1. News from Princeton Flatlands!
Probing Exotic Phases of Interacting 2D Systems
Mansour Shayegan
Princeton University

2. News from Princeton Flatlands!
Wigner crystal and its melting phase diagram
Deng, PRL (2019)

3. Cast: Edwin Chung Hao Deng (now @ AliBaba) Shafayat Hossain Meng Ma
Kevin Villegas-Rosales
Kirk Baldwin
Ken West
Loren Pfeiffer
Mansour Shayegan

4. So many states in one (magnetic field) sweep!
ν = number of occupied Landau levels
Shayegan, arXiv (2005)

5. Wigner crystal
Jiang, PRL 1990
Goldman, PRL 1990
Sajoto, PRL 1993

6. Phase diagram—nonlinear IV
Goldman, PRL 1990

7. Phase diagram—nonlinear IV
Goldman, PRL 1990

8. Phase diagram—microwave resonance
Chen, Nat. Phys. 2006

9. Phase diagram—microwave resonance
Chen, Nat. Phys. 2006

10. Probing the Wigner crystal through its screening efficiency
front gate
2DEG
Back gate
Capacitive measurement:
Penetrating current: Ip
70 nm QW
n = 4.2 x 1010 cm-2
μ = 8.5 x 106 cm2/Vs
4 x 4 mm2 van der Pauw

11. Basic data Transport Rxx and Rxy Ip: Large IP when in QHE
High field range:
2/9, IP, 1/5, IP
Ip large
Between these states
Three sharp minima

12. Main Result

13. Main Result

14. Main Result

15. Main Result

16. Main Result

17. Measured Critical Temperature vs. Filling Factor
WC?
Goldman, PRL 1990

18. Measured Critical Temperature vs. Filling Factor

19. Conclusions Tc vs. v phase diagram Wigner crystal melting?
Why is screening maximum near melting?
Needs theoretical explanation!

20. Conclusions Tc vs. v phase diagram Wigner crystal melting?
Why is screening maximum near melting?
Needs theoretical explanation!
Many illuminating discussions:
R. N. Bhatt
M. Dykman
D. Huse
J. K. Jain
S. Kivelson
S. Sondhi

21. Rest of this talk …
Composite fermions waltz to the tune of a Wigner crystal !

22. Probing a Wigner crystal with composite fermions
Landau level filling factor:
ν = (n/B)(h/e)

23. Idea: Use composite fermioms to probe a Wigner crystal!
So, if we can bring a layer of Cfs and a layer of WC close with each other, we would expect the WC can introduce periodic modulation to the CF. Once the cyclotron motion of CF matches resonance condition, we would expect to see some features in Rxx measurement of the Cfs.
The position of the COs can tell the information of the period of the WC, meanwhile the sequence can provide the clue of WC's lattice shape.
Goal: Directly measure the micro-structure of Wigner crystal
- period
- lattice shape

24. Data for electrons moving in an anti-dot periodic array
COs might be a solution.
The principle of CO is easy to understand. If we can introduce periodic modulation to 2DEG with some way, for example in this work is the anti-dot array, once the cyclotron motion diameter of ele or CF matches the period, resonance in Rxx would appear.
For example here, it means when the orbit contains 1, 3, 7 dots, peaks in Rxx appear.
Meckler, PRB (2005)

25. Data for composite fermions moving in an anti-dot periodic array
As we mentioned before, CF near ½ fling performs like the electron at zero B.
So we would also expect that CF could show COs with periodic potential modulation on it.
For example, in this work, the R_xx in the lower panel is from the reference segment of the sample without any pattern, which shows very typical trace of 2DES.
But for the segment of the sample with anti-dot array on it, R_xx near zero field shows COs, also R_xx near ½ filling has new features.
Based on the CF theory, this semi-classical formula should also work if we replace B and k_F with B_eff and CF’s k_F.
Because 2DES is spin-polarized at high field, k_F of CF is 2^1/2 times of zero-field electrons’ k_F.
This formula tells that if we plot R_xx near ½ filling in B_eff with a factor of 1/2^1/2, the resonance peak should match the one at zero field.
Indeed, if we plot R_xx near ½ with B_eff devided by 2^1/2, which is the top trace, the resonance peaks match the ones in low-field trace.
Kang, PRL (1993) 25

26. Double-layer sample structure
Here is the sample structure. It's double-QW but has very different density in each layer. Under high B-field, top layer would be CF near ½ and bottom layer would have very low FF and it should be WC.
So it's a very ultra-unbalanced bilayer system.
We prepared different sample with different interlayer barrier thickness d, which is from 100 to 800A.

27. Composite fermions waltz to the tune of a Wigner crystal !
nT ~ 1.6 x 1011 cm-2
Here is the result for 100A barrier sample.
We see some anomalous features which are suggestive COs.
Hao Deng et al., PRL (2016)

28. Composite fermions waltz to the tune of a Wigner crystal !
nT ~ 1.6 x 1011 cm-2
Here is the result for 100A barrier sample.
We see some anomalous features which are suggestive COs.

29. Wigner crystal returns the favor!
96 nm 83 71 59 49 62
10^10 /cm2, 10^-7 m, 100nm nL max~nH/3
Hatke, Engel, et al., Sci. Advances 2019

30. Supplemental Material

31. Supplemental Material