Energy transfer in the pairwise scattering between the electrons of counter propagating

edge channels in presence of disorder

M.G.Prokudina,

V.S.KhrapaiISSP RAS, Chernogolovka, Russia

2012

г.

Quasi one-dimensional edge channels

The diagonal conductance in quantizing magnetic field is exponentially small σxx

→0

The electron transport is often described in terms of quasi one-dimensional (q1D) edge channels (M.Buttiker, Physical Review B 38, 9375 (1988))

Chiral 1D system backscattering is impossible

Quasi 1D systemIf interaction between edges of opposite chirality is absent

1D Fermi liquid with parameter interaction (g=1)

M.P. A. Fisher, L. Glazman, arXiv:condmat/9610037v1 (1996)

Experiment with tunneling in extra clean systems:W.Kang, H.L.Stormer et al., Nature 403, 59(2000)M.Hable, W.Wegscheider, Phys.Stat.Sol.B 245,260(2008)

Unique system: Luttinger liquid with interaction parameter g≈1 without backscattering and with independent control over right and left movers

2 coplanar electron systems can be separated by opaque

barrier coupling left and right moves modes

without tunneling

Drag in the absence of backscattering

1.

Only if dispersion is nonlinearM.Pustilnik, E.G.Mishchenko et al, PRL 91,126805(2003)

2. Drag is absent in infinite systemD.Polyakov, unpublished

Energy transfer (e.g. from hot to cold) survives even when momentum transfer forbidden!

Inelactic

scattering processes lead to energy transfer between nonequilibrium chiral systems.

Energy transfer in the e-e

scattering in 1D system

Counter-propagating edge channels:

scattering is impossible

2) disorder:some momentum uncertainty A.M. Lunde et al, PRB 81, 041311(R) (2010)H. le Sueur et al, PRL 105, 056803 (2010)

Exclusion1) “exotic”:three particles interaction + nonlinear dispersion T.Karzig et al, PRL 105, 226407 (2010)T.Micklitz et al, PRL 106, 196402 (2011)G. Barak et al., Nature Phys. 6, 489 (2010).

Investigation of energy relaxation between left and right moving modes in drag-type experiment

Counter propagating edge channels

Drag experiments: T.G.Gramila et al, PRL 66, 1216 (1991)P.Debray et al, J. Phys.: Cond. Matt. 13 3389–3402 (2001)A.D.K.Finck et al, PRL 106, 236807 (2011)

Energy relaxation experiments: H. le Sueur et al, PRL 105, 056803 (2010)C.Altimiras et al, Nature Phys. 6, 34 (2010)

Sample

2DEG:mobility carrier densityDepth

Basics of the experiment: drive

Nonequilibrium distribution of electrons in the edge channel can

be created by a partially transmitting drive QPC

Same nonequilibrium channels regardless the sign of the current (bias) in the QPC.

before interaction

after interaction

Basics of the experiment: excite and detect

The resulting non-equilibrium electron distribution in the second edge channel is detected with QPC, by measuring its thermoelectric

response IDET and/or change in conductance

Dectector

current: sign and drive bias dependence

Linear dependence at relatively high drive bias voltage and parabolic dependence at small drive bias

T=60mKB=3.8T

Picture is independent of drive bias sign.Induced current flows from hot to cold edge channel

Different detector conductances

Detector conductance

Approximately linear drive bias dependence of thermoelectric current is observed for different detector QPC conduction.

How to quantify the energy exchange?

1.Can the distribution be described by an effective excess temperature ΔTeff

?How to determine the effective excess temperature?

2. What is the interaction mechanism?

Electrons flow from hot to cold thermoelectric effect

Temperature dependence of the detector conductance

Detector conductance Linear approximation

The

measurements of detector QPC

differential

conductance as a drive bias and temperature functions

allows to quantify the degree of detector

heating in dependence of

drive bias.

The degree of detector heating

Detector conductance

The effective excess temperature ΔT increases by ~ 20 mK approximately linear with drive bias up to 1mV

There are large difference between temperature dependences of detector conductance, but the curves of detector heating

degree are similar

Correspondence of induced current and excess temperature dependence

Figures look identicalThermoelectric analogy is correct!

pairwise scattering in the presence of disorder 3-particles interaction

Linear dependence and interaction mechanism

1.

Small transfer energy quantum

2. Power

A.M. Lunde et al, PRB 81, 041311(R) (2010)V.S.Khrapai, M.G.Prokudina, unpublished

Interaction mechanism: phonon or Coulomb?Calculation in the frame of perturbation theory

small distance between edge channels phonon scattering can be neglected

large distance d>>l between edge channels Coulomb and phonon parts are comparable

PC /Pph

≥

105

Quantitative agreement with experiment

• quite good fit• transfer energy quantum ΔE≈50μeV, l≈700nm,w≈14nm (vF

=107cm/s)

Conclusions

•

Observation of energy transfer between counter- propagating edge channels

•

Quantitative agreement with pairwise Coulomb scattering with disorder.

•

Transferred

energy quantum

of

~50μeV

We acknowledge discussions with

I.S.Burmistrov, I.V.Gornyi, D.V.Shovkun, A.A.Shashkin and D.G.Polyakov

Energy transfer in the pairwise scattering between the electrons of counter propagating edge channels in presence of disorder�Slide Number 2Quasi 1D systemDrag in the absence of backscatteringSlide Number 5SampleBasics of the experiment: driveBasics of the experiment: excite and detectDectector current: sign and drive bias dependenceDifferent detector conductancesHow to quantify the energy exchange?Slide Number 12The degree of detector heatingCorrespondence of induced current and excess temperature dependenceSlide Number 15Slide Number 16Quantitative agreement with experimentConclusions