Transcript Separation of neutral and charge modes in one dimensional chiral

Separation of neutral and charge modes
in one dimensional chiral edge channels
[email protected]
Electronic Hong-Ou-Mandel dip
1
2
fermions
3
f=2.1 GHz
4
D1  D2  0.4
1
2
1
2
3
4
3
4
bosons
 e  58 ps
Single electron
emitter
1  0.45 e
  / e
 e  62 ps
Dip not going to zero.
Decoherence effect !
E. Bocquillon et al., Science 339 no. 6123 pp. 1054-1057
GDR méso Aussois 2013 – [email protected]
An electronic Mach-Zehnder interferometer
Gaz 2D
B
V
Noisy inner
edge channel
 reduction of 𝑙𝜑


e 2V
I
1  Re g (1) ( )
2h
1 m

visibility : 62%
VG
Y. Ji et al., Nature 422, 415 (2003)
P. Roulleau et al., Phys. Rev. Lett.100, 126802 (2008) VG(mV)
P. Roulleau et al., Phys. Rev. Lett.101, 186803 (2008)
P.-A. Huynh et al., Phys. Rev. Lett. 108, 256802 (2012)
GDR méso Aussois 2013 – [email protected]
Energy relaxation between channels at υ=2
H. Le Sueur et al., PRL 105, 056803 (2010).
Outer edge channel driven
out of equilibrium.
 non-equilibrium double dip
relaxes over ~3µm.
 broader dip than equilibrium.
Inner edge channel driven
out of equilibrium.
 dip broadens as L is
increased.
 outer edge channel
heats up.
Energy exchanges between
copropagating channels.
GDR méso Aussois 2013 – [email protected]
Separation in charge and neutral modes
Capacitive coupling between channels
decoupled
propagation
in ch. 1 & 2
2 new eigenmodes :
- slow neutral mode
- fast charge mode
𝑣𝜌
𝑣 ≃ 105 m/s
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)
In nanowires:
O.M. Auslaender et al., Science 308 5718 (2005)
H. Steinberg et al., Nat. Phys. 4 3 (2007)
GDR méso Aussois 2013 – [email protected]
Edge magneto-plasmons
In frequency domain: edge magneto-plasmons (EMP)
In the "frequency domain": charge oscillations
• Sine wave induced in outer edge channel
GDR méso Aussois 2013 – [email protected]
Edge magneto-plasmons
In frequency domain: edge magneto-plasmons (EMP)

In the "frequency domain": charge oscillations
• Sine wave induced in outer edge channel
• Phase shift between both modes:
GDR méso Aussois 2013 – [email protected]
Edge magneto-plasmons
In frequency domain: edge magneto-plasmons (EMP)
In the "frequency domain": charge oscillations
• Sine wave induced in outer edge channel
• Phase shift between both modes:
 
l
vn

 𝒇 ≃ 𝟏 − 𝟏𝟎 GHz
𝑣 ≃ 105 m/s
GDR méso Aussois 2013 – [email protected]
Experimental realisation
Scattering of EMP over propagation
length between source and QPC
Sine excitation.
1
2
i1 (0)
i1 (l )  S11 ( )i1 (0)
i2 (l )  S 21 ( )i1 (0)
No tunneling (capacitive coupling).
GDR méso Aussois 2013 – [email protected]
Experimental realisation
𝑉𝑞𝑝𝑐
𝑉𝑞𝑝𝑐
𝑉𝑞𝑝𝑐
𝛼 𝑖2
𝛼(𝑖1 + 𝑖2 )
QPC partially open
𝑉𝑞𝑝𝑐
QPC completely closed
GDR méso Aussois 2013 – [email protected]
Experimental results
𝑅 ≃ 𝑆21
 Points spiraling in the complex plane
(damping).
 Charge oscillations.
E. Bocquillon et al., Nature Comm. 4, 1839 (2013).
GDR méso Aussois 2013 – [email protected]
Dispersion relation of the neutral mode
E. Bocquillon et al., Nature Comm. 4, 1839 (2013).
𝑅 ≃ 𝑆21
1 − 𝑒 𝑖𝑘𝑛
=
2
𝜔 𝑙
Dispersion relation
• 2 non-dispersive regimes.
• non-zero imaginary part
reveals damping.
Short
range

Long
range
GDR méso Aussois 2013 – [email protected]
Short-range model
Local (zero-range) density-density
interactions ⇔ distributed capacitance
between channels
•No characteristic length
⇔ 1 timescale
⇔ constant velocity
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)
Short-range model
Low-frequency regime: well reproduced
Oscillations: 1 timescale ⇒ not enough
GDR méso Aussois 2013 – [email protected]
Long-range model
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
Low-frequency regime: well reproduced
Oscillations: 2 timescales ⇒ sufficient
Dissipation: well reproduced, origin unknown ?
GDR méso Aussois 2013 – [email protected]
Conclusion
In IQHR:
- Capacitive coupling between channels (Coulomb interactions),
- Range of the coupling: propagation length,
- Two propagation regimes:
𝜆≫𝑙
then 𝑣𝑛 ≃ 4.6 × 104 m/s
𝜆≪𝑙
then 𝑣𝑛 ≃ 2.2 × 104 m/s
Both non dispersive.
Perspectives:
- Understand the effect of coupling probed using EMP (collective
modes) in term of two particle interferences (HOM).
GDR méso Aussois 2013 – [email protected]
People involved
Mesoscopic Physics group, LPA ENS, pièce L175
A. Marguerite
V. Freulon
G. Fève
J.-M. Berroir
B. Plaçais
former members : E. Bocquillon, J. Gabelli, A. Mahé , F. D. Parmentier,
Samples Fab,
LPN Marcoussis
Theory,
ENS Lyon
A. Cavanna
P. Degiovanni
Y. Jin
C. Grenier
D. Ferraro
E. Thibierge
GDR méso Aussois 2013 – [email protected]