S. Nanot1, B. Lassagne1, B. Raquet1, J.M. Broto1 and W. Escoffier1

J.P. Cleuziou2, M. Monthioux2, T. Ondarçuhu2 R. Avrilier3, S. Roche3

Abstract : We report giant quantum flux modulation of the conductance in ballistic multi wall carbon nanotubes threaded by a 55T magnetic field in the high temperature regime (100K). This is the first evidence of the Aharonov-Bohm effect on conductance in ballistic carbon nanotubes. Our experimental data are well reproduced assuming a

variable electronic transmission coefficient due to band bending at the contacts, under magnetic field.

Results analysis

Flat band regime with ohmic contacts

Ballistic carbon nanotube (72,72) of diameter 10nm at T=100K. Under magnetic field, an energy gap Ec opens which scales as :

Band bending at the contact sc-CNT/Pd

e- Ec

Ev

Contact 2

f

e+

B = 26T; Φ = Φ0/2

Kubo formalism with determination of the magneto-dependent TDOS and the Fermi level shift.

Good agreement between theoretical predictions and measurements assuming a p-doped CNT with CNP at Vg ~ 10V : maximum of gap opening at Φ0/2.

Semi-analytical model with Landauer formula.

Magneto-conductance of sample B at 146KMagnetic field B up to 35T

Nanotube synthesis Arc-discharge MWCNT from EPFL (Ecole Polytechnique Fédérale de Lausanne)

Nanotubes A & B diametersSample A: d ~ 9-10 nmSample B : d ~ 7-8 nm

Transistor configurationInter-electrodes distance: L ~ 200 nmLow bias voltage (10mV)Fermi level depends on gate voltage

Preliminary measurementsTwo probe conductance around 1G0

Mean free path: le >> LBallistic transport regime

Vg

Vb

SiO2

Si n++

Pd

CNT

1 µm

gF VE ~

Sample and measurement characteristics

00

00

12

3

2

3

CE

00

0

2

20

if

if

(tight-binding calculation)

Problem with the evolution between Φ and Φ0/2 : far from CNP, the conductance decreases two slowly in the theoretical predictions.

Aharonov-Bohm effect in carbon nanotubes

0

////

2

kk

kkPeriodical phenomenon:Flux quantum Φ0 = h/e

B k┴

DO

S

S. RocheФ/ Ф0=0E

Ф/ Ф0=1/2

A magnetic field applied parallel to the nanotube axis modifies by a factor where Φ0 is the magnetic flux inside the nanotube.

k0

2

E

DOS

CNP = 0Magneto-conductance of sample A at 103KMagnetic field up to 55T

0 10 20 30 40 50

0,2

0,4

0,6

0,8

1,0

G (

2e

²/h

)

Vg=-10V

-6V

0V

4V 6V10V

B (T)

0 10 20 30

0,6

0,8

1,0

-10V-7.5V-3.5V

0V

7.5V

10V15V

20V

Vg

B (T)

G (

2e²/

h)

-10 0 100,0

0,6

1,2

G (

2e

²/h

)

Vg (V)

126K 80K 40K 20K

12K 4K 2K

0,0 0,2 0,4 0,6 0,8 1,0

0,8

1,0

1,2

1,4

1,6

1,8

2,0

Experience Flat band model

G(2

e2 /h)

/0

Vg=-10V

Vg=0V

1 National Pulsed Magnetic Field Laboratory, LNCMP, 143 Avenue de Rangueil 31400 Toulouse (France)2 Centre for material elaboration and structural studies, CEMES, 29 Rue Jeanne Marvig 31055 Toulouse3 Commissariat à l’Energie Atomique, DRFMC/SPSMS, 17 rue des Martyrs 38042 Grenoble (France)

In the ballistic regime, we expect a strong magneto-conductance behaviour depending on the Fermi level position with respect to the Charge Neutrality Point.

is symmetric and centered at B=24T, suggesting a 48T periodic behaviour at higher fields. This result is in agreement with the expected Aharonov-Bohm theory for a ballistic carbon nanotube diameter of 10nm.

BG

G(Vg) shows quasi-periodic oscillations of period ~3,3V. Such a modulation is Fabry-Perot like interferences, with the nanotube acting as an electronic waveguide between non-perfect contacts. This effect provides support for the ballistic regime.

Realistic barrier profile estimations lead to an excellent agreement between theory and experiment.

Solely DoS effect scenario.

Transport is dominated by thermally assisted tunnel processes (WKB).

The formation of Schottky barriers limits the transmission coefficient

Different barrier profiles have been tested (triangular, polynomial and logarithmic)

Best agreement with logarithmic barrier profile.

B=0 B≠0

Experiment SB model