S. Nanot 1, B. Lassagne 1, B. Raquet 1, J.M. Broto 1 and W. Escoffier 1 J.P. Cleuziou 2, M. Monthioux 2, T. Ondarçuhu 2 R. Avrilier 3, S. Roche 3 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-e- EcEc EvEv Contact 2 f e+e+ B = 26T; Φ = Φ 0 /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 Φ 0 /2. Semi-analytical model with Landauer formula. Magneto-conductance of sample B at 146K Magnetic field B up to 35T Nanotube synthesis Arc-discharge MWCNT from EPFL (Ecole Polytechnique Fédérale de Lausanne) Nanotubes A & B diameters Sample A: d ~ 9-10 nm Sample B : d ~ 7-8 nm Transistor configuration Inter-electrodes distance: L ~ 200 nm Low bias voltage (10mV) Fermi level depends on gate voltage Preliminary measurements Two probe conductance around 1G 0 Mean free path: l e >> L Ballistic transport regime VgVg VbVb SiO 2 Si n ++ Pd CNT 1 µm Sample and measurement characteristics (tight-binding calculation) Problem with the evolution between Φ and Φ 0 /2 : far from CNP, the conductance decreases two slowly in the theoretical predictions. Aharonov-Bohm effect in carbon nanotubes Periodical phenomenon: Flux quantum Φ 0 = h/e B k┴k┴ DOS S. Roche Ф/ Ф 0 =0 E Ф/ Ф 0 =1/2 A magnetic field applied parallel to the nanotube axis modifies by a factor where Φ 0 is the magnetic flux inside the nanotube. E DOS CNP = 0 Magneto-conductance of sample A at 103K Magnetic field up to 55T 1 National Pulsed Magnetic Field Laboratory, LNCMP, 143 Avenue de Rangueil Toulouse (France) 2 Centre for material elaboration and structural studies, CEMES, 29 Rue Jeanne Marvig Toulouse 3 Commissariat à l’Energie Atomique, DRFMC/SPSMS, 17 rue des Martyrs 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. 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=0B≠0B≠0 Experiment SB model