in hcp (4)He, our findings lend support to assumptions in the literature that inherently classical models remain useful for the description of mechanical behavior in quantum crystals.

Out of equilibrium plasticity dynamics and the annealing of supersolidity in solid ⁴He

We present a numerical study of a continuum plasticity field coupled to a Ginzburg-Landau model for superfluidity. The results suggest that a supersolid fraction may appear as a long-lived transient during the time evolution of the plasticity field at higher temperatures where both dislocation climb and glide are allowed. Supersolidity, however, vanishes with annealing. As the temperature is decreased, dislocation climb is arrested and any residual supersolidity due to incomplete annealing remains frozen. Our results may provide a resolution of many perplexing issues concerning a variety of experiments on bulk solid (4)He.

Observation of a superfluid component within solid helium

We demonstrate by neutron scattering that a localized superfluid component exists at high pressures within solid helium in aerogel. Its existence is deduced from the observation of two sharp phonon-roton spectra which are clearly distinguishable from modes in bulk superfluid helium. These roton excitations exhibit different roton gap parameters than the roton observed in the bulk fluid at freezing pressure. One of the roton modes disappears after annealing the samples. Comparison with theoretical calculations suggests that the model that reproduces the observed data best is that of superfluid double layers within the solid and at the helium-substrate interface.

Stress-induced dislocation roughening: a phase transition in one dimension at finite temperature

We present an example of a generically forbidden phase transition in 1D at finite temperature-stress induced and thermally assisted roughening of a superclimbing dislocation in a Peierls potential. We also argue that such roughening is behind the strong suppression of the superflow through solid (4)He in a narrow temperature range recently observed by Ray and Hallock [Phys. Rev. Lett. 105, 145301 (2010)].

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.

Dislocation mobility in a quantum crystal: the case of solid 4He

We investigate the structure and mobility of dislocations in hcp 4He crystals. In addition to fully characterizing the five elastic constants of this system, we obtain direct insight into dislocation core structures on the basal plane, which demonstrates a tendency toward dissociation into partial dislocations. Moreover, our results suggest that intrinsic lattice resistance is an essential factor in the mobility of these dislocations. This insight sheds new light on the possible correlation between dislocation mobility and the observed macroscopic behavior of crystalline 4He.

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.

Supersolid behavior in confined geometry

We have carried out torsional oscillator and heat capacity measurements on solid 4He samples grown within a geometry which restricts the helium to thin (150 microm) cylindrical disks. In contrast with previously reported values from Rittner and Reppy of 20% nonclassical rotational inertia for similar confining dimensions, 0.9% nonclassical rotational inertia (consistent with that found in bulk samples and samples embedded in porous media) was observed in our torsional oscillator cell. In this confined geometry, the heat capacity peak is consistent with that found in bulk solid samples of high crystalline quality.

Classical and quantum physics of hydrogen clusters

We present results of a comprehensive theoretical investigation of the low temperature (T) properties of clusters of para-hydrogen (p-H(2)), both pristine as well as doped with isotopic impurities (i.e., ortho-deuterium, o-D(2)). We study clusters comprising up to N = 40 molecules, by means of quantum simulations based on the continuous-space Worm algorithm. Pristine p-H(2) clusters are liquid-like and superfluid in the [Formula: see text] limit. The superfluid signal is uniform throughout these clusters; it is underlain by long cycles of permutation of molecules. Clusters with more than 22 molecules display solid-like, essentially classical behavior at temperatures down to T∼1 K; some of them are seen to turn liquid-like at sufficiently low T (quantum melting).

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.

Torsional oscillator and synchrotron X-Ray experiments on solid 4He in aerogel

X-ray diffraction experiments show that solid 4He grown in aerogel is highly polycrystalline, with an hcp crystal structure (as in bulk) and a crystallite size of approximately 100 nm. In contrast to the expectation that the highly disordered solid will have a large supersolid fraction, torsional oscillator measurements show a behavior that is strikingly similar to high purity crystals grown from the superfluid phase. The low temperature supersolid fraction is only approximately 3 x 10(-4), and the onset temperature is approximately 100 mK.

Probing the upper limit of nonclassical rotational inertia in solid helium 4

We study the effect of confinement on solid 4He's nonclassical rotational inertia fraction (NCRIF) in a torsional oscillator by constraining it to narrow annular cells of various widths. The NCRIF exhibits an observed maximum value of 20% for annuli of approximately 100 microm width. Samples constrained to porous media or to larger geometries both have smaller NCRIF, mostly below approximately 1%. In addition, we extend the blocked-annulus experiment of Kim and Chan to solid samples with large supersolid fractions. Blocking the annulus suppresses the nonclassical decoupling from 17.1% to below the limit of our detection of 0.8%. This result demonstrates the nonlocal nature of the supersolid phenomena. At 20 mK, NCRIF depends on velocity history showing a closed hysteresis loop in different thin annular cells.

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.

Local stress and superfluid properties of solid 4He

We provide a semiquantitative tool, derived from first-principles simulations, for answering the question of whether certain types of defects in solid 4He support mass superflow. Although ideal crystals of 4He are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) can turn superfluid.

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.

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.

Wetting Properties of Grain Boundaries in Solid 4He

We have observed boundaries between hcp 4He crystal grains in equilibrium with liquid 4He. We have found that, when emerging at the liquid-solid interface, a grain boundary makes a groove whose dihedral angle 2theta is nonzero. This measurement shows that grain boundaries are not completely wet by the liquid phase, in agreement with recent Monte Carlo simulations. Depending on the value of theta, the contact line of a grain boundary with a solid wall may be wet by the liquid. In this case, the line is a thin channel with a curved triangular cross section, whose measured width agrees with predictions from a simple model. We discuss these measurements in the context of grain boundary premelting and for a future understanding of the possible supersolidity of 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.

Luttinger liquid in the core of a screw dislocation in helium-4

On the basis of first-principles Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp 4He crystal features a superfluid (at T-->0) core. This is the first example of a regular quasi-one-dimensional supersolid--the phase featuring both translational and superfluid orders, and one of the cleanest cases of a Luttinger-liquid system. In contrast, the same type of screw dislocation in solid H2 is insulating.

Quantum and thermal transitions out of the supersolid phase of a 2D quantum antiferromagnet

We investigate the thermodynamic properties of a field-induced supersolid phase in a 2D quantum antiferromagnet model. Using quantum Monte Carlo simulations, a very rich phase diagram is mapped out in the temperature-magnetic-field plane, with an extended supersolid region where a diagonal (solid) order coexists with a finite XY spin stiffness (superfluid). The various quantum and thermal transitions out of the supersolid state are characterized. Experimental consequences in the context of field-induced magnetization plateau materials are briefly discussed.