We describe thermal melting of the two-dimensional vortex lattice in a rotating superfluid by generalizing the Halperin and Nelson theory of dislocation-mediated melting. and derive a melting temperature proportional to the renormalized shear modulus of the vortex lattice. The rigid-body rotation of the superfluid attenuates the effects of lattice compression on the energy of dislocations and hence the melting temperature, while not affecting the shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the temperature -- rotation rate plane, and infer that the thermal melting temperature should lie below the Bose-Einstein transition temperature.
The microscopic mechanism of the melting of a crystal is analyzed by the constant pressure Monte Carlo simulation of a Lennard-Jones fcc system. Beyond a temperature of the order of 0.8 of the melting temperature, we found that the relevant excitations are lines of defects. Each of these lines has the structure of a random walk of various lengths on an fcc defect lattice. We identify these lines with the dislocation ones proposed in recent phenomenological theories of melting. Near melting we find the appearance of long lines that cross the whole system. We suggest that these long lines are th…
The behavior of the shear modulus caused by proliferation of dipoles of non-singular screw dislocations with finite-sized core is considered. The representation of two-dimensional Coulomb gas with smoothed-out coupling is used, and the stress-stress correlation function is calculated. A convolution integral expressed in terms of the modified Bessel function $K_0$ is derived in order to obtain the shear modulus in approximation of interacting dipoles. Implications are demonstrated for the shear modulus near the melting transition which are due to the singularityless character of the dislocation…
The melting of a polydisperse hard disk system is investigated by Monte Carlo simulations in the semigrand canonical ensemble. This is done in the context of possible continuous melting by a dislocation unbinding mechanism, as an extension of the 2D hard disk melting problem. We find that while there is pronounced fractionation in polydispersity, the apparent density-polydispersity gap does not increase in width, contrary to 3D polydisperse hard spheres. The point where the Young's modulus is low enough for the dislocation unbinding to occur moves with the apparent melting point, but stays wit…
Dislocations are shown to be smooth at zero temperature because of the effective Coulomb-type interaction between kinks. Crossover to finite temperature rougnehing is suggested to be a mechanism responsible for the softening of \he4 shear modulus recently observed by Day and Beamish (Nature, {\bf 450}, 853 (2007)). We discuss also that strong suppresion of superfuidity along the dislocation core by thermal kinks can lead to locking in of the mechanical and superfluid responses.
Elastic moduli and dislocation core energy of the triangular solid of hard disks of diameter $σ$ are obtained in the limit of vanishing dislocation- antidislocation pair density, from Monte Carlo simulations which incorporates a constraint, namely that all moves altering the local connectivity away from that of the ideal triangular lattice are rejected. In this limit, we show that the solid is stable against all other fluctuations at least upto densities as low as $ρσ^2 = 0.88$. Our system does not show any phase transition so diverging correlation lengths leading to finite size effects and sl…
Structural and superfluid properties of para-Hydrogen clusters of size up to N=40 molecules, are studied at low temperature (0.5 K < T < 4 K) by Path Integral Monte Carlo simulations. The superfluid fraction displays an interesting, non-monotonic behavior for 22 < N < 30. We interpret this dependence in terms of variations with N of the cluster structure. Superfluidity is observed at low T in clusters of as many as 27 molecules; in the temperature range considered here, quantum melting is observed in some clusters, which freeze at high temperature.
We present results of a theoretical study of para-hydrogen and ortho-deuterium clusters at low temperature (0.5 K < T < 3.5 K), based on Path Integral Monte Carlo simulations. Clusters of size up to N=21 para-hydrogen molecules are nearly entirely superfluid at T < 1 K. For 21 < N < 30, the superfluid response displays strong variations with N, reflecting structural changes that occur on adding or removing even a single molecule. Some clusters in this size range display quantum melting, going from solid- to liquid-like as T tends to 0. Melting is caused by quantum exchanges of molecules. The l…
Dislocation model of the supersolid state of $^4$He was proposed in 1987 by one of the authors of the review. The model obtained strong support by numerous experimental and theoretical investigations from 2007 to date. In these investigations the validity of the idea put forward in 1987 was confirmed, and new conceptions of superclimb of dislocations and of the giant isochoric compressibility or the syringe effect were proposed. In this paper we review main achievements of theoretical and experimental studies of dislocation-induced supersolid and present current understanding of this phenomeno…
Motivated by the recently developed duality between elasticity of a crystal and a symmetric tensor gauge theory by Pretko and Radzihovsky, we explore its classical analog, that is a dual theory of the dislocation-mediated melting of a two-dimensional crystal, formulated in terms of a higher derivative vector sine-Gordon model. It provides a transparent description of the continuous two-stage melting in terms of the renormalization-group relevance of two cosine operators that control the sequential unbinding of dislocations and disclinations, respectively corresponding to the crystal-to-hexatic…
We study 2D solids with weak substrate disorder, using Coulomb gas renormalisation. The melting transition is found to be replaced by a sharp crossover between a high $T$ liquid with thermally induced dislocations, and a low $T$ glassy regime with disorder induced dislocations at scales larger than $ξ_{d}$ which we compute ($ξ_{d}\gg R_{c}\sim R_{a}$, the Larkin and translational correlation lengths). We discuss experimental consequences, reminiscent of melting, such as size effects in vortex flow and AC response in superconducting films.
We investigate by direct numerical solution of appropriate renormalization flow equations, the validity of a recent dislocation unbinding theory for laser induced freezing/melting in two dimensions. The bare elastic moduli and dislocation fugacities which are inputs to the flow equations are obtained for three different 2-d systems (hard disk, inverse $12^{th}$ power and the Derjaguin-Landau-Verwey-Overbeek potentials) from a restricted Monte Carlo simulation sampling only configurations {\em without} dislocations. We conclude that (a) the flow equations need to be correct at least up to third…
We report an experimental investigation of the transition from a hexagonally ordered solid phase to a disordered liquid in a monolayer of vibrated spheres. The transition occurs as the intensity of the vibration amplitude is increased. Measurements of the density of dislocations and the positional and orientational correlation functions show evidence for a dislocation-mediated continuous transition from a solid phase with long-range order to a liquid with only short-range order. The results show a strong similarity to simulations of melting of hard disks in equilibrium, despite the fact that t…
There is a deep analogy between the physics of crystalline solids and the behavior of superfluids, dating back to pioneering work of Phillip Anderson, Paul Martin and others. The stiffness to shear deformations in a periodic crystal resembles the superfluid density that controls the behavior of supercurrents in neutral superfluids such as He^4. Dislocations in solids have a close analogy with quantized vortices in superfluids. Remarkable recent experiments on the way rod-shaped bacteria elongate their cell walls have focused attention on the dynamics and interactions of point-like dislocation …
By large-scale quantum Monte Carlo simulations we show that grain boundaries in Helium-4 crystals are generically superfluid at low temperature, with a transition temperature of the order of ~0.5K at the melting pressure; insulating grain boundaries are found only for special orientations of the grains. We also find that close vicinity to the melting line is not a necessary condition for superfluid grain boundaries, and a grain boundary in direct contact with the superfluid liquid at the melting curve is found to be mechanically stable and the grain boundary superfluidity observed by Sasaki et…
The theory describing quantum-smectics in 2+1 dimensions, based on topological quantum melting is presented. This is governed by a dislocation condensate characterized by an ordering of Burger's vector and this `dual shear superconductor' manifests itself in the form of a novel spectrum of phonon-like modes.
In the experiment on superfluid transport in solid He4 [PRL {\bf 100}, 235301 (2008)], Ray and Hallock observed an {\it anomalously large isochoric compressibility}: the supersolid samples demonstrated a significant and apparently spatially uniform response of density and pressure to chemical potential, applied locally through Vycor "electrodes". We propose that the effect is due to {\it superclimb} : edge dislocations can climb because of mass transport along superfluid cores. We corroborate the scenario by {\it ab initio} simulations of an edge dislocation in solid He4 at $T=0.5K$. We argue …
According to the Kosterlitz-Thouless-Theory two-dimensional solid films melt by the unbinding of dislocation pairs. A model including quenched random impurities was already studied by Nelson [Phys. Rev. B 27 (1983) 2902], who predicted a reentrance into the disordered phase at low temperatures and weak disorder. New investigations of the physically related XY-model [e.g. T. Nattermann et al., J. Phys. (France) 5 (1995), 565] and a work of Cha and Fertig [Phys. Rev. Lett. 74 (1995) 4867] refuse this reentrant melting. In this work we map the system onto a two-dimensional vector Coulomb gas and …
We study lattice melting in two dimensional antiferromagnets. We argue that, for strong enough magnetic interactions, single lattice dislocations are prohibitive due to magnetic frustration. This leads to a melting scenario in which a tetratic phase, composed of free dislocation pairs and bound disclinations, separates the solid from the liquid phases. We demonstrate this phase numerically in a system of hard spheres confined between parallel plates, where spins are represented by the the heights of the spheres. We find that, in the tetratic phase, the spins are as antiferromagnetically ordere…
We suggest that below a certain temperature T_k, the free energy for the creation of kinks-antikinks pairs in the dislocation network of solid He4 becomes negative. The underlying physical mechanism is the related liberation of vacancies which initiate Feynman's permutation cycles in the bulk. Consequently, dislocations should wander and sweep an increasingly larger volume at low temperatures. This phenomenon should lead both to a stiffening of the solid below T_k and to the appearance of a non zero superfluid fraction at a second temperature T_c < T_k.
I show using Landau theory that quenched dislocations can facilitate the supersolid (SS) to normal solid (NS) transition, making it possible for the transition to occur even if it does not in a dislocation-free crystal. I make detailed predictions for the dependence of the SS to NS transition temperature T_c(L), superfluid density %ρ_S(T, L), and specific heat C(T,L) on temperature T and dislocation spacing L, all of which can be tested against experiments. The results should also be applicable to an enormous variety of other systems, including, e.g., ferromagnets.
We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.
A theory accounting for the dynamical aspects of the superfluid response of one dimensional (1D) quantum fluids is reported. In long 1D systems the onset of superfluidity is related to the dynamical suppression of quantum phase slips at low temperatures. The effect of this suppression as a function of frequency and temperature is discussed within the framework of the relevant correlation function that is accessible experimentally, namely the momentum response function. Application of these results to the understanding of the superfluid properties of helium confined in nanometer-size pores, edg…
A molecular dynamics study of a two dimensional system of particles interacting through a Lennard-Jones pairwise potential is performed at fixed temperature and vanishing external pressure. As the temperature is increased, a solid-to-liquid transition occurs. When the melting temperature $T_c$ is approached from below, there is a proliferation of dislocation pairs and the elastic constant approaches the value predicted by the KTHNY theory. In addition, as $T_c$ is approached from above, the relaxation time increases, consistent with an approach to criticality. However, simulations fail to prod…
A phenomenological criterion for the superfluid transition is proposed, which is similar to the Lindemann criterion for the crystal melting. Then we derive a new formula for the critical temperature, relating $T_λ$ to the mean kinetic energy per particle above the transition. The suppression of the critical temperature in a sufficiently dense liquid is described as a result of the quantum decoherence phenomenon. The theory can account for the observed dependence of $T_λ$ on density in liquid helium and results in an estimate $T_λ \sim 1.1$ K for molecular hydrogen.
Motivated by recent experiments on possible supersolid behavior of $^4$He solids at low temperature, we consider a model of superfluidity in a defected solid containing a system spaning network of correlated linear dislocations, or planar grain boundaries. Using arguments based on the Harris criterion, as well as numerical simulations, we find that such correlated quenched disorder shifts the familiar superfluid lambda transition to a new disordered universality class in which the correlation length exponent $ν\ge 1$. This results in the temperature-derivates for the superfluid density, $dρ_{\…
We study crystal melting in two-dimensional antiferromagnets, by analyzing the statistical mechanics of the six-state clock model on a lattice in which defects (dislocations and disclinations) are allowed to appear. We show that the elementary dislocations bind to fractional magnetic vortices. We compute the phase diagram by mapping the system into a Coulomb gas model. Surprisingly, we find that in the limit of dominant magnetic interactions, antiferromagnetism can survive even in the hexatic and liquid phases. The ensuing molten antiferromagnets are topologically ordered and are characterized…
The superfluid density is calculated theoretically for incompressible vortex lattices in two dimensions that have isolated dislocations quenched in by a random arrangement of pinned vortices. The latter are assumed to be sparse and to be fixed to material defects. It is shown that the pinned vortices act to confine a single dislocation of the vortex lattice along its glide plane. Plastic creep of the two-dimensional vortex lattice is thereby impeded, and macroscopic phase coherence results at low temperature in the limit of a dilute concentration of quenched-in dislocations.
Adsorption of para-hydrogen films on Alkali metals substrates at low temperature is studied theoretically by means of Path Integral Monte Carlo simulations. Realistic potentials are utilized to model the interaction between two para-hydrogen molecules, as well as between a para-hydrogenmolecule and the substrate, assumed smooth. Results show that adsorption of para-hydrogen on a Lithium substrate, the most attractive among the Alkali, occurs through completion of successive solid adlayers. Each layer has a two-dimensional density approximatley equal 0.070 inverse square Angstroms. A solid para…
We study the nature of melting of a two dimensional (2D) Lennard-Jones solid using large scale Monte Carlo simulation. We use systems of up to 102,400 particles to capture the decay of the correlation functions associated with translational order (TO) as well as the bond-orientational (BO) order. We study the role of dislocations and disclinations and their distribution functions. We computed the temperature dependence of the second moment of the two order parameters, i.e., of the TO order parameter as well as of the order parameter associated with BO order and using finite-size scaling we det…
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 provide a resolution of many perplexing issues concerning a variety of experi…
