1. Observations of Nascent Superfluidity in a Bilayer Two-Dimensional
Electron System at nT=1
Melinda Kellogg
Jim Eisenstein
Loren Pfeiffer
Ken West
July 11, 2005
EP2DS-16
Albuquerque, New Mexico

2. Double Quantum Wells Rtun ~ 100 M
Barrier heights: center ~1eV; cladding ~1/4eV. GaAs lattice constant 5.65 Angstroms.
To bring in pictures from Corel, export as WMF file, then ungroup in Power Point.

3. Counterflow Measurement

4. Mesa Geometry current leads current leads
Barrier heights: center ~1eV; cladding ~1/4eV. GaAs lattice constant 5.65 Angstroms.
current leads

5. Correlated Electrons n = 1/3 Bob Laughlin, 1983 Bert Halperin, 1983
The Laughlin pap: PRL 50, p (lowest energy ground state for this situation AND an additional electron would greatly disturb it (increase the energy) – thus is has an energy gap.) And it’s the *quasiparticles* -- the excitations, that are fractionally charged.
If want to understand better the normalization term, it is the same as comes up for the normal quantum solution for a single particle – but done in symmetric gauge.
Power m>1 – electrons avoid each other more strongly.
The halperin, Helv. Phys. Acta 56, 75 (1983).
Top equation, I don’t remember, same source as top equation on next page. (it might have been that 33-1 paper with demler and nayak et al)
Bottom equation from Wen and Zee
Bert Halperin, 1983

6. The (1,1,1) State nT = ½ + ½ nT = 1 nTotal = bottom + top
bottom layer
n = 1/2
top layer
n = 1/2
Where the hell did I get that top equation? Demler Nayak et al?
I can write up the equation myself, using z and w. Even keeping on the last part…
Another lmn state: 3,3,-1 (has different properties though).
The low energy spin-waves (Goldstone modes ian saw) are neutral and do not affect transport.
nT = ½ + ½
nT = 1
nTotal = bottom + top

7. D. Yoshioka, Shou-Cheng Zhang, 1994
Equivalence of (1,1,1) state to easy-plane
spin-1/2 ferromagnet:
Kun Yang, K. Moon, L. Zheng,
A. H. MacDonald, S. M. Girvin,
D. Yoshioka, Shou-Cheng Zhang, 1994
These two equations from Girvin’s DC transformer pap (2001ish on condmat)
The 2D XY model supports ferromagnetism only at T=0, at finite temperature spin waves destroy the ferromagnetism.
Pseudospin:

8. Pseudospin Ferromagnet
Pseudospin ferromagnet exist technically in 2D only at T=0 – spin waves destroy the order at any finite temperature.
and

9. Tunneling V
Ian Spielman, 2000

10. predict superfluid mode
Xiao-Gang Wen and A. Zee
predict superfluid mode
for (1,1,1) state, 1992
Superfluid Mode
Pseudospin current: J
2D XY model, in the limit of zero tunneling.
The conjugate variable to the phase is m_z, which is the z-component of the pseudospin vector.
A ferromagnet has broken rotational symmetry, a superfluid has broken gauge symmetry. J

11. I I Equivalence of (1,1,1) state to
Bose-Einstein Condensate (BEC) of Excitons J v e- h
H.A. Fertig, 1989
A.H. MacDonald, 2001 e - e - e - e - e - I e - e - e - h e - e - e - e - e - e - e - e - e - e - e - e - e - e - e - e - e - e - e - e - e - I

12. Hall Resistance in Counterflow Mode
Temperatures: 30, 100, 150, 200, 250, 300, 400 K.
M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, cond-mat/ (2004).

13. Longitudinal Resistance in Counterflow Mode
Temperatures: 30, 100, 150, 200, 250, 300, 400 K.

14. Hall Resistance in Parallel Mode
Temperatures: 30, 100, 150, 200, 250, 300, 400 K.

15. Longitudinal Resistance in Parallel Mode
Temperatures: 30, 100, 150, 200, 250, 300, 400 K.

16. Temperature Dependence at νT=1

17. 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
Top meron has negative charge, bottom, positive. Now this well!!! Know that log thing.
The pair you show is neutral, and not a skyrmion – if they were opposite voriticity but same charge, they would be a skyrmion.
It is the entropy that increases when the pairs unbind at TKT, and so the free energy decreases.
Merons are charged excitations which can dissipate energy.
Moon et al, PRB 51, p 5159: "in this system, the KT phase transition, whcih separates the superfluid and the normal states, is expected to be associated with the unbinding of meron pairs of opposite charge and opposite vorticity.“
TKT is predicted to be ~ 0.5K (hell, what a coincidence– although, T_KT is not the same as an energy gap)
Good articles on KT: 'Percolation, etc.' articles by Mooij and Minnhagen. On p.325, Mooij says, "the number of free vortices above TKT grows slowly.“
In the 2D XY model, there is no finite temperature conventional ferromagnet transition. But it does support another kind of phase transition at finite temperature, one from a disordered phase to an infinitely susceptible phase

18. 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.
Merons are ‘logarithmically’ bound.
Maybe leave that plot out and just discuss that there is an energy gap that depends on current, and
Maybe show a picture of what tunneling does to the pairs.
S.M. Girvin and
A.H. MacDonald, 1997
Disorder creates free merons regardless; energy gap due to hopping energy.

19. Conductivity at νT=1

20. Coulomb Drag = Parallel - Counterflow

21. Coulomb Drag = Parallel - Counterflow

22. Hall Drag locates Phase Boundary
A few times l l d h e 2 25
T = 0.05 K
d/l =1.60
(1,1,1)
state 20 20
d/l =1.72
Rxy,D (kW)
T = 0.03 K
Rxy,D at nT=1 (kW) 15
d/l =1.76 10
d/l =1.83 10
uncorrelated
state 5
1.6
1.7
1.8
1.9
0.8
0.9
1.0
1.1
1.2
d/l d
A few times l n T -1
M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, PRL 90, (2003).

23. Phase Boundary vs. Density Imbalance
nT = n1 + n2
Dn = n1 – n2

24. Phase Boundary vs. Density Imbalance
nT = n1 + n2
(d/ { ) c D
n/n T
1.78
1.76
1.74
1.72
-0.1
0.0
0.1
NO QHE
QHE
Dn = n1 – n2
Dn/nT = 0
Dn/nT = +0.1
Dn/nT = - 0.1
Y.N. Joglekar and A.H. MacDonald, 2002

25. In Conclusion We have observed very large conductivities
in the counterflow mode of a bilayer two-
dimensional electron system at νT=1
consistent with the Bose-Einstein
condensation of interlayer excitons.
We have observed the phase boundary shift to
higher d/ with density imbalance.