separation of neutral and charge modes in one dimensional chiral edge channels...
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4.021 DDf=2.1 GHz
pse 62ee / 45.01
pse 58
bosons1 2
3 4
1 2
3 4fermions
1 2
3 4
Single electron emitter
Dip not going to zero.Decoherence effect !
Electronic Hong-Ou-Mandel dip
E. Bocquillon et al., Science 339 no. 6123 pp. 1054-1057
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VG
m 1
Gaz 2D
B
V
VG(mV)
An electronic Mach-Zehnder interferometer
)(Re12
)1(2
gh
VeI
visibility : 62%
Y. Ji et al., Nature 422, 415 (2003)P. Roulleau et al., Phys. Rev. Lett.100, 126802 (2008)P. Roulleau et al., Phys. Rev. Lett.101, 186803 (2008)P.-A. Huynh et al., Phys. Rev. Lett. 108, 256802 (2012)
Noisy inneredge channelÞ reduction of
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Energy relaxation between channels at υ=2
H. Le Sueur et al., PRL 105, 056803 (2010).
Outer edge channel drivenout of equilibrium.
Þ non-equilibrium double dip relaxes over ~3µm.Þ broader dip than equilibrium.
Inner edge channel drivenout of equilibrium.
Þ dip broadens as L is increased.
Þ outer edge channel heats up.
Energy exchanges between copropagating channels.
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Separation in charge and neutral modes
In nanowires:O.M. Auslaender et al., Science 308 5718 (2005)H. Steinberg et al., Nat. Phys. 4 3 (2007)
I.P. Levkivskyi et al., PRB 78, 045322 (2008)P. Degiovanni et al., PRB 80, 241307(R) (2009)D.L. Kovrizhin et al., PRB 81, 155318 (2010)Neder et al., PRL 96 016804 (2006)
decoupled propagationin ch. 1 & 2
2 new eigenmodes :- slow neutral mode- fast charge mode
m/s
Capacitive coupling between channels
𝑣 𝜌
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In frequency domain: edge magneto-plasmons (EMP)
Edge magneto-plasmons
In the "frequency domain": charge oscillations
• Sine wave induced in outer edge channel
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In frequency domain: edge magneto-plasmons (EMP)
Edge magneto-plasmons
In the "frequency domain": charge oscillations
• Sine wave induced in outer edge channel
• Phase shift between both modes:
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In frequency domain: edge magneto-plasmons (EMP)
Edge magneto-plasmons
In the "frequency domain": charge oscillations
• Sine wave induced in outer edge channel
• Phase shift between both modes:
nv
l
Þ GHz
m/s
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Scattering of EMP over propagationlength between source and QPC
Experimental realisation
Sine excitation.
No tunneling (capacitive coupling).
1
2
)0()()( 1111 iSli
)0()()( 1212 iSli
)0(1i
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QPC completely closedQPC partially open
𝛼𝑖2 )
𝑉 𝑞𝑝𝑐
𝑉 𝑞𝑝𝑐
𝑉 𝑞𝑝𝑐
𝑉 𝑞𝑝𝑐
Experimental realisation
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Experimental results
Þ Points spiraling in the complex plane (damping).
Þ Charge oscillations.E. Bocquillon et al., Nature Comm. 4, 1839 (2013).
𝑅≃𝑆21
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• 2 non-dispersive regimes.• non-zero imaginary partreveals damping.
Dispersion relation
Dispersion relation of the neutral mode
𝑅≃𝑆21=1−𝑒𝑖 𝑘𝑛
❑ (𝜔 ) 𝑙
2
E. Bocquillon et al., Nature Comm. 4, 1839 (2013).
Short range
Long range
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Short-range model Low-frequency regime: well reproduced Oscillations: 1 timescale ⇒ not enough
Local (zero-range) density-density interactions ⇔ distributed capacitance between channels
•No characteristic length ⇔ 1 timescale⇔ constant velocity
Short-range model
I.P. Levkivskyi et al., PRB 78, 045322 (2008)P. Degiovanni et al., PRB 80, 241307(R) (2009)D.L. Kovrizhin et al., PRB 81, 155318 (2010)Also in non-chiral Lüttinger liquids: I. Safi et al., PRB 52, R17040 (1995)
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Long-range model Low-frequency regime: well reproduced Oscillations: 2 timescales ⇒ sufficient Dissipation: well reproduced, origin unknown ?
Long-range charge-charge interactions ⇔ capacitance between channels
•Range propagation length ≃⇔ 2 time-scales
⇔ 2 different velocities
•Dissipation: compatible with RC circuit description
Long-range model
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Conclusion
In IQHR:- Capacitive coupling between channels (Coulomb interactions),- Range of the coupling: propagation length,- Two propagation regimes:
then m/s
then m/s
Both non dispersive.
Perspectives:- Understand the effect of coupling probed using EMP (collective
modes) in term of two particle interferences (HOM).
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G. Fève
former members : E. Bocquillon, J. Gabelli, A. Mahé , F. D. Parmentier,
J.-M. Berroir B. Plaçais
Mesoscopic Physics group, LPA ENS, pièce L175
Samples Fab,LPN Marcoussis
A. Cavanna
Y. Jin
V. FreulonA. Marguerite
Theory,ENS Lyon
P. Degiovanni
C. Grenier
D. Ferraro
E. Thibierge
People involved
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