Absence of supersolidity in solid helium in porous Vycor glass

Giant magnetocaloric effect in spin supersolid candidate Na2BaCo(PO4)2

Supersolid, an exotic quantum state of matter that consists of particles forming an incompressible solid structure while simultaneously showing superfluidity of zero viscosity1, is one of the long-standing pursuits in fundamental research2,3. Although the initial report of 4He supersolid turned out to be an artefact4, this intriguing quantum matter has inspired enthusiastic investigations into ultracold quantum gases5-8. Nevertheless, the realization of supersolidity in condensed matter remains elusive. Here we find evidence for a quantum magnetic analogue of supersolid-the spin supersolid-in the recently synthesized triangular-lattice antiferromagnet Na2BaCo(PO4)2 (ref. 9). Notably, a giant magnetocaloric effect related to the spin supersolidity is observed in the demagnetization cooling process, manifesting itself as two prominent valley-like regimes, with the lowest temperature attaining below 100 mK. Not only is there an experimentally determined series of critical fields but the demagnetization cooling profile also shows excellent agreement with the theoretical simulations with an easy-axis Heisenberg model. Neutron diffractions also successfully locate the proposed spin supersolid phases by revealing the coexistence of three-sublattice spin solid order and interlayer incommensurability indicative of the spin superfluidity. Thus, our results reveal a strong entropic effect of the spin supersolid phase in a frustrated quantum magnet and open up a viable and promising avenue for applications in sub-kelvin refrigeration, especially in the context of persistent concerns about helium shortages10,11.

Tuning Photon-Mediated Interactions in a Multimode Cavity: From Supersolid to Insulating Droplets Hosting Phononic Excitations

Ultracold atoms trapped in laser-generated optical lattices serve as a versatile platform for quantum simulations. However, as these lattices are infinitely stiff, they do not allow to emulate phonon degrees of freedom. This restriction can be lifted in emerged optical lattices inside multimode cavities. Motivated by recent experimental progress in multimode cavity QED, we propose a scheme to implement and study supersolid and droplet states with phononlike lattice excitations by coupling a Bose gas to many longitudinal modes of a ring cavity. The interplay between contact collisional and tunable-range cavity-mediated interactions leads to a rich phase diagram, which includes elastic supersolid as well as insulating droplet phases exhibiting roton-type mode softening for a continuous range of momenta across the superradiant phase transition. The nontrivial dynamic response of the system to a local density perturbation further proves the existence of phononlike modes.

Absence of Off-Diagonal Long-Range Order in hcp ^{4}He Dislocation Cores

The mass transport properties along dislocation cores in hcp ^{4}He are revisited by considering two types of edge dislocations as well as a screw dislocation, using a fully correlated quantum simulation approach. Specifically, we employ the zero-temperature path-integral ground state (PIGS) method together with ergodic sampling of the permutation space to investigate the fundamental dislocation core structures and their off-diagonal long-range order properties. It is found that the Bose-Einstein condensate fraction of such defective ^{4}He systems is practically null (≤10^{-6}), just as in the bulk defect-free crystal. These results provide compelling evidence for the absence of intrinsic superfluidity in dislocation cores in hcp ^{4}He and challenge the superfluid dislocation-network interpretation of the mass-flux-experiment observations, calling for further experimental investigation.

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Can Angular Oscillations Probe Superfluidity in Dipolar Supersolids?

Angular oscillations can provide a useful probe of the superfluid properties of a system. Such measurements have recently been applied to dipolar supersolids, which exhibit both density modulation and phase coherence, and for which robust probes of superfluidity are particularly interesting. So far, these investigations have been confined to linear droplet arrays, which feature relatively simple excitation spectra, but limited sensitivity to the effects of superfluidity. Here, we explore angular oscillations in systems with 2D structure which, in principle, have greater sensitivity to superfluidity. In both experiment and simulation, we find that the interplay of superfluid and crystalline excitations leads to a frequency of angular oscillations that remains nearly unchanged even when the superfluidity of the system is altered dramatically. This indicates that angular oscillation measurements do not always provide a robust experimental probe of superfluidity with typical experimental protocols.

Supersolid gap soliton in a Bose-Einstein condensate and optical ring cavity coupling system

The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.

Discovery of quantum phases in the Shastry-Sutherland compound SrCu2(BO3)2 under extreme conditions of field and pressure

The 2-dimensional layered oxide material SrCu₂(BO₃)₂, long studied as a realization of the Shastry-Sutherland spin topology, exhibits a range of intriguing physics as a function of both hydrostatic pressure and magnetic field, with a still debated intermediate plaquette phase appearing at approximately 20 kbar and a possible deconfined critical point at higher pressure. Here, we employ a tunnel diode oscillator (TDO) technique to probe the behavior in the combined extreme conditions of high pressure, high magnetic field, and low temperature. We reveal an extensive phase space consisting of multiple magnetic analogs of the elusive supersolid phase and a magnetization plateau. In particular, a 10 × 2 supersolid and a 1/5 plateau, identified by infinite Projected Entangled Pair States (iPEPS) calculations, are found to rely on the presence of both magnetic and non-magnetic particles in the sea of dimer singlets. These states are best understood as descendants of the full-plaquette phase, the leading candidate for the intermediate phase of SrCu₂(BO₃)₂.

SrCu2(BO3)2 is a 2D quantum antiferromagnet on a particular frustrated lattice showing multiple magnetization plateaus and quantum phase transitions under high pressure. Here the authors uncover novel magnetic phases in this material under combined effects of extreme magnetic field and pressure.

Self-Organization in Cold Atoms Mediated by Diffractive Coupling

This article discusses self-organization in cold atoms via light-mediated interactions induced by feedback from a single retro-reflecting mirror. Diffractive dephasing between the pump beam and the spontaneous sidebands selects the lattice period. Spontaneous breaking of the rotational and translational symmetry occur in the 2D plane transverse to the pump. We elucidate how diffractive ripples couple sites on the self-induced atomic lattice. The nonlinear phase shift of the atomic cloud imprinted onto the optical beam is the parameter determining coupling strength. The interaction can be tailored to operate either on external degrees of freedom leading to atomic crystallization for thermal atoms and supersolids for a quantum degenerate gas, or on internal degrees of freedom like populations of the excited state or Zeeman sublevels. Using the light polarization degrees of freedom on the Poincaré sphere (helicity and polarization direction), specific irreducible tensor components of the atomic Zeeman states can be coupled leading to spontaneous magnetic ordering of states of dipolar and quadrupolar nature. The requirements for critical interaction strength are compared for the different situations. Connections and extensions to longitudinally pumped cavities, counterpropagating beam schemes and the CARL instability are discussed.

Evidence of superfluidity in a dipolar supersolid from nonclassical rotational inertia

A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Nonclassical rotational effects have also been considered in the context of the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here, we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. Using a dipolar gas of dysprosium atoms, we studied a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, previously investigated in ordinary superfluids. From the measured moment of inertia, we deduced a superfluid fraction that is different from zero and of order of unity, providing direct evidence of the superfluid nature of the dipolar supersolid.

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.

Superfluid and Supersolid Phases of ^{4}He on the Second Layer of Graphite

We revisited the phase diagram of the second layer of ^{4}He on top of graphite using quantum Monte Carlo methods. Our aim was to explore the existence of the novel phases suggested recently in experimental works, and determine their properties and stability limits. We found evidence of a superfluid quantum phase with hexatic correlations, induced by the corrugation of the first Helium layer, and a quasi-two-dimensional supersolid corresponding to a 7/12 registered phase. The 4/7 commensurate solid was found to be unstable, while the triangular incommensurate crystals, stable at large densities, were normal.

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.

Rotating a Supersolid Dipolar Gas

Distinctive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment of inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation, we show that the moment of inertia determines the value of the frequency of the scissors mode, which is significantly affected by the reduction of superfluidity in the supersolid phase. The case of an in-plane isotropic trapping is instead well suited to study the formation of quantized vortices, which are shown to be characterized, in the supersolid phase, by a sizeable deformed core, caused by the presence of the surrounding density peaks.

Formation of Nuclear-Polarized Phases of H Atoms Embedded in Solid H_{2} Films

We report on an experimental observation of two phases of hydrogen atoms in solid H_{2} films at temperatures of 0.1-0.8 K, characterized by a large enhancement of the nuclear spin polarization compared to that given by Boltzmann statistics (p=0.15 at T=0.15  K). The first phase with p=0.35(5) is formed spontaneously during sample storage in a high magnetic field (B=4.6  T). The second phase with an even higher nuclear polarization, p=0.75(7), can be achieved at T≤0.55  K by repeating sequences of dynamic nuclear polarization followed by a system relaxation. Upon warming through the range 0.55-0.65 K, the highly nuclear-polarized phase undergoes a phase transition to the spontaneously polarized phase which breaks down at T≃0.8  K, and the nuclear polarization gradually converges to the Boltzmann distribution. We discuss possible scenarios for explaining the nature of the observed phenomena.

Observation of a Dipolar Quantum Gas with Metastable Supersolid Properties

The competition of dipole-dipole and contact interactions leads to exciting new physics in dipolar gases, well illustrated by the recent observation of quantum droplets and rotons in dipolar condensates. We show that the combination of the roton instability and quantum stabilization leads under proper conditions to a novel regime that presents supersolid properties due to the coexistence of stripe modulation and phase coherence. In a combined experimental and theoretical analysis, we determine the parameter regime for the formation of coherent stripes, whose lifetime of a few tens of milliseconds is limited by the eventual destruction of the stripe pattern due to three-body losses. Our results open intriguing prospects for the development of long-lived dipolar supersolids.

Mass Flow through Solid ^{3}He in the bcc Phase

A number of experiments have shown that mass can be transported through solid ^{4}He at temperatures as low as 16 mK, with features that suggest superflow. But the nature of this flow remains unclear. The Fermi isotope ^{3}He provides the possibility of a direct comparison to a solid in which quantum effects are even more important but superfluidity is not expected. We have made flow measurements on high purity bcc ^{3}He, using the same cell in which we observed a superfluidlike response in hcp ^{4}He when pressure differences were applied. We observed flow but, in marked contrast to ^{4}He, it decreased monotonically with temperature. Near melting, the flow was thermally activated with an energy of 0.85 K, but some flow remained even at 30 mK. The flow rates in the solid were essentially constant below 100 mK, even in low density samples that remelted at low temperatures. The very different behaviors of solid ^{3}He and ^{4}He support the interpretation of superflow in ^{4}He. Although such superflow is not possible in ^{3}He, the temperature-independent flow below 100 mK indicates that the flow in this regime also has a quantum origin. The flow must involve defects and, based on the magnitude of the flow and comparisons to other experiments, we conclude that in both the thermal and the quantum regimes the flow involves motion of dislocations via thermally activated or tunneling motion of kinks.

Searching for Supersolidity in Ultracold Atomic Bose Condensates with Rashba Spin-Orbit Coupling

We developed a functional integral formulation for the stripe phase of spinor Bose-Einstein condensates with Rashba spin-orbit coupling. The excitation spectrum is found to exhibit double gapless band structures, identified to be two Goldstone modes resulting from spontaneously broken internal gauge symmetry and translational invariance symmetry. The sound velocities display anisotropic behavior with the lower branch vanishing in the direction perpendicular to the stripe in the x-y plane. At the transition point between the plane-wave phase and the stripe phase, physical quantities such as fluctuation correction to the ground-state energy and quantum depletion of the condensates exhibit discontinuity, characteristic of the first-order phase transition. Despite strong quantum fluctuations induced by Rashba spin-orbit coupling, we show that the supersolid phase is stable against quantum depletion. Finally, we extend our formulation to finite temperatures to account for interactions between excitations.

Driven-Dissipative Supersolid in a Ring Cavity

Supersolids are characterized by the counterintuitive coexistence of superfluid and crystalline order. Here we study a supersolid phase emerging in the steady state of a driven-dissipative system. We consider a transversely pumped Bose-Einstein condensate trapped along the axis of a ring cavity and coherently coupled to a pair of degenerate counterpropagating cavity modes. Above a threshold pump strength the interference of photons scattered into the two cavity modes results in an emergent superradiant lattice, which spontaneously breaks the continuous translational symmetry towards a periodic atomic pattern. The crystalline steady state inherits the superfluidity of the Bose-Einstein condensate, thus exhibiting genuine properties of a supersolid. A gapless collective Goldstone mode correspondingly appears in the superradiant phase, which can be nondestructively monitored via the relative phase of the two cavity modes on the cavity output. Despite cavity-photon losses the Goldstone mode remains undamped, indicating the robustness of the supersolid phase.

Dipolar Bose Supersolid Stripes

We study the superfluid properties of a system of fully polarized dipolar bosons moving in the XY plane. We focus on the general case where the polarization field forms an arbitrary angle α with respect to the Z axis, while the system is still stable. We use the diffusion Monte Carlo and the path integral ground state methods to evaluate the one-body density matrix and the superfluid fractions in the region of the phase diagram where the system forms stripes. Despite its oscillatory behavior, the presence of a finite large-distance asymptotic value in the s-wave component of the one-body density matrix indicates the existence of a Bose condensate. The superfluid fraction along the stripes direction is always close to 1, while in the Y direction decreases to a small value that is nevertheless different from zero. These two facts confirm that the stripe phase of the dipolar Bose system is a clear candidate for an intrinsic supersolid without the presence of defects as described by the Andreev-Lifshitz mechanism.

Disordered Supersolids in the Extended Bose-Hubbard Model

The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.

Vortices and vortex lattices in quantum ferrofluids

The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.

Ultra-robust high-field magnetization plateau and supersolidity in bond-frustrated MnCr2S4

Frustrated magnets provide a promising avenue for realizing exotic quantum states of matter, such as spin liquids and spin ice or complex spin molecules. Under an external magnetic field, frustrated magnets can exhibit fractional magnetization plateaus related to definite spin patterns stabilized by field-induced lattice distortions. Magnetization and ultrasound experiments in MnCr₂S₄ up to 60 T reveal two fascinating features: (i) an extremely robust magnetization plateau with an unusual spin structure and (ii) two intermediate phases, indicating possible realizations of supersolid phases. The magnetization plateau characterizes fully polarized chromium moments, without any contributions from manganese spins. At 40 T, the middle of the plateau, a regime evolves, where sound waves propagate almost without dissipation. The external magnetic field exactly compensates the Cr-Mn exchange field and decouples Mn and Cr sublattices. In analogy to predictions of quantum lattice-gas models, the changes of the spin order of the manganese ions at the phase boundaries of the magnetization plateau are interpreted as transitions to supersolid phases.

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.

Integrable model for density-modulated quantum condensates: Solitons passing through a soliton lattice

An integrable model possessing inhomogeneous ground states is proposed as an effective model of nonuniform quantum condensates such as supersolids and Fulde-Ferrell-Larkin-Ovchinnikov superfluids. The model is a higher-order analog of the nonlinear Schrödinger equation. We derive an n-soliton solution via the inverse scattering theory with elliptic-functional background and reveal various kinds of soliton dynamics such as dark soliton billiards, dislocations, gray solitons, and envelope solitons. We also provide the exact bosonic and fermionic quasiparticle eigenstates and show their tunneling phenomena. The solutions are expressed by a determinant of theta functions.

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.

Helium mass flow through a solid-superfluid-solid junction

We report the results of flow experiments in which two chambers containing solid ^{4}He are connected by a superfluid Vycor channel. At low temperatures and pressures, mechanically squeezing the solid in one chamber produced a pressure increase in the second chamber, a measure of mass transport through our solid-superfluid-solid junction. This pressure response is very similar to the flow seen in recent experiments at the University of Massachusetts: it began around 600 mK, increased as the temperature was reduced, then decreased dramatically at a temperature, T_{d}, which depended on the ^{3}He impurity concentration. Our experiments indicate that the flow is limited by mass transfer across the solid-liquid interface near the Vycor ends, where the ^{3}He collects at low temperature, rather than by flow paths within the solid ^{4}He.

Supersolid phase accompanied by a quantum critical point in the intermediate coupling regime of the Holstein model

We reveal that electron-phonon systems described by the Holstein model on a bipartite lattice exhibit, away from half filling, a supersolid (SS) phase characterized by coexisting charge order (CO) and superconductivity (SC), and an accompanying quantum critical point (QCP). The SS phase, demonstrated by the dynamical mean-field theory with a quantum Monte Carlo impurity solver, emerges in the intermediate-coupling regime, where the peak of the Tc dome is located and the metal-insulator crossover occurs. On the other hand, in the weak- and strong-coupling regimes the CO-SC boundary is of first order with no intervening SS phases. The QCP is associated with the continuous transition from SS to SC and characterized by a reentrant behavior of the SS around it. We further show that the SS-SC transition is hallmarked by diverging charge fluctuations and a kink (peak) in the superfluid density.

Universal temperature dependence, flux extinction, and the role of 3He impurities in superfluid mass transport through solid 4He

The mass flux, F, carried by as-grown solid (4)He in the range 25.6-26.3 bar rises with falling temperature, and at a concentration-dependent temperature, T(d), the flux decreases sharply within a few mK. We study F as a function of (3)He impurity concentration, χ. We find that T(d) is an increasing function of increasing χ. At temperatures above T(d) the flux has a universal temperature dependence and the flux terminates in a narrow window near a characteristic temperature T(h) ≈ 625 mK, which is independent of χ.

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.

Microscopic molecular superfluid response: theory and simulations

Since its discovery in 1938, superfluidity has been the subject of much investigation because it provides a unique example of a macroscopic manifestation of quantum mechanics. About 60 years later, scientists successfully observed this phenomenon in the microscopic world though the spectroscopic Andronikashvili experiment in helium nano-droplets. This reduction of scale suggests that not only helium but also para-H2 (pH2) can be a candidate for superfluidity. This expectation is based on the fact that the smaller number of neighbours and surface effects of a finite-size cluster may hinder solidification and promote a liquid-like phase. The first prediction of superfluidity in pH2 clusters was reported in 1991 based on quantum Monte Carlo simulations. The possible superfluidity of pH2 was later indirectly observed in a spectroscopic Andronikashvili experiment in 2000. Since then, a growing number of studies have appeared, and theoretical simulations have been playing a special role because they help guide and interpret experiments. In this review, we go over the theoretical studies of pH2 superfluid clusters since the experiment of 2000. We provide a historical perspective and introduce the basic theoretical formalism along with key experimental advances. We then present illustrative results of the theoretical studies and comment on the possible future developments in the field. We include sufficient theoretical details such that the review can serve as a guide for newcomers to the field.

Defect-induced supersolidity with soft-core bosons

More than 40 years ago, Andreev, Lifshitz and Chester suggested the possible existence of a peculiar solid phase of matter, the microscopic constituents of which can flow superfluidly without resistance due to the formation of zero-point defects in the ground state of self-assembled crystals. Yet, a physical system where this mechanism is unambiguously established remains to be found, both experimentally and theoretically. Here we investigate the zero-temperature phase diagram of two-dimensional bosons with finite-range soft-core interactions. For low particle densities, the system is shown to feature a solid phase in which zero-point vacancies emerge spontaneously and give rise to superfluid flow of particles through the crystal. This provides the first example of defect-induced, continuous-space supersolidity consistent with the Andreev-Lifshitz-Chester scenario.

Multicritical behavior in models with two competing order parameters

We employ the nonperturbative functional renormalization group to study models with an O(N(1) ⊕O(N)(2)) symmetry. Here different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N(1),N(2) plane. We study the fate of nontrivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of noncanonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.

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.

A cryogenic high pressure cell for inelastic neutron scattering measurements of quantum fluids and solids

We present our new development of a high pressure cell for inelastic neutron scattering measurements of helium at ultra-low temperatures. The cell has a large sample volume of ~140 cm(3) and a working pressure of ~7 MPa, with a relatively thin wall-thickness (1.1 mm)--thanks to the high yield strength aluminum used in the design. Two variants of this cell have been developed. The first cell is permanently joined components using electron-beam welding and explosion welding, methods that have little or no impact on the global heat treatment of the cell. The second cell discussed has modular and interchangeable components, which includes a capacitance pressure gauge, that can be sealed using the traditional indium wire technique. The performance of the cells have been tested in recent measurements on superfluid liquid helium near the solidification line.