Nascent Superfluidity in Bilayer Two-Dimensional Electron Systems

1. Nascent Superfluidity in Bilayer Two-Dimensional Electron Systems Melinda Kellogg Jim Eisenstein Loren Pfeiffer Ken West April 29, 2004 MIT-Harvard Center for Ultracold Atoms

2. Double Quantum Well GaAs AlGaAs AlGaAs Energy 100 A

3. E F Two-Dimensional Electron Gas conduction bands E F valence bands U G C U

4. k F Fermi Disk

5. Coulomb Drag

6. ~ ~ Coulomb Drag without Magnetic Field drag layer drive layer M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, Solid State Commun. 123, 515 (2002). A. Yurtsever, V. Moldoveanu, B. Tanatar, Solid State Commun. 123, 575 (2002). E.H. Hwang, S. Das Sarma, V. Braude, A. Stern, PRL 90, 086801 (2003).

7. B 2D Electrons in a Strong Magnetic Field: Classical Hall Effect

8. rxy von Klitzing 1980 Quantization of orbits: 2D Electrons in a Strong Magnetic Field: Quantum Hall Effect

9. Degeneracy of the Landau levels: √ h B e p 2D Electrons in a Strong Magnetic Field: Landau Levels h √ p x ≥ ~ D D 2 p √ √ 1 B e h p pRMS ~ = D 2 2 p √ one filled Landau level

10. Degeneracy of the Landau levels: √ h B e p B e h 2D Electrons in a Strong Magnetic Field: Landau Levels 2 ) ( h x ( ) 2 ~ D B e p 1 = none Landau level x ( ) 2 p D second Landau level one filled Landau level

11. rxy von Klitzing 1980 2D Electrons in a Strong Magnetic Field: Density of States Density of States Energy

12. E F Density of States Density of States Density of States 2D Electrons in a Strong Magnetic Field: Localized States  Quantum Hall Plateaus 30 w w w h h 1 3 5 h c c 2 2 c 2 20 ) W k ( y x R 10 w w 1 h w 3 5 h h 2 c c c 2 2 0 0.0 0.5 1.0 1.5 Magnetic Field (Tesla) w w 3 h 1 h c 2 c 2 Energy

13. 6 ) c / 4 W ( g a r D 2 0 0.10 0.15 0.20 0.25 Coulomb Drag in a Strong Magnetic Field n = 10 n = 14 n = 12 T = 0.3 K Magnetic Field (Tesla)

14. Coulomb Drag in a Strong Magnetic Field =½

15. 300 250 200 150 ) c W/ Drag ( 100 T = 0.3 K 50 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 n 1/

16. l B l A few times B l B l d ~ B intralayer Coulomb energy ~ interlayer Coulomb energy d Effective Layer Separation: d/l B l B d

17. ) c W/ Drag ( d/lB=1.79 1500 1000 d/lB=1.85 d/lB=1.93 T = 0.3 K 500 d/lB=2.03 d/lB=2.16 d/lB=2.56 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 n 1/

18. Coulomb Drag at low d/lB and low Temperature 10 T = 0.03 K d/lB=1.60 ) c / d/lB=1.72 W 5 (k d/lB=1.76 xx,D d/lB=1.83 R 0 0.8 0.9 1.0 1.1 1.2 -1 n T

19. Hall Drag at low d/lB and low Temperature T = 0.03 K d/lB=1.60 20 ) d/lB=1.72 W (k d/lB=1.76 xy,D d/lB=1.83 10 R 0 0.8 0.9 1.0 1.1 1.2 -1 n T

20. y / c ) Quantum Phase Transition as d/lB is lowered 25 T = 0.05 K 8 20 layers strongly-coupled 6 15 layers weakly-coupled 4 10 2 5 0 0 1.6 1.7 1.8 1.9 d/lB M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, PRL 90, 246801 (2003).

21. Quantum Phase Transition as d/lB is lowered T = 0.1 K T = 0.05 K layers strongly-coupled 8 T = 0.25 K T = 0.3 K 6 4 layers weakly-coupled 2 0 1.2 1.4 1.6 1.8 2.0 d/lB

22. The Nature of the Strongly-Coupled Phase: Correlated Electron Physics Bob Laughlin, 1983 fractional quantum Hall effect Bert Halperin, 1983

23. The (1,1,1) State bottom layer n = 1/2 top layer n = 1/2 nT = 1 Xiao-Gang Wen and A. Zee predict superfluid mode for (1,1,1) state, 1992

24. Equivalence of (1,1,1) state to easy-plane spin-1/2 ferromagnet: Pseudospin: Kun Yang, K. Moon, L. Zheng, A. H. MacDonald, S. M. Girvin, D. Yoshioka, Shou-Cheng Zhang, 1994

25. Pseudospin Ferromagnet and

26. V Tunneling Ian Spielman, 2000

27. Superfluid Mode Pseudospin current: J J

28. J e- v h J November, 2002 Equivalence of (1,1,1) state to Bose-Einstein Condensate of Excitons A.H. MacDonald and E.H. Rezayi, 1990 A.H. MacDonald, 2001

29. J J J J J J J J J e- v h J Current Channels: Parallel & Counterflow Coulomb drag parallel channel counterflow channel J J + = J J

30. ) ) c / c / W W (k (k -1 -1 n n xx,D xy,D T T R R Coulomb drag parallel channel counterflow channel _ J J J J = J J J J Coulomb Drag in Strongly-Coupled Phase: Indirect Detection of Counterflow Superfluid Mode d/lB=1.60 10 20 T = 0.03 K 5 10 0 0 0.9 1.0 1.1 1.2 0.8 0.8 0.9 1.0 1.1 1.2

31. Counterflow Measurement

32. Hall Resistivity in Counterflow Channel M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, cond-mat/0401521 (2004).

33. Longitudinal Resistivity in Counterflow Channel

34. Hall Resistivity in Parallel Channel

35. Longitudinal Resistivity in Parallel Channel

36. Temperature Dependence at νT=1

37. Topological Excitations: Meron-Antimeron Pairs low energy topologically stable excitations e carry charge ; vorticity 1 + + - - 2 T < T , only appear in neutral bound pairs KT T > T , unbound vortices appear; order is destroyed KT

38. Possible Sources of Energy Gap Finite current creates energy gap for the dissociation of meron-antimeron pairs. Finite tunneling affects binding of meron-antimeron pairs; energy gap for creation of charged meron-antimeron pair. Disorder creates free merons regardless; energy gap due to hopping energy.

39. Conductivity at νT=1

40. In Conclusion We have observed very large conductivities in the counterflow channel of bilayer two- dimensional electron systems at νT=1 consistent with the Bose-Einstein condensation of interlayer excitons. Future: less disordered samples – may show Kosterlitz-Thouless phase transition higher tunneling samples, watch tunneling’s effect on meron pair binding