slide1
Download
Skip this Video
Download Presentation
ENS-Paris

Loading in 2 Seconds...

play fullscreen
1 / 41

ENS-Paris - PowerPoint PPT Presentation


  • 186 Views
  • Uploaded on

ENS-Paris. Experiments on Luttinger liquid properties of Fractional Quantum Hall effect and Carbon Nanotubes. Christian Glattli CEA Saclay / ENS Paris). Nanoelectronic Group (SPEC, CEA Saclay) Patrice Roche ( join in 2000 ) (FQHE) Fabien Portier ( join in 2004 )

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' ENS-Paris' - amiel


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

ENS-Paris

Experiments on Luttinger liquid properties of

Fractional Quantum Hall effect

and Carbon Nanotubes.

Christian Glattli CEA Saclay /ENS Paris)

Nanoelectronic Group (SPEC, CEA Saclay)

Patrice Roche ( join in 2000) (FQHE)

Fabien Portier (join in 2004)

Keyan Bennaceur (Th. 07 - … ) (QHEGraphene)

Valentin Rodriguez ( Th. 97 - 00 ) (FQHE)

H. Perrin ( Post-Doc. 99 ) (FQHE)

Laurent Saminadayar ( Th. 94 - 97) (FQHE)

(+ L.-H. Bize, J. Ségala, E. Zakka-Bajani, P. Roulleau, …)

Mesoscopic Physics Group (LPA, ENS Paris)

J.M. Berroir

B. Plaçais

A. Bachtold (now in Barcelona) (LL in CNT)

T. Kontos (Shot noise in CNT)

Gao Bo (PhD 2003 - 2006 (LL in CNT)

L. Herrmann (Diploma arbeit 07)

+ Th. Delattre ( Shot noise in CNT)

( +G. Gève, A. Mahé, J. Chaste, C. Feuillet Palma, B. Bourlon)

slide2

OUTLINE

  • Fractional Quantum Hall effectEdges as Chiral LL:
  • Carbone Nanotubes signatures of T-LL:
  • (on going or foreseen experimental projects)
slide3

V xx

V

Hall

I

I

I

Edwin Hall

1879

K. von Klitzing

G. Dorda

M. Pepper

1980

E

Landau levels

Integer Quantum Hall Effect

B (Tesla)

slide4

(1982)

Laughlin’s predictions:

for filling factors n:

(D.C. Tsui, H. Störmer, and A.C. Gossard, 1982)

(1996)

( IQHE )

m

( FQHE )

D

0

1/3

2/3

1

FQHE Gap : fundamental incompressibility due to interactions

(different from IQHE incompressibility due to Fermi statistics)

Fractional Quantum Hall Effect

slide5

Example :n=1/3

i.e. 3 flux quanta (or 3 states) for 1 electron

single particle

wavefunction :

Gap D

Laughlin trial wavefunction for n = 1/3, 1/5, … :

(Ground State)

- e / 3

- satisfies Fermi statistics

- minimizes interactions

- uniform incompressible quantum liquid

a quasi-hole excitation = to add a quantum flux

= to create a charge (- e / 3)

quasi-hole wavefunction at z = z a

fractionally charged quasiparticles obey fractional statistics

anyons !!!

Laughlin quasiparticles

slide6

electron drift velocity

edge

channels

current flows only on the edges (edge channels)

confining

potential

(Landau levels)

slide7

OUTLINE

  • Fractional Quantum Hall effectEdges as Chiral LL:
      • probing quasiparticles via tunneling experiments
  • Carbone Nanotubes signatures of T-LL:
  • on going or foreseen experimental projects
slide8

e

-e/3

=1/3

e/3

=1/3

e/3

q = e/3

Laughlin quasiparticles

on the edge

q

probing quasiparticles via tunneling experiments,

two different approaches:

1) non-equilibrium tunneling current measurements:

probes excitations above the ground state

tunneling density of states :

how quasiparticles are created

2) shot-noise associated with the

tunneling current:

probes excitations above the ground states :

direct measure of quasi-particle charge

B (Tesla)

e/3

metal

e

=1/3

e/3

e/3

slide9

Tomonaga (1950), Luttinger (1960)

Haldane (1979)

1-D fermions short range interactions

(connection with exactly integrable quantum models: Calogero, Sutherland, …)

Tunneling electrons into Tomonaga-Luttinger liquids

tunelling density of states depends on energy

 differential conductance is non-linear with voltage

non-linear conductance:

(métal)

e

plasmon

(1D conductor)

plasmon

example : SW Carbone Nanotube

slide10

+ field quantization:

+ electron creation operator on the edge

e

+ Fermi statistics :

Tunneling into Chiral Luttinger liquid (FQHE regime)

X.G. Wen (1990)

periphery deformation of 1/3 incompressible

FQHE electron liquid

Classical hydrodynamics

(excess charge density / length)

slide11

(excess charge density / length)

+ field quantization:

+ electron creation operator on the edge

e

+ Fermi statistics :

properties of a Luttinger liquid with g = n

Tunneling into Chiral Luttinger liquid (FQHE regime)

X.G. Wen (1990)

periphery deformation of 1/3 incompressible

FQHE electron liquid

Classical hydrodynamics

slide12

e

2 DEG

n+ GaAs

V

tunneling from a metal to a FQHE edge

power law variation

of the current / voltage

Chiral-Luttinger prediction:

A.M. Chang (1996)

also observed :

(voltage and temperature play the same role)

slide13

tunneling from a metal to a FQHE edge

Simplest theory predicts for

power laws are stille observed as expected

but exponent found is different.

Not included

-interaction of bosonic mode dynamics with finite

conductivity in the bulk

- long range interaction

- acuurate description of the edge in real sample.

Grayson et al. (1998)

slide14

Si

+

GaAlAs

GaAs

tunneling between FQHE edges

2D electrons

Atomically controlled epitaxial growth

GaAs/Ga(Al)As heterojunction

CLEAN 2D electron gas

heterojunction

100 nm

constriction

(Quantum Point Contact)

200nm

(top view )

(edge channel)

slide15

low energy

even the weakest barrier

leads to strong reflection

at low energy !

weak barrier

large energy

energy

tunneling between FQHE edges

high barrier

(doubled)

energy

slide16

tunneling between FQHE edges (TBA solution of the B.Sine-Gordon model)

folded into:

kink / anti-kink (charged solitons ) in the phase field f(x,t)

breather (neutral soliton )

thermodynamic Bethe Ansatz self consistent equations

Expression of the current

P. Fendley, A. W. W. Ludwig, and H. Saleur,

Phys. Rev. Lett. 74, 3005 (1995); 75, 2196 (1995);

… similar calculation for shot noise

slide17

(impurity, strength TB )

eV >> TB

eV << TB

Numerical calculation of G(V) using the exact solution by FLS (1996)

tunneling between FQHE edges

(P.Roche + C. Glattli 2002 )

slide19

tunneling between FQHE edges : experimental comparison

scaling V/T is OK

… but dI/dV varies as the second

instead of the fourth power of V( or T)

predicted by perturbative renormalization

approach.

solid line:

renormalization fixed point limit

slide20

Finite temperature calculation using the TBA

solution of the boundary Sine-Gordon model

(Saclay 2000)

(scaling law experimentally observed (Saclay 1998) )

to observe exponent =4 one needs very low temperature and conductance 10-4 X e2/3h !

weak barrier

slide21

Finite temperature calculation using the

Fendley, Ludwig, Saleur (1995) exact solution

e/3

e

(Saclay 2000)

(scaling law experimentally observed (Saclay 1998) )

to observe exponent =4 one needs very low temperature and conductance 10-4 X e2/3h !

weak barrier

slide22

q

probing quasiparticles via tunneling experiments,

two different approaches:

1) non-equilibrium tunneling current measurements:

probes excitations above the ground state

tunneling density of states :

how quasiparticles are created

2) shot-noise associated with the

tunneling current:

probes excitations above the ground states :

direct measure of quasi-particle charge

B (Tesla)

e/3

metal

e

=1/3

e/3

e/3

e

-e/3

=1/3

e/3

=1/3

e/3

q = e/3

Laughlin quasiparticles

on the edge

slide23

( i )

( t )

( r )

2 limiting cases:

The binomial statistics of Shot Noise (no interactions)

incoming current :

(noiseless thanks

to Fermi statistics)

transmitted current :

current noise in B.W. Df :

Variance of partioning

binomial statistics

slide24

1,0

1

.8

.6

.4

.2

0

(

)

-

1

T

0,8

1

0,6

(

)

Fano reduction factor

-

T

1

T

2

2

0,4

+

1

T

2

0,2

0,0

0. 0.5 1. 1.5 2. 2.5

Conductance 2e² / h

quantum point contact (B=0)

Gate

2-D

electron

gas

Gate

(ballistic conductor)

(Saclay 1996)

first mode :

slope ~ (1 - D1 )

Kumar et al. PRL (1996)

M. I. Reznikov et al., Phys. Rev. Lett. 75 (1995) 3340.

A. Kumar et al. Phys. Rev. Lett. 76 (1996) 2778..

slide25

V

Shot Noise in IQHE regime

strong barrier :

e

= 1

= 1

transmitted (D) reflected (1-D)

e

e

(rarely transmitted electrons)

(incoming electrons)

weak barrier :

(rarely transmitted holes)

e

slide26

V

e

Shot Noise in IQHE regime

strong barrier :

transmitted (D) reflected (1-D)

e

= 1/3

= 1/3

e

e

e

(rarely transmitted electrons)

e/3

e/3

(incoming electrons)

weak barrier :

(rarely transmitted holes)

e/3

slide27

e / 3

Direct evidence of fractional charge

L. Saminadayar et al. PRL (1997).

De Picciotto et al. Nature (1997)

n = 1/3

charge q=e/3

n = 2

charge q=e

measure of the anti-correlated transmitted X reflected

current fluctuations (electronic Hanbury-Brown Twiss)

slide28

From fractional to integer charges

chargee/3

charge e

??

V. Rodriguez et al (2000)

slide30

numerical calculation of

the finite temperature

shot noise

P. Fendley and H. Saleur,

Phys. Rev. B 54, 10845 (1996)

exact

solution

(Bethe

Ansatz)

dotted line:

empirical binomial noise

formula for backscattered

e/3 quasiparticles

(P.Roche + C. Glattli 2002 )

extremely good !

slide31

heuristic formula for shot noise

(binomial stat. noise

of backscattered qp )

(binomial stat. noise

of transmitted electrons )

e* as free parameter

B. Trauzettel, P. Roche, D.C. Glattli, H. Saleur

Phys. Rev. B 70, 233301 (2004)

slide32

OUTLINE

  • Fractional Quantum Hall effectEdges as Chiral LL:
      • probing quasiparticles via tunneling experiments
  • Carbone Nanotubes signatures of T-LL:
  • on going or foreseen experimental projects
slide34

Luttinger Liquid effects in Single Wall Nanotubes

Electron tunneling into a SWNT excites

1D plasmons in the nanotubes

giving rise to Luttinger liquid effects

SWNT

e

Non-linear conductance:

plasmon

plasmon

provided kT or eV < hvF / L

slide36

Luttinger Liquid effects in Single Wall Nanotubes

Observation of LL effects requires

slide38

~700 nm

e

V

I

differential tube-tube conductance

Luttinger-Liquid behavior in Crossed Metallic Single-Wall Nanotubes

B. Gao, A. Komnik, R. Egger, D.C. Glattli and A. Bachtold, Phys. Rev. Lett. 92, 216804 (2004)

Mesoscopic Physics group, Lab. P. Aigrain, ENS Paris

1D conductor :

quantum transport + e-e interaction

lead to non-linear I-V for tunneling

from one nanotube to the other (zero-bias anomaly):

g = 0.16

slide39

OBSERVEDPREDICTED

A current flowing through NT ‘ B ’ changes in a

non trivial way the conductance of NT ‘ A ’

additonal demonstration that Luttinger theory is

the good description of transport in CNT at large V

B. Gao, A. Komnik, R. Egger, D.C. Glattli and A. Bachtold,

Phys. Rev. Lett. 92, 216804 (2004)

slide40

OUTLINE

  • Fractional Quantum Hall effectEdges as Chiral LL:
      • probing quasiparticles via tunneling experiments
  • Carbone Nanotubes signatures of T-LL:
  • on going or foreseen experimental projects
slide41

E. Zakka-Bajani PRL 2007

Possible future experimental investigations

  • High frequency shot noise of fractional charges (FQHE in GaAs/GaAlAs)
  • seearXiv:0705.0156 by C. Bena and I. Safi
  • shot noise singularity at e*V/h
  • Carbone Nanotubes
  • shot noise : fractional charges observation would requires >THz
  • measurements
  • FQHE in Graphene ?

R12,42

electrons

holes

K. Bennaceur (Saclay SPEC)

ad