Observation of neutral modes in the fractional quantum hall effect regime Aveek Bid Nature 585 466...
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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
Observation of neutral modes in the fractional quantum hall effect regime Aveek Bid Nature 585 466 (2010) Department of Physics, Indian Institute of Science,
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
Slide 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
Slide 3
LDQS 2011, October; HRI Classical Hall Effect 3 R xx - B
independent R xy - Linear in B
Slide 4
LDQS 2011, October; HRI Integer Quantum Hall Effect Quantum
Hall Effect 4
Slide 5
LDQS 2011, October; HRI Fractional Quantum Hall Effect Quantum
Hall Effect J.P.Eisenstein and H.L.Stormer, Science 248,1461(1990)
5
Slide 6
LDQS 2011, October; HRI Quantum Hall Effect Landau levels
Quantization of cyclotron orbits Landau levels 6
Slide 7
LDQS 2011, October; HRI Quantum Hall Effect energy landscape
Plateau of =2 x 7
Slide 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
Slide 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
Slide 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
Slide 11
LDQS 2011, October; HRI Quantum Hall Effect direction of edge
states? Velocity ~ E/ k Modes on a given edge move in same
direction Right edge Left edge k E 11
Slide 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
Slide 13
LDQS 2011, October; HRI Quantum Hall Effect edge states No
backscattering perfect quantization 13
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
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
Slide 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
Slide 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
Slide 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?
Slide 24
LDQS 2011, October; HRI x z y Schematic of device 24
LDQS 2011, October; HRI split metal gate Shot noise due to
partitioning by QPC 26 t At finite V and T
Slide 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
Slide 28
LDQS 2011, October; HRI Detection of neutral mode at =2/3
28
Slide 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
Slide 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
Slide 31
LDQS 2011, October; HRI QPC transmission and shot noise 31 S i
~ t(1-t)
Slide 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
Slide 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
Slide 34
LDQS 2011, October; HRI Sanity check comparison between 2/5 and
3/5 34
Slide 35
LDQS 2011, October; HRI injecting from source #3 qp no current
no excess noise (no heating) More checks- neutral modes flowing
clockwise 35
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 41
LDQS 2011, October; HRI Shot noise in the presence of neutral
mode, =2/3 41
Slide 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
Slide 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
Slide 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
Slide 45
LDQS 2011, October; HRI Does temperature affect neutral mode?
Charge evolution due to neutral mode 45
Slide 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
Slide 47
LDQS 2011, October; HRI No significant affect on the
transmission neutral mode at = 5/2 47
Slide 48
LDQS 2011, October; HRI Shot noise of neutral mode at =5/2
48
Slide 49
LDQS 2011, October; HRI 5.2 V Shot noise in the presence of
neutral mode at = 5/2 49
Slide 50
LDQS 2011, October; HRI Charge evolution in the presence of
neutral mode at = 5/2 50
Slide 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
Slide 52
LDQS 2011, October; HRI Acknowledgements Moty Heiblum Nissim V.
Umansky D. Mahalu Hiroyuki C. Kane 52
Slide 53
LDQS 2011, October; HRI THANK YOU 53
Slide 54
LDQS 2011, October; HRI Quantum Hall Effect energy landscape
Quantization of cyclotron orbits Landau levels 54
Slide 55
LDQS 2011, October; HRI 2/3 data 55
Slide 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
Slide 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
Slide 58
LDQS 2011, October; HRI qp no current no excess noise (no
heating) Configuration #1 neutral injecting current from source #3
58
Slide 59
LDQS 2011, October; HRI 3/5 data 59
Slide 60
LDQS 2011, October; HRI Expected - two upstream neutral modes
and one downstream charge mode Detection of neutral mode at =3/5
60
Slide 61
LDQS 2011, October; HRI Upstream neutral mode at = 3/5
Transmission hardly affected by the presence of neutral mode
61
Slide 62
LDQS 2011, October; HRI shot noise in the presence of neutral
mode v =3/5 Upstream neutral mode at = 3/5 62
Slide 63
LDQS 2011, October; HRI e * ~e/4 e * ~(2/5)e Charge evolution
in the presence of neutral mode, =3/5 63
Slide 64
LDQS 2011, October; HRI Summary 5/2 data 64
Slide 65
LDQS 2011, October; HRI t 5/2-2 ~ 0.85 Charge evolution with
temperature at = 5/2 65