thermal boundary resistance of the superfluid 3 he a-b phase interface d.i. bradley s.n. fisher a.m....
TRANSCRIPT
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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
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Outline
• Helium Background
• Experiment
• Low Field B Phase Results
• A Phase Layer in Cell
• Distorted B Phase in Cell
• Conclusions – Kapitza Resistance, Thermal Conductivity
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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”
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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?
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A Phase has only parallel components
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Anisotropic gap
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B Phase has all 3 components:
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Pseudo-isotropic gap
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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
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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
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Vibrating Wire Resonators
Width Parameters
W = f2* T * E Power
Few mms
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VWR Range of Measurement
Critical Velocity
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The Experimental Cell
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Do this to check the cell’s working as a BBR
i.e. VWR damping is proportional to Power
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LOW FIELD ISOTROPIC GAP B PHASE
The cell appears to be hotter at the bottom than at the top! Why?
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Magnetic Field Profile used to Produce A Phase Layer
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QUASIPARTICLE TRANSPORTA PHASE “SANDWICH”
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QUASIPARTICLE TRANSPORTHIGH FIELD DISTORTED B PHASE
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This extra resistance may be caused by a textural defect remaining after the A phase layer has been removed
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Thermal Resistance of Cell
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Thermal Resistance of Cell
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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)
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Thermal Conductivity of Cell
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Thermal Conductivity of Cell
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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.
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How do we get smoothly from the anisotropic A phase with gap nodes to . . .
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. . . . the B phase with an isotropic (or nearly isotropic) gap?
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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.
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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.
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The up spin and down spin nodes (and L-vector directions) separate
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The up spin and down spin nodes (and L-vector directions) separate
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. . . . . and separate further.
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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.
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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.
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But think for a moment about the excitations!
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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.