Observation of neutral modes in the fractional quantum hall effect regime. Aveek Bid
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1 Observation of neutral modes in the fractional quantum hall effect regime Aveek Bid Department of Physics, Indian Institute of Science, Bangalore Nature (2010)
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 Classical Hall Effect R xx - B independent R xy - Linear in B Classical Hall Effect 3
4 Quantum Hall Effect Integer Quantum Hall Effect 4
5 Quantum Hall Effect Fractional Quantum Hall Effect J.P.Eisenstein and H.L.Stormer, Science 248,1461(1990) 5
6 Quantum Hall Effect Landau levels Quantization of cyclotron orbits Landau levels 6
7 Quantum Hall Effect energy landscape Plateau of n=2 7
8 Quantum Hall Effect energy landscape E Plateau of n=2 two completely filled Landau levels x Bulk of 2DEG no states at m No net current flows in bulk 8
9 Quantum Hall Effect edge states E Near sample edges confining potential causes Landau levels to curl upwards Left edge x Right edge One-dimensional ballistic conduction channels near edges edge states 9
10 Quantum Hall Effect direction of edge states? E For 2-D magneto-electric sub-bands k ~ x 0 /l 0 2 Left edge x Right edge 10
11 Quantum Hall Effect direction of edge states? E Velocity ~ δe/ δk Left edge k Right edge Modes on a given edge move in same direction 11
12 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 Quantum Hall Effect edge states No backscattering perfect quantization 13
14 Quantum Hall Effect - Neutral edge modes predicted e LL1 LL2 no interactions charge modes are eigen states e/2 neutral e/2 e/2 charge e/2 interactions neutral and charge modes are eigen states co-propagating neutral and charge modes (if they exist) are difficult to separate Berg et al, PRL (2009) 14
15 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 Quantum Hall Effect counter-propagating modes 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 16
17 n = 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 n = 2/3 with disorder and interactions Disorder scattering allows equilibration of edges Two counter-propagating modes on each edge Prediction of a counter-propagating charge-neutral mode Kane et al, PRL (1994) 18
19 Why counter-propagating modes? 19
20 Why counter-propagating modes? Composite Fermions n=1/3 three flux quanta per electron e - e - e - Landau level n=1 for composite fermions! 20
21 Why counter-propagating modes? 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 B B eff eff B 2 0 n B
22 Why counter-propagating modes Case of n=2/3 n,n 2/3 1/2 B eff eff x x As sample edge is approached n decreases n decreases B eff B 1 2 B 1 2 eff E ( n 1/ 2) eff V con 22
23 How to detect neutral modes? via their effect on the tunnelling exponent in narrow constrictions via heat transfer, dissipation, heating of edges Can shot noise help in identifying neutral modes? 23
24 Schematic of device x y z 24
25 Schematic of device Ohmic contacts Metallic gates 25
26 S i (10-28 A 2 /Hz) Shot noise due to partitioning by QPC split metal gate t 6 4 T = 57mK t = At finite V and T current, I (na) S ( 0 ) i 4k B Tg qv 2qI(1 t) coth 2kBT 2kBT qv 26
27 Detection of neutral mode at n =2/3 injecting current from source #2 charge neutral Charge Neutral mode flows clockwise counter-clockwise reaches goes QPC to ground #1 27
28 Detection of neutral mode at n =2/3 28
29 Detection of neutral mode at n =2/3 injecting current from source #2 charge neutral Charge noise created Can be sensed by voltage probe 29
30 Detection of neutral mode at n =2/3 injecting current from source #2 Charge noise created Can be sensed by voltage probe Noise due to fragmentation of neutral quasiparticles 30
31 QPC transmission and shot noise S i ~ t(1-t) 31
32 Sanity check measurements at n=2/5 n=2/5 supports two co-propagating modes on each edge No signature of neutral mode at n=2/5 32
33 Upstream neutral mode at n = 2/5? charge Charge mode flows counter-clockwise no observed effect of I n on shot noise due to I s 33
34 Sanity check comparison between 2/5 and 3/5 34
35 More checks- neutral modes flowing clockwise injecting from source #3 qp no current no excess noise (no heating) 35
36 More checks - what about other normal states? n = 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 Interaction of neutral mode with charge mode injecting current from source #1 Charge mode flows counter - clockwise towards QPC Neutral mode flows clockwise reaches ground contact 37
38 Interaction of neutral mode with charge mode injecting current from source #2 what will be the total noise? Charge mode flows counter clockwise - reaches ground contact Neutral mode flows clockwise towards QPC 38
39 Shot noise in the presence of neutral mode, n=2/3 Noise due to charge mode only 20 na 39
40 Shot noise in the presence of neutral mode, n=2/3 e * ~(2/3)e I n = 0 na I n = 2 na e * ~0.45e Quasiparticle charge decreases Temperature increases 40
41 Shot noise in the presence of neutral mode, n=2/3 41
42 Charge evolution in the presence of neutral mode, n=2/3 quasiparticle charge drops to ~1/3e from 2/3e temperature increases by ~15-20mK 42
43 Temperature evolution of e * at n = 2/3 charge drops significantly only at ~ 100mK neutral mode does not affect the charge via temperature increase 43
44 Does temperature affect neutral mode? Shot noise due to neutral mode fragmentation P l 0 exp( l T 2 / l 0 ) l 0 T=10mK l 0 T=25mK 44
45 Does temperature affect neutral mode? Charge evolution due to neutral mode 45
46 What about n = 5/2? what is expected for n =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 Is there a neutral mode for n =5/2? 46
47 neutral mode at n = 5/2 No significant affect on the transmission 47
48 Shot noise of neutral mode at n=5/2 48
49 Shot noise in the presence of neutral mode at n = 5/2 5.2mV 49
50 Charge evolution in the presence of neutral mode at n = 5/2 50
51 Summary Experimentally demonstrated the existence of neutral mode Produces shot noise at QPC - proportional to t(1-t) and current; depends on the number of neutral modes. Affects Fano factor of shot noise of charge mode and temperature of the tunneling quasiparticles Neutral modes in n=5/2 strong indication of their non-abelian nature Aveek Bid, N. Ofek, H. Inoue, M. Heiblum, V. Umansky and D. Mahalu; Nature (2010) 51
52 Acknowledgements Moty Heiblum Nissim Hiroyuki C. Kane D. Mahalu V. Umansky 52
53 THANK YOU 53
54 Quantum Hall Effect energy landscape Quantization of cyclotron orbits Landau levels 54
55 2/3 data 55
56 Configuration #4 - neutral modes flowing counter - clockwise injecting from source #1 qp quasiparticle quasihole created? Any charge noise created does not reach voltage probe 56
57 Configuration #4 - neutral modes flowing counter - clockwise injecting from source #1 qp partitioned neutral mode? no current no excess noise (no heating) 57
58 Configuration #1 injecting current from source #3 qp neutral no current no excess noise (no heating) 58
59 3/5 data 3/5 data 59
60 Detection of neutral mode at n =3/5 Expected - two upstream neutral modes and one downstream charge mode 60
61 Upstream neutral mode at n = 3/5 Transmission hardly affected by the presence of neutral mode 61
62 Upstream neutral mode at n = 3/5 shot noise in the presence of neutral mode v=3/5 62
63 Charge evolution in the presence of neutral mode, n=3/5 e * ~(2/5)e e * ~e/4 63
64 Summary 5/2 data 64
65 quasiparticle charge e * (e) Charge evolution with temperature at n = 5/ t 5/2-2 ~ 0.85 sample 1 sample 2 sample 3 sample temperature, T (mk) 65
66 spectral density S i x (A 2 /Hz) spectral density S i x (A 2 /Hz) Charge dependent transmision at n = 5/2 T=10mK 1 1 t 5/ mound-like t 5/ valley-like e * =0.15e 30 e * =0.16e e * =0.8e impinging current, I imp (na) e * =0.625e impinging current, I imp (na) 66
67 Low- energy charge evolution at n = 5/2 1.2 T=10mK effective charge e * (e) sample 1 sample 2 sample 3 sample 4 valley-like linear regime e * =e/4 mound-like Average transmission t 5/2-2 what is the role of temperature? 67
68 Summary 2/5 data 68
69 Transmission of QPC, t Shot noise (10-30 A 2 /Hz) Weak backscattering n = 2/5 r ~ n = 2/5 T=9mK Voltage (mv) T=9mK q=2e/5 n = 2/5 T=82mK q=e/ Back Scattered Current, I B (pa) 69
70 quasiparticle charge (e/5) Temperature evolution of e * at n = 2/ electron temperature (mk) temperature affects the partitioned charge dramatically Very similar to n=2/3 70
71 Quantum Hall Effect energy landscape Quantization of cyclotron orbits Landau levels 71
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