Separation of neutral and charge modes in one dimensional chiral edge channels

Separation of neutral and charge modes in one dimensional chiral edge channels

[email protected]

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

GDR méso Aussois 2013 – [email protected]

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


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.


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


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:






• Phase shift between both modes:

nv

l

Þ GHz

m/s


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


QPC completely closedQPC partially open

𝛼𝑖2 )

𝑉 𝑞𝑝𝑐

𝑉 𝑞𝑝𝑐

𝑉 𝑞𝑝𝑐

𝑉 𝑞𝑝𝑐

Experimental realisation


Experimental results

Þ Points spiraling in the complex plane (damping).

Þ Charge oscillations.E. Bocquillon et al., Nature Comm. 4, 1839 (2013).

𝑅≃𝑆21


• 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


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)


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


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).


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


Documents

Separation of neutral and charge modes in one dimensional chiral edge channels