Kosterlitz-Thouless transition in helium films

Parylene-bonded micro-fluidic channels for cryogenic experiments at superfluid He-4 temperatures

We present the manufacturing process of a (24.5 × 100) μm2-sized on-chip flow channel intended for flow experiments with normal and superfluid phases of 4He and showcase such a proof-of-concept experiment. This work proves the suitability of chip-to-chip bonding using a thin layer of Parylene-C for cryogenic temperatures as a simpler alternative to other techniques, such as anodic bonding. A monocrystalline silicon chip embeds the etched meander-shaped micro-fluidic channel and a deposited platinum heater and is bonded to a Pyrex glass top. We test the leak tightness of the proposed bonding method for superfluid 4He, reaching temperatures of ≈1.6 K and evaluate its possible effects on flow experiments. We demonstrate that powering an on-chip platinum heater affects the superfluid flow rate by local overheating of a section of the micro-fluidic channel.

Spatially Modulated Superfluid State in Two-Dimensional ^{4}He Films

The second layer of ^{4}He films adsorbed on a graphite substrate is an excellent experimental platform to study the interplay between superfluid and structural orders. Here, we report a rigid two-frequency torsional oscillator study on the second layer as a function of temperature and ^{4}He atomic density. For the first time, we show experimentally that the superfluid density is independent of frequency, which can be interpreted as unequivocal evidence of genuine superfluidity. The phase diagram established in this work reveals that a superfluid phase coexists with hexatic density-wave correlation and a registered solid phase. This suggests the second layer as a candidate for hosting two exotic quantum ground states: the spatially modulated superfluid and supersolid phases resulting from the interplay between superfluid and structural orders.

Vortex Motion Quantifies Strong Dissipation in a Holographic Superfluid

Holographic duality provides a description of strongly coupled quantum systems in terms of weakly coupled gravitational theories in a higher-dimensional space. It is a challenge, however, to quantitatively determine the physical parameters of the quantum systems corresponding to generic holographic theories. Here, we address this problem for the two-dimensional holographic superfluid, known to exhibit strong dissipation. We numerically simulate the motion of a vortex dipole and perform a high-precision matching of the corresponding dynamics resulting from the dissipative Gross-Pitaevskii equation. Excellent agreement is found for the vortex core shape and the spatiotemporal trajectories. A further comparison to the Hall-Vinen-Iordanskii equations for point vortices interacting with the superfluid allows us to determine the friction parameters of the holographic superfluid. Our results suggest that holographic vortex dynamics can be applied to experimentally accessible superfluids like strongly coupled ultracold Bose gases or thin helium films with temperatures in the Kelvin range. This would make holographic far-from-equilibrium dynamics and turbulence amenable to experimental tests.

Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip

Quantized vortices are fundamental to the two-dimensional dynamics of superfluids, from quantum turbulence to phase transitions. However, surface effects have prevented direct observations of coherent two-dimensional vortex dynamics in strongly interacting systems. Here, we overcome this challenge by confining a thin film of superfluid helium at microscale on the atomically smooth surface of a silicon chip. An on-chip optical microcavity allows laser initiation of clusters of quasi-two-dimensional vortices and nondestructive observation of their decay in a single shot. Coherent dynamics dominate, with thermal vortex diffusion suppressed by five orders of magnitude. This establishes an on-chip platform with which to study emergent phenomena in strongly interacting superfluids and to develop quantum technologies such as precision inertial sensors.

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.

Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: Irrelevance of amplitude and out-of-plane fluctuations

We develop a functional renormalization group (FRG) approach for the two-dimensional XY model by combining the lattice FRG proposed by Machado and Dupuis [Phys. Rev. E 82, 041128 (2010)PLEEE81539-375510.1103/PhysRevE.82.041128] with a duality transformation that explicitly introduces vortices via an integer-valued field. We show that the hierarchy of FRG flow equations for the infinite set of relevant and marginal couplings of the model can be reduced to the well-known Kosterlitz-Thouless renormalization group equations for the renormalized temperature and the vortex fugacity. Within our approach it is straightforward to include weak amplitude as well as out-of-plane fluctuations of the spins, which lead to additional interactions between the vortices that do not spoil the Berezinskii-Kosterlitz-Thouless transition. This demonstrates that previous failures to obtain a line of true fixed points within the FRG are a mathematical artifact of insufficient truncation schemes.

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.

Kosterlitz-Thouless physics: a review of key issues

This article reviews, from a very personal point of view, the origins and the early work on transitions driven by topological defects such as vortices in the two dimensional planar rotor model and in (4)Helium films and dislocations and disclinations in 2D crystals. I cover the early papers with David Thouless and describe the important insights but also the errors and oversights since corrected by other workers. I then describe some of the experimental verifications of the theory and some numerical simulations. Finally applications to superconducting arrays of Josephson junctions and to recent cold atom experiments are described.

Anisotropic superfluidity of (4)He on a C36 fullerene molecule

We have performed path-integral Monte Carlo calculations to study the adsorption of (4)He atoms on two different C36 isomers with the D6h and the D2d symmetries. The radial (4)He density distributions reveal layer-by-layer growth with the first layer being located at a distance of ∼5.5 Å from the C36 molecular center and the second layer at ∼8.3 Å. From the angular density profiles of (4)He, we find different quantum states as the number of (4)He adatoms N varies. For N = 20, we observe commensurate solid structures on both D6h and D2d isomers, where each of 8 hexagon and 12 pentagon centers of the fullerene surfaces is occupied by a single (4)He atom. The second-layer promotion starts beyond N = 38 on both isomers, where a compressible incommensurate structure is observed on the D6h isomer and another commensurate structure on D2d. Between N = 20 and N = 38, the (4)He monolayer on D6h shows several distinct rings of delocalized (4)He atoms along with strongly anisotropic superfluid responses at low temperatures, while isotropic but weak superfluid responses are observed in the (4)He layer on D2d.

4He adsorption on a H(2)-plated C20 molecular surface: the formation of helium buckyballs

We perform path-integral Monte Carlo calculations to study the adsorption of 4He atoms on a H2-plated C20 molecular surface. It is found that 32 H2 molecules form a complete solid layer on C20, where each H2 molecule is located either above one of the 12 pentagon centers or above one of the 20 carbon atoms. The angular density profiles of the first 4He layer on the (H2)32-C20 surface reveal different quantum states as the number of 4He atoms N varies. Especially, the helium layer exhibits an icosidodecahedron structure for N=30, where each 4He atom is located at one of the vertices of 20 corner-sharing triangles. While the 4He density peaks for N=60 constitute a truncated icosahedron with 12 pentagonal and 20 hexagonal faces, the additional atoms beyond N=60 are found to be placed at the hexagon centers of the truncated icosahedron to form a hexakis truncated icosahedron for N=80. The superfluid response of the 4He layer at a temperature of T=0.6 K is found to be completely quenched for N=30 and to be significantly suppressed for N=60 and 80, reflecting the formation of compact buckyball structures.

Temperature-dependent pinning or depinning of a 3He overlayer in a 3He-4He mixture film

We report the results of a quartz crystal microbalance experiment at 100 MHz for a 3He-4He mixture film on a planar gold substrate. The results reveal temperature-dependent pinning or depinning of 3He overlayers above a critical oscillation velocity and indicate that the appearance of a macroscopic condensed state in the underlying 4He layer possibly affects the interfacial friction.

Quasi-2D liquid 3He

Quantum Monte Carlo simulations at zero temperature of an ensemble of 3He atoms adsorbed on Mg and Alkali substrates yield strong evidence of a thermodynamically stable liquid 3He monolayer on all Alkali substrates, with the possible exception of Li. The effective two-dimensional density is θ≈0.02  Å-2 on Na, making it the lowest density liquid in nature. Its existence is underlain by zero-point atomic motion perpendicular to the substrate, whose effect is softening the short-range repulsion of the helium interatomic potential. The monolayer films should turn superfluid at a temperature Tc∼1  mK. No liquid film is predicted to form on Mg, or on stronger substrates such as graphite.

Integrated electronic transport and thermometry at milliKelvin temperatures and in strong magnetic fields

We fabricated a He-3 immersion cell for transport measurements of semiconductor nanostructures at ultra low temperatures and in strong magnetic fields. We have a new scheme of field-independent thermometry based on quartz tuning fork Helium-3 viscometry which monitors the local temperature of the sample's environment in real time. The operation and measurement circuitry of the quartz viscometer is described in detail. We provide evidence that the temperature of two-dimensional electron gas confined to a GaAs quantum well follows the temperature of the quartz viscometer down to 4 mK.

Small-angle x-ray scattering measurements of the microstructure of liquid helium mixtures adsorbed in aerogel

Small-angle x-ray scattering (SAXS) was used to measure the microstructure of isotopic mixtures of 3He and 4He adsorbed into silica aerogels as a function of temperature and 3He concentration. The SAXS measurements could be well described by the formation of a nearly pure film of 4He which separates from the bulk mixture onto the aerogel strands and which thickens with decreasing temperature. Previous observations of a superfluid 3He -rich phase are consistent with superfluidity existing within this film phase. Observed differences between different density aerogels are explained in terms of the depletion of 4He from the bulk mixture due to film formation.

Vortex proliferation in the Berezinskii-Kosterlitz-Thouless regime on a two-dimensional lattice of Bose-Einstein condensates

We observe the proliferation of vortices in the Berezinskii-Kosterlitz-Thouless regime on a two-dimensional array of Josephson-coupled Bose-Einstein condensates. As long as the Josephson (tunneling) energy J exceeds the thermal energy T, the array is vortex free. With decreasing J/T, vortices appear in the system in ever greater numbers. We confirm thermal activation as the vortex-formation mechanism and obtain information on the size of bound vortex pairs as J/T is varied.

Unexpected Mass Decoupling for 3He-4He Films on a Solid Hydrogen Substrate

Quartz oscillator measurements reveal new behavior in 3He-4He mixture films on a H2 substrate. For mixture films of total coverage greater than one monolayer, in addition to the expected Kosterlitz-Thouless transition, a second mass decoupling event is observed, which behaves differently from the Kosterlitz-Thouless transition.

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.

Kosterlitz-Thouless transition for 4He films adsorbed to rough surfaces

We report the study of adsorption isotherms of 4He on several well characterized rough CaF2 surfaces using a quartz crystal microbalance technique at 1.672 K. The signature of decoupled mass observed on crossing the Kosterlitz-Thouless transition as a function of 4He film thickness decreases and becomes increasingly difficult to identify as the surface roughness is increased. A peak in the dissipation, indicative of the onset of superfluidity, changes little with roughness.

Superfluid-insulator transition in commensurate disordered bosonic systems: large-scale worm algorithm simulations

We report results of large-scale Monte Carlo simulations of superfluid-insulator transitions in disordered commensurate 2D bosonic systems. In the off-diagonal disorder case, we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is z=1.5(2). In the diagonal-disorder case, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in crossover to the generic universality class (apparently with z=2). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of smaller clusters mimicked a direct superfluid-Mott-insulator transition.

Critical point of a weakly interacting two-dimensional Bose gas

We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical absolute value psi(4) model on a lattice. The critical density and chemical potential are given by relations n(c) = (mT/2piPlanck's(2))ln(xiPlanck's(2)/mU) and mu(c) = (mTU/piPlanck's(2))ln(xi(mu)Planck's(2)/mU), where T is the temperature, m is the mass, and U is the effective interaction. The dimensionless constant xi = 380+/-3 is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For xi(mu) our result is xi(mu) = 13.2+/-0.4. We also report the study of the quasicondensate correlations at the critical point.

Effect of 3He on submonolayer superfluidity

We have studied the superfluid response of 3He-4He mixture films adsorbed onto porous gold for a wide range of 3He and 4He coverages, focusing on submonolayer superfluidity. At T = 0, 3He appears to float on top of 4He and can be viewed as a second substrate that induces its own inert layer. Depending on the 4He content, the zero-temperature superfluid mass and the superfluid onset temperature either saturate or vanish with the addition of 3He. The T = 0 superfluid-insulator phase boundary, which can be described by a simple function, is found in the 3He-4He coverage plane.