Compound Torsional Oscillator: Frequency
Dependence and Hysteresis of Supersolid
4He
(and Search for Superfluid Sound Mode)
Harry Kojima
Rutgers University
in collaboration with Yuki Aoki and Joe Graves
outline
• Compound Torsional Oscillator
 motivation
 oscillator
 results on NCRI(T, ), dissipation(T, ), dependence of NCRI on
drive displacement, velocity and acceleration
 relaxation effects of dissipation
 vortex analogies with HTSC
• Search for superfluid sound mode
 motivation
 generator and detector – heater/bolometer
 ballistic phonon propagation
 search for propagation with low velocity
Compound Torsional Oscillator
motivation
probing NCRI of identical solid 4He as
function of frequency
 glassy solid 4He (Nussinov, et al, cond-mat/0610743)
 critical displacement, velocity or acceleration?
 vortex liquid (Anderson, Nature Physics 3, 160(2007))
“Clearly the crucial experiment for our
hypothesis is to change the torsional vibration
frequency, holding all other variables constant.
This has not been done. It would seem to be
urgent to do so, because no other hypothesis
yet proposed is consistent with any appreciable
fraction of the data.”
Compound Torsion Oscillator
in-phase mode: 496 Hz, Q~1.3106
out-phase mode: 1.2 kHz, Q~ 0.76 106
dilution refrigerator
BeCu rods
driver
detector1
sample cell (stycast 1266)
Cell volume=0.6 cm3
Inner Diameter=10 mm
Inner Height= 8 mm
S/V=7 cm-1
detector2
“raw” data, 496 Hz mode
“raw” data, 1.2 kHz mode
NCRI fraction: rim velocity < 20 m/s
Change in Dissipation due to Solid 4He
rim velocity ~ 20 m/s
dissipation vs. frequency shift
Critical Velocity
and Hysteresis
T = 19 mK
velocity =100- 200 m/s
T = 63 mK
Note: no
hysteresis!
reversible!
hysteresis at 30 mK
Start here.
supersolid – type II HTSC
vortex – flux lines analogy
rotation --- magnetic field
ac oscillation --- ac magnetic field
angular momentum
--- magnetization
picture (T): increasing superfluid fraction (or NCRIf)
 decreasing number of vortices
analogies to vortices in sc
T < 45 mK: vortices cannot
enter as, V
is increased.
1172.8
Hz
rs/r [%]
T < 45 mK: vortices
can go out, as V is
decreased.
T > 45 mK: vortices can go
in and out reversibly.
19 mK
62 mK
T [mK]
Velocity [m/sec]
T < 45 mK: hysteresis  “vortex glass state”
T > 45 mK: reversible  “vortex liquid state”
field cooled
relaxation effects T = 30 mK
relaxation at T = 10 mK
drive level
time
“relaxation time” vs. T
ring down
time ~ 120 s
long time behavior after decreasing drive
vortex-matter phase diagram
supersolid
V
vortex
glass
vortex
liquid
T
Summary
• Small ρs/ρ : ~ 0.1%
• No frequency dependence in rs/r below 20 mK, v=20
m/sec.
• Possible frequency dependence at higher temperature
and at high velocity.
• Comparison with glassy solid 4He theory on-going.
• Hysteresis and reversible regimes in NCRIf and oscillator
response.
• Analogy with vortex phase diagram of HTSC.
Heat Pulse Experiment (Experimental Setup)
Heater
Pressure
gauge
Fill line
2.8 mm
4.3 mm
bolometer
0.5 mm
Magnet
M.C.
Ti bolometer
3 mm
signal (t, T)
time derivative of signal(t,T)
pulse propagation velocity vs. T
“expected” velocity shift = C – C0 ~ (1/2)(rs/r)C0
P=53. 6bar (rs/r Penn State)
P=30bar (rs/r from
Penn State)
P=30 bar
(Rutgers)
37 bar
56 bar
56 bar
37 bar
rs
CT  1 
r
Search for fourth sound 3D plot
expected T dependence of fourth sound
Transverse ballistic
phonon propagation
conclusions
Temperature dependence of the transverse ballistic phonon
velocity below 200 mK did not change within ±0.15 % which is
expected to increase 0.5 % from the theory at low temperature if
the rs is 1 % (Pulse energy = 3 nJ/pulse).
Search of the Fourth sound like propagation mode.
Heat pulse response of solid 4He was measured up to 10
msec(=0.4 m/sec), using the high sensitivity Ti bolometer at 38
bar.
Signature of new mode has not been observed within
DT=5 K.
conclusions
• compound torsional oscillator with cylinder
– frequency dependence of NCRIf and
dissipation
– critical velocity (not amplitude or acceleration)
– hysteresis – possible analogy with HTSC
• fourth sound
– not yet observed, but crucial
– search is continuing by increasing sensitivity,
etc
Vortex
Liquid
comparison with vortex liquid theory
Anderson (Nature Physics 3, 160(2007) )
comparison with glassy behaviour
f0=495.8 Hz
Fitting parameters;
A=2.0x10-3 sec-1
s0=6.7 sec
D/kB=219 mK
As
DQ 
[1  (2 f 0 s) 2 ]
1
s  s0 exp(D / kBT )
Nussinov et. al.
(cond-mat/0610743)
Using; s0, D
Fitting parameter; B=0.3 sec-2
1
Df 
f0 
B
f 0 [1  (2 f 0 s ) 2 ]
f0=1172.8 Hz
Using; A, s0, D
Using; B, s0, D