High quality graphene heterostructures host an array of fractional quantum Hall isospin ferromagnets hosting diverse spin and valley orders. While a variety of phase transitions have been observed, disentangling the isospin phase diagram of these states is hampered by the absence of direct probes of spin and valley order. I will describe nonlocal transport measurements based on launching spin waves from a gate defined lateral heterojunction, performed in ultra-clean Corbino geometry graphene devices. At high magnetic fields, we find that the spin-wave transport signal is detected in all FQH states between ν = 0 and 1; however, between ν = 1 and 2 only odd numerator FQH states show finite nonlocal transport, despite the identical ground state spin polarizations in odd- and even numerator states. The results reveal that the neutral spin-waves are both spin and sublattice polarized making them a sensitive probe of ground state sublattice structure. Armed with this understanding, we use nonlocal transport signal to a magnetic field tuned isospin phase transition, showing that the emergent even denominator state at $\nu=\pm 1/2$ in monolayer graphene is indeed a multicomponent state featuring equal populations on each sublattice.

1. Valley-resolved spin wave transport through
graphene fractional quantum Hall states
Haoxin Zhou1, Hryhoriy Polshyn1, Takashi Taniguchi2,
Kenji Watanabe2, Andrea F. Young1
1University of California, Santa Barbara
2National Institute for Materials Science, Japan
APS March Meeting
Denver 2020

2. Graphene zeroth Landau level (LL)
• N = 0 LL: 4-fold degenerate in
presence of spin and valley
• Symmetry breaking from:
• Coulomb interactions
• Zeeman effect
• AB sublattice splitting
Kharitonov, Phys. Rev. B 85, 155439 (2012)
2

3. Transport measurement
3
Zibrov et al. Nat. Phys. 14, 930–935 (2018)
Polshyn et al. Phys. Rev. Lett. 121, 226801 (2018)
𝜈=0
𝜈=1
𝜈=1
𝜈=2

4. Are there phase transitions at 𝜈 = 0?
4
Zibrov et al. Nat. Phys. 14, 930–935 (2018)
Polshyn et al. Phys. Rev. Lett. 121, 226801 (2018)
𝜈=0
𝜈=1
𝜈=1
𝜈=2
Zibrov et al. Nat. Phys. 14, 930–935 (2018)
Kharitonov, Phys. Rev. B 85, 155439 (2012)
Canted antiferromagnet (CAF)
Partially-sublattice polarized phase (PSP)
Charge density wave (CDW)

5. What are the phases at fractional fillings?
5
Zibrov et al. Nat. Phys. 14, 930–935 (2018)
Polshyn et al. Phys. Rev. Lett. 121, 226801 (2018)
𝜈=0
𝜈=1
𝜈=1
𝜈=2
Sodemann et al. Phys. Rev. Lett. 112, 126804(2014)

6. Spin wave transport
6
𝜈 = 1
𝜈 = 2
Stepanov et al. Nat. Phys. 14, 907-911 (2018)
Wei et al. Science 362, 229-233(2018)

7. Spin wave transport
7
𝜈 = 1
𝜈 = 2
Stepanov et al. Nat. Phys. 14, 907-911 (2018)
Wei et al. Science 362, 229-233(2018)

8. Spin wave transport
8
𝜈 = 1
𝜈 = 2
Stepanov et al. Nat. Phys. 14, 907-911 (2018)
Wei et al. Science 362, 229-233(2018)

9. Spin wave transport
9
𝜈 = 1
𝜈 = 2
Stepanov et al. Nat. Phys. 14, 907-911 (2018)
Wei et al. Science 362, 229-233(2018)

10. Spin wave transport
10
𝜈 = 1
𝜈 = 2
Stepanov et al. Nat. Phys. 14, 907-911 (2018)
Wei et al. Science 362, 229-233(2018)

11. Phase transitions at ν = 0
11
CAFPSP/CDW
Zibrov et al. Nat. Phys. 14, 930–935 (2018)
Kharitonov, Phys. Rev. B 85, 155439 (2012)
𝝂 = 𝟎

12. Phase transitions at ν = 0
12
CAFPSP/CDW
Zibrov et al. Nat. Phys. 14, 930–935 (2018)
Kharitonov, Phys. Rev. B 85, 155439 (2012)
𝝂 = 𝟎

13. FQH regime
13
Zhou et al., Nat Phys. 16, 154-158 (2019)

14. 1 < 𝜈 < 2
14

15. 1 < 𝜈 < 2
15
5
3
11
7
7
5

16. Valley-sensitive
16
5
3
4
3
8
5
11
7
10
7
7
5
ν = 5/3, 7/5: spin and valley-polarized state
Abanin et al. Phys. Rev. B 88, 115407 (2013)
Sodemann et al. Phys. Rev. Lett. 112, 126804(2014)
Dean et al. Nat. Phys. 7, 693–696(2011)
Feldman et al. Science 7, 693–696(2012)
ν = 4/3, 8/5: spin-polarized valley singlet state

17. Lifetime of the spin excitations
17
Spin- and valley-polarized state
Spin-polarized and valley-unpolarized state
Chunli Huang
UT Austin
Allan MacDonald
UT Austin
Γ = 0 + 𝑜(𝑘4
)

18. FQH states between 0 < 𝜈 < 1
18
𝜈=0
𝜈=1 𝜈 =
1
3
𝜈 =
2
3

19. Isospin phase transitions between 0 < ν < 1
19
𝜈=0
𝜈=1 𝜈 =
1
3
𝜈 =
2
3

20. Isospin phase transitions between 0 < ν < 1
20
𝜈=0
𝜈=1 𝜈 =
1
3
𝜈 =
2
3

21. 𝜈 = 1/3
21
High field: spin-ordered states
Low field: valley-ordered states
Sodemann et al. Phys. Rev. Lett. 112, 126804(2014)
Only 1,1,
1
3
is allowed in the experiment field range

22. 𝜈 = 1/3
22
Only 1,1,
1
3
is allowed in the experiment field range
Sodemann et al. Phys. Rev. Lett. 112, 126804(2014)
High field: spin-ordered states
Low field: valley-ordered states

23. 𝜈 = 2/3
23
High field: spin-ordered states
Two possible component fillings:
1,1,
2
3
and 1,1,
1
3
,
1
3
Sodemann et al. Phys. Rev. Lett. 112, 126804(2014)

24. 𝜈 = 2/3
24
High field: spin-ordered states
Low field: valley-ordered states
Sodemann et al. Phys. Rev. Lett. 112, 126804(2014)
Two possible component fillings:
1,1,
2
3
and 1,1,
1
3
,
1
3
Or

25. Summary
• We studied the spin and valley structure of the graphene zeroth
Landau level via spin wave transport
• At 𝜈 = 0, we observed a field-induced phase transition from CAF to
PSP.
• We find the valley order significantly influence the spin wave
transport.
25

26. Acknowledgements
Andrea Young
UCSB
Hryhoriy Polshyn
UCSB
Kenji Watanabe
NIMS, Japan
Takashi Taniguchi
NIMS, Japan
26
Chunli Huang
UT Austin
Allan MacDonald
UT Austin
Theory:
Experiment:

27. Substrate-induced valley Zeeman effect
27
hBN Graphene
heterostructure
Polshyn et al. Phys. Rev. Lett. 121, 226801 (2018)