HPD and Superfluid Hydrodynamics
Low Temperature Laboratory, Helsinki University of
J. S. Korhonen, Y. Kondo, M. Krusius, Ü. Parts, E. V.
Yu. M. Bunkov, V. V. Dmitriev
G. E. Volovik
E. B. Sonin
HPD and counterflow
• Magnetic field Þ anisotropy of rs
Þ interaction with vs.
Minimized at equilibrium by adjusting v
In the HPD
Counterflow suppresses the HPD.
Interaction of HPD with vortices.
• Vortex core rotates and rocks. j
• Rocking motion causes the dissipation h
Interaction of HPD with vortices.
When vortex end are pinned – twisting.
Twisted vortex is more rigid and rocks less.
When the vortex move – the ends are free.
Effect of field tilting
Tilting the field orients the vortex:
Reduced rocking motion.
• If we twist less?
– Rocking motion is less
• Difference in absorption
• Shorted HPD – weaker twist.
Cosmic-like soliton. Connects two half-quantum vortices.
CEA-DRECAM, Service de Physique de l'Etat
Condense, Centre d'Etudes de Saclay, France
CNRS-Laboratoire de Physique des Solides,
Universite Paris-Sud, Orsay, France
• 198 0.10x0.10 mm holes separated by 2
mm in SiliconNitride membrane ~0.1 mm thick.
Membrane: 75x60 mm, Ra=16 mm, R k=0.03 mm
•Part of the membrane where edge effects can be
strong is highlighted with yellow.
•Position of the diaphragm (equivalent
to the charge of the capacitor) is
Cap. plate recorded.
Pos. Sensor The current through the orifice/parallel
path is determined as derivative of
the diaphragm location.
The pressure across the orifice is proportion
Cd The phase across the orifice is
P L1 f proportional to the integral of
Pel L2 (orifice) pressure:
Amplitude of phase oscillations µ
amplitude of diaphragm.
Measurement technique - rotation
•Rotation changes the phase across
the weak link.
•Phase is determined by solving
Orifice Can be graphically represented by
Pos. Sensor intersection of loadline with J(f).
The dependence has period: 0.842
WÅ=5.6 10-5 rad/sec.
Inductance of the orifice is inversely
proportional to J¢(f).
As rotation changes the frequency
P L kx L1 f changes.
current Driven oscillations
1/L1 Response to ambient vibrations
Max. f. Min. f
Measurements Technique -
•Rotation results in the circulation in
the sensing loop.
Thus the rotation changes phase drop
plate across the weak link.
Pos. Sensor Earth - rotating platform.
Change in rotation - reorient apparatus
W relative to the Earth.
Effect has been calibrated in 4He
experiments: with 4.9 cm2 two-turn loop
we use, the Earth rotation produces
circulation ~0.85 k3.
Large amplitude frequency (f0)
Precision in the bias.
•Bias does not change much after
going through Tc, if it does not jump
•We assign bias ~0 to the case which
happens more often (see below).
T effect explains most of the scatter show
on the picture to the left (local overheating
Bias at fixed T, P and magnetic of the inner cell while at nominally stable
Very large energy.
Bind cores of double-core vortex.
Thought to be unstable in bulk
T-dependence of the circulation.
• Bias is stable after each cooldown (save for some time-drift, see below. There are
some minor variations from one cooldown to another.
• However there is strong temperature dependence – as T changes between ~0.99
and 0.5 Tc the bias changes by almost k3 at P=0.2 bar and much stronger at P=10
• At 10 bar the effect is much stronger with 2 amp current in the field coil.
•Often apparently the same state can have 0 or p bias.
•Not predicted by theory?
– Changing n to –n will not do.
0.0 0.1 0.2 k 0.3 0.4 0.5
• Have been predicted by Salomaa and Volovik. Though to be
conecting cores of double-cores vortex, but have have been
observed in free state.
• Solitons are thought to be unstable. But are they in toroidal
geometry? For example – rotation of the torus may provide
p/2 phase shift along it. Will then the soliton be stable
• We think that the observed p-shift can be provided by 1 or
more solitons, crossing the flow loop.
• Alternative explanation – a single vortex pinned in a
position exactly in the middle of the flow channel seems
Explanation of T-dependence
•Heat leak to inner cell, due, for
example to heat release from Stycast
or eddy heating in silver increases
Ag fountain pressure there and causes
normal current flow from the inner cell
Stycast Q vs and counterflow of superfluid into it.
Q •As observed, the circulation should
diverge towards Tc.
•Change of the sign (weak),
however, remains unexplained.
• A number (~8) of different current-phase relations
(CPR) are observed.
• Under certain conditions most of these relations are
observed shifted by p.
• The shift appears to be unrelated to the shape of the
CPR and does not change when CPR changes.
• We argue that the most probable cause is a cosmic-like
soliton(s) crossing the sensing loop.
• Temperature dependence of the trapped circulation can
be explained by thermomechanical effects.
• This has important implication for superfluid gyroscopes –
heat leaks and temperature stability become important.
• It appears that there is no remnant vorticity in the cell.