Superfluid Density of 3 He in aerogel

1. Superfluid Density of 3He in aerogel Jeevak Parpia, LASSP, Cornell University Support: NSF DMR 0202113 NSF INT-0128811 NATO-SA(PST.CLG.979379)6993/FP Thanks to: E. Nazaretski, D. M. Lee

2. Overview & Outline of Talk Experiments – Sound Cell & TO A phase, B phase superfluid density Hysteresis Results in field

3. Bulk A phase ρs/ρResults In the bulk, A phase superfluid density can be greater or less than that of the B phase, (depends on texture), but ratio ρs║/ ρsis > 0.5. Without a field, textural alignment is unlikely. (ρs) H// H (ρs//) H (ρs//) H// (ρs) Berthold, Giannetta, Smith, Reppy, PRL 37, 1138 (1976).

4. Modification of Phase Diagram by Disorder Tcaerogel (P) TA*→B Metastable A* Equilibrium A phase Tcbulk (P) Equilibrium B phase Nazaretski, Mulders, and Parpia. JETP Lett. 79, 470 (2004).

5. Original ρs/ρ measurements 29 Bulk behavior 25 5 20.2 0 20.5 15 10 15 12.9 10 8 6.9 6.1 5 3.9 3.5 Superfluid fraction shows a different power law, and is much reduced (compared to bulk) Porto, Ph. D. thesis (Cornell).

6. Onset of superfluid is sharp Question: How sharp is the superfluid transition? Heat capacity shows a width of ~ 60 μK. Superfluid density shows a much narrower transition. Period shift from torsion oscillator at 3.4bar and 15 bar Porto, Ph. D. thesis (Cornell).

7. Simultaneous Torsion Pendulum & Heat Capacity with “bulk - like” contribution removed Non-BCS-like behavior Torsional oscillator dissipation Tc (a’gel) Tc (bulk) J. He, A. D. Corwin, J. M. Parpia, and J. D. Reppy Phys. Rev. Lett. 89, 115301 (2002)

8. ρs/ρ(base catalyzed aerogel) scales well with Tc0 Left plot shows ρs/ρ (with Fermi factors removed) for 98%, 99.5% open aerogels and bulk Right plot shows how superfluid fraction scales with Tc reduction.

9. Early example of ρs/ρA→B Transition • Hybrid wire viscometer in magnetic field A phase ρs/ρmuch less than B phase result. A phase ρs/ρseen on warming is same as seen while cooling P. Brussaard et al Phys. Rev. Lett. 86, 4580, 2001

10. Signature of the A-B transition TA-B(bulk) Tc(a’gel) TA-B(a’gel) Temperature (mK) Transverse sound – Northwestern Tc(bulk) Gervais,Haard,Nomura,Mulders,Halperin. PRL 87 35701 (2001)

11. TB-A bulk Systematic investigation of the phase diagram ~200uK offset between TA→B,TB→A No TB→A on warming for less than 1.4kG fields. Gervais et al Phys. Rev. Lett. 87, 035701 (2001)

12. Low frequency sound modes in aerogel Caero≈ 50m/s << CHe, First sound → fast mode Fourth sound → slow mode A. I. Golov et al, PRL, 82 3492 (1999).

13. Sound in 3He - Filled Aerogel The slow mode shows the onset of superfluidity and the A→B transition. Helmholtz Mode Slow Mode Nazaretski, Mulders, Parpia JETP Lett. 79, 470 (2004)

14. 3He A, B phase Superfluid density in Aerogel No sign of A phase on warming? Finite width ofTA→B Nazaretski, Mulders, Parpia JETP Lett. 79, 470 (2004)

15. Making mixtures of A and B Main figure: Mixture made by cooling into TA→B. Inset: Mixture made by warming into TB→N orTB→A band. Nazaretski, Mulders, Parpia JETP Lett. 79, 470 (2004)

16. (rAs/r)/(rBs/r)=0.5 Superfluid density ratio Superfluid density in A phase is ½ that of B phase Results at 3 different pressures at right. Nazaretski, Mulders, Parpia JETP Lett. 79, 470 (2004)

17. Polycritical point Polycritical point(bulk) For 3He in aerogel, the polycritical point is eliminated Gervais, Yawata, Mulders and Halperin, PRB 66 054528 (2002)

18. Ratio ofrs/r A* and B phase, hysteresis does not change with field.No B → A* transition seen on warming? Evidence for superheating? Is the A* phase the stable phase between normal and the B phase? Range of expected B→A* transition Nazaretski, Lee, Parpia to be published.

19. B→A* transition only seen in higher field Nazaretski, Lee, Parpia to be published.

20. Single power law near Tc • Power law does not show any anomalies: unlikely that there is a hidden B→A transition. P<15 bar P>15 bar Porto, Ph. D Thesis

21. Data from Florida

22. Low pressure, low temperature behavior Dashed lines: data at 3.4, 4 bar Solid line anomalous run at 2.73bar Note lower Tc higher rs.

23. 89% 4He in aerogel - Path to study of 0D 3He superfluid High temp slow mode Helmholtz Mode Tc(bulk 3He) No evidence of 3He slow mode (below percolation threshold), but onset of 3He superfluidity visible at Tc in aerogel. Implies isolated 3He regions are superfluid. Tc (3He in aerogel) Lawes, Golov, Nazaretski, Mulders, Parpia, Phys. Rev. Lett., 90, 195301, (2003). Onset of shift of high temp slow mode

24. Schematic Phase Transformations Energy Temperature Normal State Zero field warming Warming in field A-like Phase B Phase

25. Conclusions • 1. Aerogel introduces disorder into the purest material -- 3He. • 2. So called A-B phase interface strongly pinned. • 3. Why is the ρs/ρin the A phase so much lower than B phase? • 3. Significant alteration of phase diagram by aerogel. • Puzzles & Some Future experiments • Is the A phase in aerogel the same as bulk? • Why is it so reliably nucleated on cooling? Why not on warming? • Region between the Tc’s? Is there meta superfluidity? • Opportunity to study effects of fractally correlated disorder.