1. Superfluid 3He in aerogel I.A. Fomin, P.L. Kapitza Institute for Physical Problems, Moscow. XV INTERNATIONAL SUMMER SCHOOL NICOLÁS CABRERA 100 YEARS LIQUID HELIUM: NEW PHYSICS AT THE EDGE OF ABSOLUTE ZERO 14-19 September 2008

3. This ordering is characterized by the order parameter gauge symmetry is broken At liquid 3 He is a normal Fermi liquid, it can became superfluid via Cooper pairing at lower temperatures. At4He becomes superfluid.

4. Singlet Cooper pairing S=0, l=0 l= 0,2,4… S=0, l=0 s-wave, or conventional Cooper pairing. It is realized in most of superconductors: Hg, Pb, Sn, Al, etc.. The order parameter is a one-component complex function: only gauge symmetry is broken. S=0

5. Triplet Cooper pairing (unconventional) S=1l=1,3,5… The order parameter is multi-component:. Each of the three components is a function of direction in the momentum space. Except for the gauge symmetry other symmetries are broken as well.

6. The order parameter of 3 He: s=1, l=1 momentum (orbital) index j=1,2,3 - px,py,pz orbitals spin index = 1,2,3 pxpy pz

7. Cooper pairing in a triplet (S=1) state

8. Unconventional superconductors: UPt 3, UGe 2, Sr 2 RuO 4, high-T c, etc. Additional complications: anisotropy, complicated Fermi-surfaces, impurities. 3 He – canonical unconventional superfluid: spherical Fermi-surface, well known Fermi-liquid parameters, no impurities. All floating impurities stick to the walls of a container.

9. Self-supporting structure – high porosity silica aerogel. Aerogels with the porosity up to 99.5% can be made. Mostly used with the porosity close to 98% Porosity P= (empty volume/total volume)

13. Why Aerogel? Silica ball size:   3 nm Correlation length:  a ~ 10 - 100 nm Superfluid coherence length:  ≈ 20 - 80 nm (P = 34 - 0 bar) Expect interesting physics when:  ~  a DLCA simulation of a silica aerogel depicting the length scales  and  a (courtesy of T.M. Lippman).

14. According to the theory of superconducting alloys for conventional superconductors for unconventional How does aerogel effect the Tc of 3He?

15. Application of the Theory of superconducting alloys for a triplet p-wave Cooper pairing (Homogenious Scattering Model (HSM))

16. solid 3 He normal phase «A» «B» T (mK) P (bar) Suppression of T c

18. Homogenious scattering model

19. W.F. Halperin and J.A. Sauls, cond-mat/0408593

20. FLUCTUATIONS-1

21. FLUCTUATIONS-2

24. Landau free energy

25. Tc Tc2 Tc1 Tc3 Ginzburg and Landau equation

26. delocalized solution no delocalized solutions

27. x Long-range order -- mobility edge

28. DLCA simulation of a silica aerogel depicting the length scales  and  a (courtesy of T.M. Lippman).

29. Perturbation expansion mobility edge: k=0 + ++= average over realizations

30. Coincides with the homogeneous scattering model

33. Fractal structure (Sierpinski gasket)

38. Conclusions 1. It is possible to introduce impurities in the superfluid 3He. 2. Effect of impurities depends on correlation of their positions. 3. One can expect effects, analogous to discussed here in unconventional superconductors with a short correlation length, e.g. in high-Tc superconductors.