Thermal Boundary Resistance of the
Superfluid 3He A-B Phase Interface
D.I. Bradley
S.N. Fisher
A.M. Guénault
R.P. Haley
H. Martin
G.R. Pickett
J.E. Roberts
V. Tsepelin
Outline
„ Helium Background
„ Experiment
„ Low Field B Phase Results
„ A Phase Layer in Cell
„ Distorted B Phase in Cell
„ Conclusions ‟ Kapitza Resistance, Thermal
Conductivity
Helium 3 Phase Diagram
P = O bar
T = 130-200µK
Critical Field ~ 340mT
2 nd order transition
through Tc
1st order transition Superfluid 3He is a
between A and B BCS condensate with “spin triplet p-wave
pairing”
Why study the A-B interface?
The A-B interface is the interface with the
highest order, highest purity and in principle best-understood
phase interface to which we have access.
It’s a phase boundary between two quantum vacuum states.
We find that we are able to measure the transport of
quasiparticle excitations between these two order parameters.
A Phase has only parallel components
\ Anisotropic gap
B Phase has all 3 components:
\ Pseudo-isotropic gap
Apply a magnetic field to the B phase ‟ gap becomes distorted:
Dp
De
Opposite spins suppressed \ Polar gap suppressed
Parallel spins enhanced Equatorial gap enhanced
Zeeman splitting decreases the
energy of the down-spin qp’s,
so the low energy ones are
Andreev reflected. Any that reach the A-phase are
high enough in energy to travel straight through.
The energy of the up-spin qp’s is increased.
Those with energy below the A-phase gap
are Andreev reflected
Vibrating Wire Resonators
Few mms
Width Parameters
W = Df2* T * E a Power
VWR Range of Measurement
Critical Velocity
The Experimental Cell
Do this to check the
cell’s working as a BBR
i.e. VWR damping is
proportional to Power
LOW FIELD ISOTROPIC GAP B PHASE
The cell appears to be hotter at the
bottom than at the top! Why?
Magnetic Field Profile used to Produce A Phase Layer
QUASIPARTICLE TRANSPORT
A PHASE “SANDWICH”
QUASIPARTICLE TRANSPORT
HIGH FIELD DISTORTED B PHASE
This extra resistance may be caused by a
textural defect remaining after the A phase
layer has been removed
Thermal Resistance of Cell
Thermal Resistance of Cell
The “Kapitza Resistance” of the A-B interface is:
Measured :
R K (AB) = 0.3 µK/pW at 140µK
Predicted by S.Yip1:
R K (AB) = 2.6*10-3 µK/pW
We can now calculate the thermal conductivity
through the cell:
1 S. Yip. Phys Rev B 32, 2915 (1985)
Thermal Conductivity of Cell
Thermal Conductivity of Cell
Summary
„ Have we measured the “Kapitza resistance” of the A-B interface in
superfluid Helium -3?
„ Resistance decreases as temperature increases.
„ The thermal conductivity appears to have an exponential dependence on
temperature.
\ The thermal conductivity is dominated by the heat capacity of the helium
3.
How do we get smoothly from the anisotropic A phase with gap nodes
to . . .
. . . . the B phase with an isotropic (or
nearly isotropic) gap?
We start in the A phase
with nodes in the gap and
the L-vector for both up
and down spins pairs
parallel to the nodal line.
We start in the A phase
with nodes in the gap and
the L-vector for both up
and down spins pairs
parallel to the nodal line.
The up spin and down
spin nodes (and L-vector
directions) separate
The up spin and down
spin nodes (and L-vector
directions) separate
. . . . . and separate
further.
The up spin and down
spin nodes finally become
antiparallel (making the
topological charge of the
nodes zero) and can
then continuously fill
to complete
the transformation to
the B phase.
The up spin and down
spin nodes finally become
antiparallel (making the
topological charge of the
nodes zero) and can
then continuously fill
to complete
the transformation to
the B phase.
But think for a moment about the
excitations!
Why is the B-phase gap distorted?
In zero magnetic field L and S are both zero.
However, a small field breaks the symmetry between the spins and the
spins, the energy gap becomes distorted and a small L and S appear.