Pressure-driven flow of solid helium

The recent torsional oscillator results of Kim and Chan suggest a supersolid phase transition in solid 4He. We have used a piezoelectrically driven diaphragm to study the flow of solid helium through an array of capillaries. Our measurements showed no indication of low temperature flow, placing stringent restrictions on supersolid flow in response to a pressure difference. The average flow speed at low temperatures was less than 1.2x10-14 m/s, corresponding to a supersolid velocity at least 7 orders of magnitude smaller than the critical velocities inferred from the torsional oscillator measurements.Comment: 4 pages, 3 figure

Observation of Mass Transport through Solid 4He

By use of a novel experimental design, one that provides for superfluid helium in contact with bulk hcp 4He off the melting curve, we have observed the DC transport of mass through a cell filled with solid 4He in the hcp region of the phase diagram. Flow, which shows characteristics of a superflow, is seen to be independent of the method used to grow the solid, but depends on pressure and temperature. The temperature dependence suggests the possibility of hysteresis.Comment: 1 zipped file, produces 16 page paper, with 20 figures; resubmitted with typos corrected, a figure corrected, some discussion improved, and additional references - still 16 pages and 20 figure

Absence of Pressure-Driven Supersolid Flow at Low Frequency

An important unresolved question in supersolid research is the degree to which the non-classical rotational inertia (NCRI) phenomenon observed in the torsional oscillator experiments of Kim and Chan, is evidence for a Bose-condensed supersolid state with superfluid-like properties. In an open annular geometry, Kim and Chan found that a fraction of the solid moment of inertia is decoupled from the motion of the oscillator; however, when the annulus is blocked by a partition, the decoupled supersolid fraction is locked to the oscillator being accelerated by an AC pressure gradient generated by the moving partition. These observations are in accord with superfluid hydrodynamics. We apply a low frequency AC pressure gradient in order to search for a superfluid-like response in a supersolid sample. Our results are consistent with zero supersolid flow in response to the imposed low frequency pressure gradient. A statistical analysis of our data sets a bound, at the 68% confidence level, of 9.6$\times 10^{-4}$ nm/s for the mass transport velocity carried by a possible supersolid flow. In terms of a simple model for the supersolid, an upper bound of 3.3$\times 10^{-6}$ is set for the supersolid fraction at 25 mK, at this same confidence level. These findings force the conclusion that the NCRI observed in the torsional oscillator experiments is not evidence for a frequency independent superfluid-like state. Supersolid behavior is a frequency-dependent phenomenon, clearly evident in the frequency range of the torsional oscillator experiments, but undetectably small at frequencies approaching zero.Comment: 6 pages, 5 figure

Suppression of a charge density wave ground state in high magnetic fields: spin and orbital mechanisms

The charge density wave (CDW) transition temperature in the quasi-one dimensional (Q1D) organic material of (Per)$_2$Au(mnt)$_2$ is relatively low (TCDW = 12 K). Hence in a mean field BCS model, the CDW state should be completely suppressed in magnetic fields of order 30 - 40 T. To explore this possibility, the magnetoresistance of (Per)$_2$Au(mnt)$_2$ was investigated in magnetic fields to 45 T for 0.5 K < T < 12 K. For fields directed along the Q1D molecular stacking direction, TCDW decreases with field, terminating at about ~ 37 T for temperatures approaching zero. Results for this field orientation are in general agreement with theoretical predictions, including the field dependence of the magnetoresistance and the energy gap, $\Delta_{CDW}$. However, for fields tilted away from the stacking direction, orbital effects arise above 15 T that may be related to the return of un-nested Fermi surface sections that develop as the CDW state is suppressed. These findings are consistent with expectations that quasi-one dimensional metallic behavior will return outside the CDW phase boundary.Comment: 12 pages, 5 figure

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

We present the mechanics of a model of supersolid in the frame of the Gross-Pitaevskii equation at $T=0K$ that do not require defects nor vacancies. A set of coupled nonlinear partial differential equations plus boundary conditions is derived. The mechanical equilibrium is studied under external constrains as steady rotation or external stress. Our model displays a paradoxical behavior: the existence of a non classical rotational inertia fraction in the limit of small rotation speed and no superflow under small (but finite) stress nor external force. The only matter flow for finite stress is due to plasticity.Comment: 6 pages, 2 figure

Non Classical Rotational Inertia Fraction in a One Dimensional Model of Supersolid

We study the rotational inertia of a model of supersolid in the frame of the mean field Gross-Pitaevskii theory in one space dimension. We discuss the ground state of the model and the existence of a non classical inertia (NCRI) under rotation that models an annular geometry. An explicit formula for the NCRI is deduced. It depends on the density profil of the ground state, in full agreement with former theories. We compare the NCRI computed through this theory with direct numerical simulations of rotating 1D systems

Liquid Nitrogen Energy Storage Units

Presented at the 16th International Cryocooler Conference, held May 17-20, 2008 in Atlanta, Georgia.The energy storage units (ESU) described in this article are to be attached to the cold finger of a cryocooler with the objective of holding the low temperature environment constant while the cooler may be temporarily stopped to provide a totally vibration-free environment. Or, it may be used to damp out temperature fluctuations if a sudden cooling power increase is momentarily necessary. The developed ESU consists of a nitrogen cell coupled to a GM cryocooler by a gas-gap heat switch, and connected to an expansion volume at room temperature to limit the pressure increase. It was designed to store ≈3600 J between ≈65 K and ≈80 K. After condensing the nitrogen into the liquid phase, the heat switch is used to decouple the cell from the cryocooler, and a constant heating power is applied. During the liquid evaporation, the temperature drift obtained is very slow. In this paper, we present the tests performed using a 35 cm³ cell and an expansion volume of 6 litres or 24 litres. Applying 1 W to the ESU, about 4 kJ were stored with a slow drift from 76 K up to 80 K using the 24 litres expansion volume. Modelling of the experiment agrees within 5% with the experimental results. Software, written for sizing such an ESU, includes parameters for the ESU's stored energy, the cell and expansion volumes, and the cryogenic fluid used. An ESU using the liquid-gas latent heat leads to a slow temperature drift, while a triple-point cell keeps the temperature strictly constant. However, such an ESU stores a thermal energy one order of magnitude larger than a triple-point one for the same low temperature cell volume. Preliminary results for a gravity insensitive ESU are presented

Phase Diagram for Charge Density Waves in a Magnetic Field

The influence of an external magnetic field on a quasi one-dimensional system with a charge density wave (CDW) instability is treated within the random phase approximation which includes both CDW and spin density wave correlations. We show that the CDW is sensitive to both orbital and Pauli effects of the field. In the case of perfect nesting, the critical temperature decreases monotonously with the field, and the wave vector of the instability starts to shift above some critical value of magnetic field. Depending on the ratio between the spin and charge coupling constants and on the direction of the applied magnetic field, the wave vector shift is either parallel ($CDW_x$ order) or perpendicular ($CDW_y$ order) to the most conducting direction. The $CDW_x$ order is a field dependent linear combination of the charge and spin density waves and is sensible only to the Pauli effect. The wave vector shift in $CDW_y$ depends on the interchain coupling, but the critical temperature does not. This order is affected by the confinement of the electronic orbits. By increasing the relative strength of the orbital effect with respect to the Pauli effect, one can destroy the $CDW_y$, establishing either a $CDW_x$, or a $CDW_0$ (corresponding to perfect nesting wave vector). We also show that by increasing the imperfect nesting parameter, one passes from the regime where the critical temperature decreases with the field to the regime where it is initially enhanced by the orbital effect and eventually suppressed by the Pauli effect. For a bad nesting, the quantized phases of the field-induced CDW appear.Comment: 30 pages (LaTeX) + 15 figure

The glassy response of solid He-4 to torsional oscillations

We calculated the glassy response of solid He-4 to torsional oscillations assuming a phenomenological glass model. Making only a few assumptions about the distribution of glassy relaxation times in a small subsystem of otherwise rigid solid He-4, we can account for the magnitude of the observed period shift and concomitant dissipation peak in several torsion oscillator experiments. The implications of the glass model for solid He-4 are threefold: (1) The dynamics of solid He-4 is governed by glassy relaxation processes. (2) The distribution of relaxation times varies significantly between different torsion oscillator experiments. (3) The mechanical response of a torsion oscillator does not require a supersolid component to account for the observed anomaly at low temperatures, though we cannot rule out its existence.Comment: 9 pages, 4 figures, presented at QFS200