Thermal Boundary Resistance of theSuperfluid 3He A-B Phase Interface

D.I. BradleyS.N. FisherA.M. GuénaultR.P. HaleyH. MartinG.R. PickettJ.E. RobertsV. 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

2nd order transition through Tc

P = O barT = 130-200µKCritical Field ~ 340mT

1st order transition between A and B

Superfluid 3He is a BCS condensate with “spin triplet p-wave pairing”

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.

Why study the A-B interface?

A Phase has only parallel components

Anisotropic gap

B Phase has all 3 components:

Pseudo-isotropic gap

Opposite spins suppressed

Parallel spins enhanced

Polar gap suppressed

Equatorial gap enhanced

Apply a magnetic field to the B phase – gap becomes distorted:

p

e

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

Width Parameters

W = f2* T * E Power

Few mms

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 TRANSPORTA PHASE “SANDWICH”

QUASIPARTICLE TRANSPORTHIGH 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:

We can now calculate the thermal conductivitythrough the cell:

Measured :RK(AB) = 0.3 µK/pW at 140µK

Predicted by S.Yip1: RK(AB) = 2.6*10-3 µK/pW

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.