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Thermal Boundary Resistance of the Superfluid 3He A-B Phase Interface

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

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Thermal Boundary Resistance of the Superfluid 3He A-B Phase Interface

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  1. Thermal Boundary Resistance of the Superfluid 3He A-B Phase Interface D.I. BradleyS.N. FisherA.M. GuénaultR.P. Haley H. Martin G.R. PickettJ.E. RobertsV. Tsepelin

  2. Outline • Helium Background • Experiment • Low Field B Phase Results • A Phase Layer in Cell • Distorted B Phase in Cell • Conclusions – Kapitza Resistance, Thermal Conductivity

  3. Helium 3 Phase Diagram P = O bar T = 130-200µK Critical Field ~ 340mT 2nd order transition through Tc 1st order transition between A and B Superfluid 3Heis a BCS condensate with “spin triplet p-wave pairing”

  4. 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.

  5. A Phase has only parallel components

  6. \Anisotropicgap

  7. B Phase has all 3components:

  8. \Pseudo-isotropic gap

  9. Apply a magnetic field to the B phase – gap becomes distorted: Dp ßÝ, ßÝ De ÝÝ, ßß Opposite spins suppressed Parallel spins enhanced \Polar gap suppressed Equatorial gap enhanced

  10. 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

  11. Vibrating Wire Resonators Few mms Width Parameters W = Df2* T * E a Power

  12. VWR Range of Measurement Critical Velocity

  13. The Experimental Cell

  14. Do this to check the cell’s working as a BBR i.e. VWR damping is proportional to Power

  15. LOW FIELD ISOTROPIC GAP B PHASE The cell appears to be hotter at the bottom than at the top! Why?

  16. Magnetic Field Profile used to Produce A Phase Layer

  17. QUASIPARTICLE TRANSPORT A PHASE “SANDWICH”

  18. QUASIPARTICLE TRANSPORT HIGH FIELD DISTORTED B PHASE

  19. This extra resistance may be caused by a textural defect remaining after the A phase layer has been removed

  20. Thermal Resistance of Cell

  21. Thermal Resistance of Cell

  22. The “Kapitza Resistance” of the A-B interface is: Measured : RK(AB) = 0.3 µK/pW at 140µK Predicted by S.Yip1: RK(AB) =2.6*10-3µK/pW We can now calculate the thermal conductivity through the cell: 1 S. Yip. Phys Rev B 32, 2915 (1985)

  23. Thermal Conductivity of Cell

  24. Thermal Conductivity of Cell

  25. 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.

  26. How do we get smoothly from the anisotropic A phase with gap nodes to . . .

  27. . . . . the B phase with an isotropic (or nearly isotropic) gap?

  28. 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.

  29. 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.

  30. The up spin and down spin nodes (and L-vector directions) separate

  31. The up spin and down spin nodes (and L-vector directions) separate

  32. . . . . . and separate further.

  33. 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.

  34. 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.

  35. But think for a moment about the excitations!

  36. 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 Ý spins and the ß spins, the energy gap becomes distorted and a small L and S appear.

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