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Search for fourth sound propagation in supersolid
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Image of FIG. 1.
FIG. 1.

Resistance versus temperature of high-resistance bolometer under bias magnetic field. In fields and below, the applied current was , and at it was reduced to .

Image of FIG. 2.
FIG. 2.

Heat pulse propagation across solid at as detected by LRB. A short (pulse width ) heat pulse is generated at the heater at . The voltage induced at the bolometer is averaged and the peak amplitudes are normalized to unity at all temperatures. The electronic cross talks during are not shown.

Image of FIG. 3.
FIG. 3.

Upper panel: induced voltage response of the bolometer to heat pulse applied at at . The pressure of the solid is . Inset is a magnified portion showing the echo which traverses over the distance . Lower panel: the time derivative of the detected signal in the upper panel. The electronic cross-talk signal prior to is not shown.

Image of FIG. 4.
FIG. 4.

Pressure dependence of measured propagation velocity. Pressure variation is expressed as a function of Debye temperature. Except for one data point near the melting pressure, all other points lie along a straight line (shown as guide to the eye). All samples were made with the blocked capillary method. See text for a discussion of the sample which does not follow the linear trend.

Image of FIG. 5.
FIG. 5.

The temperature dependence of the transverse velocity at 37 (pluses and triangles) and 56 (circles and crosses) bar. Pluses and circles were the velocities evaluated from the initial pulse arrival time. Triangles and crosses are the velocities evaluated from the echo signals (see Fig. 3). Solid lines are fits to the initial arrival velocity using the dispersion relation given by Eq. (1). Dotted lines show the propagation velocity expected for the echo signal based on the normal phonon collision time obtained from fitting the first arrival.

Image of FIG. 6.
FIG. 6.

Change in ballistic phonon propagation velocity at . The reference velocity is that measured at . Symbols have the same meaning as in Fig. 5. Dotted line and dash-line dot show the expected changes in the transverse velocity according to Eq. (4) with taken from Ref. 38 at 53.6 and , respectively. The solid line shows the expected velocity when the superfluid fraction is taken from our own torsional oscillator experiment44 with cylindrical sample cell.

Image of FIG. 7.
FIG. 7.

The temporal development of the detected signal using LRB in search of fourth sound propagation. The long tail portion of the response is highlighted where the fourth sound is expected to influence and exhibit some signature. The arrows indicate the times at which fourth sound signal is expected (see text).

Image of FIG. 8.
FIG. 8.

Temporal development of the detected signal using HRB in search of fourth sound propagation at selected temperatures. The dots indicate the times at which fourth sound signal is expected (see text). The sample solid was formed relatively slowly in about three hours at .

Image of FIG. 9.
FIG. 9.

Overall responses of the bolometer at 40, 50 and in the “fast cooling” sample at . The bolometer HRB with higher sensitivity was the detector. No likely signature for fourth sound propagation was observed.

Image of FIG. 10.
FIG. 10.

Time response of HRB with different sample preparation procedures: dots and crosses for “fast cooling” and “slow cooling” sample, respectively (see text), at . Responses of the two samples are compared at 40 and .

Image of FIG. 11.
FIG. 11.

Fitted , the thermalization time within solid (see text), as a function of temperature. The squares are from the “dirty,” “fast cooling” sample, measured with HRB, and the circles are from the “clean,” “slow cooling” sample, measured with LRB.

Image of FIG. 12.
FIG. 12.

Fitted , thermalization time to the ambient temperature (see text), as a function of temperature for “dirty,” “fast cooling” and “clean,” annealed solid samples, both at . Note that the “fast cooling” sample was measured with HRB and the “slow cooling” one with LRB.


Generic image for table
Table I.

Physical characteristics of the bolometers.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Search for fourth sound propagation in supersolid He4