1. Observation of neutral modes in the fractional quantum hall effect regime Aveek Bid Nature 585 466 (2010) Department of Physics, Indian Institute of Science, Bangalore LDQS 2011, October; HRI

2. Quantum Hall Effect Magnetic field perpendicular to plane of 2DEG Can measure two quantities: R xx (longitudinal resistance) and R xy (transverse resistance) 2

3. LDQS 2011, October; HRI Classical Hall Effect 3 R xx - B independent R xy - Linear in B

4. LDQS 2011, October; HRI Integer Quantum Hall Effect Quantum Hall Effect 4

5. LDQS 2011, October; HRI Fractional Quantum Hall Effect Quantum Hall Effect J.P.Eisenstein and H.L.Stormer, Science 248,1461(1990) 5

6. LDQS 2011, October; HRI Quantum Hall Effect – Landau levels Quantization of cyclotron orbits – Landau levels 6

7. LDQS 2011, October; HRI Quantum Hall Effect – energy landscape Plateau of =2 x 7

8. LDQS 2011, October; HRI Quantum Hall Effect – energy landscape Bulk of 2DEG – no states at  No net current flows in bulk Plateau of =2 x two completely filled Landau levels 8 x E

9. LDQS 2011, October; HRI Quantum Hall Effect – edge states Near sample edges confining potential causes Landau levels to curl upwards One-dimensional ballistic conduction channels near edges edge states x E Right edge Left edge 9

10. LDQS 2011, October; HRI Quantum Hall Effect – direction of edge states? For 2-D magneto-electric sub-bands k ~ x 0 /l 0 2 Right edge Left edge x E 10

11. LDQS 2011, October; HRI Quantum Hall Effect – direction of edge states? Velocity ~ δE/ δk Modes on a given edge move in same direction Right edge Left edge k E 11

12. LDQS 2011, October; HRI Quantum Hall Effect– co-propagating modes In IQHE and most Fractional cases ---- co-propagating charge modes All modes on an edge move in same direction Can carry a net electrical current 12

13. LDQS 2011, October; HRI Quantum Hall Effect – edge states No backscattering – perfect quantization 13

14. LDQS 2011, October; HRI Quantum Hall Effect - Neutral edge modes predicted LL1 LL2 e no interactions charge modes are eigen states Berg et al, PRL (2009) interactions neutral and charge modes are eigen states e/2 neutral charge co-propagating neutral and charge modes (if they exist) are difficult to separate 14

15. LDQS 2011, October; HRI Quantum Hall Effect– counter-propagating modes Upstream (Counter-propagating) modes were predicted : At least one mode flowing down-stream direction Possibly one/more modes flowing in the up-stream direction 15

16. LDQS 2011, October; HRI Quantum Hall Effect– counter-propagating modes 16 Upstream (Counter-propagating) modes were predicted : particle-hole conjugate states - e.g. 2/3, 3/5, …. Majorana modes in non-abelian states - e.g. v =5/2 for certain wavefunctions

17. LDQS 2011, October; HRI = 2/3 – without disorder and interactions Two counter-propagating charged modes on each edge Two terminal conductance (4/3)e 2 /h – in conflict with experiment Interactions – non-universal conductance MacDonald, PRL (1990) Wen, PRL (1990) 17

18. LDQS 2011, October; HRI = 2/3 – with disorder and interactions Kane et al, PRL (1994) Disorder scattering allows equilibration of edges Two counter-propagating modes on each edge Prediction of a counter-propagating charge-neutral mode 18

19. LDQS 2011, October; HRI Why counter-propagating modes? 19

20. LDQS 2011, October; HRI Why counter-propagating modes? e-e- e-e- e-e- Composite Fermions =1/3 three flux quanta per electron Landau level n=1 for composite fermions! 20

21. LDQS 2011, October; HRI Taken 2 flux quanta per electron – attached them to electrons to form the composite fermion Effective number of ‘free’ flux quanta in system decreases Effective B field felt by composite particles less than the applied magnetic field Why counter-propagating modes? 21

22. LDQS 2011, October; HRI Why counter-propagating modes – Case of =2/3 x B eff x n, As sample edge is approached n decreases decreases 2/3 1/2 |  eff | x 22

23. LDQS 2011, October; HRI How to detect neutral modes? via their effect on the tunnelling exponent in narrow constrictions via heat transfer, dissipation, heating of edges 23 Can shot noise help in identifying neutral modes?

24. LDQS 2011, October; HRI x z y Schematic of device 24

25. LDQS 2011, October; HRI Schematic of device Ohmic contacts Metallic gates 25

26. LDQS 2011, October; HRI split metal gate Shot noise due to partitioning by QPC 26 t At finite V and T

27. LDQS 2011, October; HRI injecting current from source #2 Charge mode flows counter-clockwise – goes to ground #1 Neutral mode flows clockwise – reaches QPC charge neutral Detection of neutral mode at  =2/3 27

28. LDQS 2011, October; HRI Detection of neutral mode at  =2/3 28

29. LDQS 2011, October; HRI Charge noise created Can be sensed by voltage probe Detection of neutral mode at  =2/3 injecting current from source #2 charge neutral 29

30. LDQS 2011, October; HRI Charge noise created Can be sensed by voltage probe Detection of neutral mode at  =2/3 injecting current from source #2 Noise due to ‘fragmentation’ of neutral quasiparticles 30

31. LDQS 2011, October; HRI QPC transmission and shot noise 31 S i ~ t(1-t)

32. LDQS 2011, October; HRI No signature of neutral mode at =2/5 Sanity check – measurements at =2/5 =2/5 supports two co-propagating modes on each edge 32

33. LDQS 2011, October; HRI no observed effect of I n on shot noise due to I s Upstream neutral mode at = 2/5 ? 33 charge Charge mode flows counter-clockwise

34. LDQS 2011, October; HRI Sanity check – comparison between 2/5 and 3/5 34

35. LDQS 2011, October; HRI injecting from source #3 qp no current no excess noise (no heating) More checks- neutral modes flowing clockwise 35

36. LDQS 2011, October; HRI More checks - what about other ‘normal’ states? = 2/3, 3/5, 5/3 and 5/2……….. evidence of neutral modes v = 1/3, 1, 4/3, 2……….. no evidence of neutral modes 36

37. LDQS 2011, October; HRI injecting current from source #1 Charge mode flows counter - clockwise towards QPC Neutral mode flows clockwise – reaches ground contact Interaction of neutral mode with charge mode 37

38. LDQS 2011, October; HRI injecting current from source #2 Charge mode flows counter clockwise - reaches ground contact Neutral mode flows clockwise – towards QPC what will be the total noise? Interaction of neutral mode with charge mode 38

39. LDQS 2011, October; HRI Shot noise in the presence of neutral mode, =2/3 0 nA 2 nA 39 Noise due to charge mode only

40. LDQS 2011, October; HRI Shot noise in the presence of neutral mode, =2/3 e * ~(2/3)e e * ~0.45e Quasiparticle charge decreases Temperature increases I n = 0 nA I n = 2 nA 40

41. LDQS 2011, October; HRI Shot noise in the presence of neutral mode, =2/3 41

42. LDQS 2011, October; HRI quasiparticle charge drops to ~1/3e from 2/3e temperature increases by ~15- 20mK Charge evolution in the presence of neutral mode, =2/3 42

43. LDQS 2011, October; HRI charge drops significantly only at ~ 100mK neutral mode does not affect the charge via temperature increase Temperature evolution of e * at = 2/3 43

44. LDQS 2011, October; HRI l 0 ~400  m @ T=10mK l 0 ~80  m @ T=25mK Does temperature affect neutral mode? Shot noise due to ‘neutral mode’ fragmentation 44

45. LDQS 2011, October; HRI Does temperature affect neutral mode? Charge evolution due to neutral mode 45

46. LDQS 2011, October; HRI what is expected for =5/2 ? abelian state - no upstream neutral mode is expected non-abelian state with an upstream neutral (Majorana) mode: Moore-Read Pfaffian wavefunction – reconstructed edge anti-Pfaffian wavefunction - reconstructed edge with disorder What about = 5/2 ? Is there a neutral mode for =5/2 ? 46

47. LDQS 2011, October; HRI No significant affect on the transmission neutral mode at = 5/2 47

48. LDQS 2011, October; HRI Shot noise of neutral mode at =5/2 48

49. LDQS 2011, October; HRI 5.2  V Shot noise in the presence of neutral mode at = 5/2 49

50. LDQS 2011, October; HRI Charge evolution in the presence of neutral mode at = 5/2 50

51. LDQS 2011, October; HRI Summary Experimentally demonstrated the existence of neutral mode Affects Fano factor of shot noise of charge mode and temperature of the tunneling quasiparticles Neutral modes in =5/2 – strong indication of their non-abelian nature Produces shot noise at QPC - proportional to t(1-t) and current; depends on the number of neutral modes. Aveek Bid, N. Ofek, H. Inoue, M. Heiblum, V. Umansky and D. Mahalu; Nature 466 585 (2010) 51

52. LDQS 2011, October; HRI Acknowledgements Moty Heiblum Nissim V. Umansky D. Mahalu Hiroyuki C. Kane 52

53. LDQS 2011, October; HRI THANK YOU 53

54. LDQS 2011, October; HRI Quantum Hall Effect – energy landscape Quantization of cyclotron orbits – Landau levels 54

55. LDQS 2011, October; HRI 2/3 data 55

56. LDQS 2011, October; HRI qp quasiparticle quasihole created? Configuration #4 - neutral modes flowing counter - clockwise Any charge noise created does not reach voltage probe injecting from source #1 56

57. LDQS 2011, October; HRI qp partitioned neutral mode ? Configuration #4 - neutral modes flowing counter - clockwise no current no excess noise (no heating) injecting from source #1 57

58. LDQS 2011, October; HRI qp no current no excess noise (no heating) Configuration #1 neutral injecting current from source #3 58

59. LDQS 2011, October; HRI 3/5 data 59

60. LDQS 2011, October; HRI Expected - two upstream neutral modes and one downstream charge mode Detection of neutral mode at  =3/5 60

61. LDQS 2011, October; HRI Upstream neutral mode at = 3/5 Transmission hardly affected by the presence of neutral mode 61

62. LDQS 2011, October; HRI shot noise in the presence of neutral mode v =3/5 Upstream neutral mode at = 3/5 62

63. LDQS 2011, October; HRI e * ~e/4 e * ~(2/5)e Charge evolution in the presence of neutral mode, =3/5 63

64. LDQS 2011, October; HRI Summary 5/2 data 64

65. LDQS 2011, October; HRI t 5/2-2 ~ 0.85 Charge evolution with temperature at = 5/2 65

66. LDQS 2011, October; HRI T=10mK ‘mound-like’ ‘valley-like’ Charge dependent transmision at = 5/2 66

67. LDQS 2011, October; HRI what is the role of temperature ? valley-likemound-likelinear regime e * =e/4 Low- energy charge evolution at = 5/2 67

68. LDQS 2011, October; HRI Summary 2/5 data 68

69. LDQS 2011, October; HRI r ~ 0.01 = 2/5 Weak backscattering = 2/5 69

70. LDQS 2011, October; HRI Temperature evolution of e * at = 2/5 temperature affects the partitioned charge dramatically Very similar to =2/3 70

71. LDQS 2011, October; HRI Quantum Hall Effect – energy landscape Quantization of cyclotron orbits – Landau levels 71