Imaging electron wave functions of quantized energy levels in carbon nanotubes

Science

Volumn 283, Issue 5398, 1999, Pages 52-55

  Venema, Liesbeth C ^a   Wildöer, Jeroen W G ^a   Janssen, Jorg W ^a   Tans, Sander J ^a   Temminck Tuinstra, Hinne L J ^a   Kouwenhoven, Leo P ^a   Dekker, Cees ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

CARBON; CRYSTAL LATTICES; ELECTRIC CONDUCTANCE; ELECTROMAGNETIC WAVES; ELECTRON ENERGY LEVELS; ELECTRONIC PROPERTIES; FERMI LEVEL; ONE DIMENSIONAL; OSCILLATIONS; QUANTUM THEORY; SCANNING TUNNELING MICROSCOPY;

ATOMIC LATTICE; CARBON NANOTUBES; DIFFERENTIAL CONDUCTANCE; FERMI WAVELENGTH; IMAGING ELECTRONWAVE FUNCTIONS; QUANTIZED ENERGY LEVELS;

NANOTUBES;

ARTICLE; ELECTRIC CONDUCTIVITY; ELECTRON TRANSPORT; MOLECULAR DYNAMICS; PRIORITY JOURNAL; SCANNING TUNNELING MICROSCOPY;

EID: 0345003851     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.283.5398.52     Document Type: Article

References (23)

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13. Exact identification of the lattice indices (n,m) [see (1)] of chiral nanotubes is quite difficult because both the nanotube diameter and the chiral angle between hexagon rows and the tube axis must be measured with high accuracy. The (n,m) indices are crucial for chiral tubes because a minor change in one of these determines whether the tube is a metal or a semi-conductor. For armchair tubes, however, the situation is easier. The nonchiral structure with hexagon rows running parallel to the tube axis can be easily observed from the atomically resolved images, and a precise determination of the diameter is not essential because armchair tubes of all diameters are metallic.
14. 4He bath cryostat. Successive STM spectroscopy line scans therefore show identical results. Over a longer period, however, the tip may change position slightly as a result of residual drift or minor changes in the tip.
15. L. C. Venema et al., Appl. Phys. Lett. 71, 2629 (1997). After this cutting event, the tip was cleaned by applying voltage pulses above the gold substrate, far away from the tube. Linear I-V spectroscopy curves on clean areas of the gold substrate demonstrated that the tip was free of debris.
16. The applied voltage is in principle divided into a part that drops over the tunnel gap and a part that drops between the nanotube and the substrate. The ratio α between these voltages is determined by the capacitance ratio. Because the capacitance between nanotube and substrate is much larger than that between the nanotube and the STM tip, the voltage will drop almost entirely over the tunnel gap, and accordingly α has a value close to 1.
17. W. T. Scott, The Physics of Electricity and Magnetism (Wiley, New York, ed. 2, 1966), pp. 163-165.
18. L. P. Kouwenhoven et al., in Mesoscopic Electron Transport, L. L. Sohn, G. Schön, L. P. Kouwenhoven, Eds. (Kluwer, Dordrecht, Netherlands, 1997), pp. 105-214.
19. Note that the exact voltages at which the peaks in dI/dV appear in Figs. 2 and 3A are different. This can be attributed to variations in the offset charge caused by trapping of charge in the environment of the tube, as is well known in Coulomb charging phenomena [see R. Wilkins and R. C. Jaclevic, Phys. Rev. Lett. 63, 801 (1989); J. G. A. Dubois, E. N. G. Verheijen, J. W. Gerritsen, H. Van Kempen, Phys. Rev. B 48, 11260 (1993)]. Variation of the offset charge may change the Coulomb gap and thus shift the exact voltage at which the discrete levels of the tube appear in the I-V measurements. In fact, switching of offset charges was observed in some of our line scans. This effect is irrelevant for the observations reported here, which are the periodic oscillations in the differential conductance of discrete energy levels.
20. Note that the exact voltages at which the peaks in dI/dV appear in Figs. 2 and 3A are different. This can be attributed to variations in the offset charge caused by trapping of charge in the environment of the tube, as is well known in Coulomb charging phenomena [see R. Wilkins and R. C. Jaclevic, Phys. Rev. Lett. 63, 801 (1989); J. G. A. Dubois, E. N. G. Verheijen, J. W. Gerritsen, H. Van Kempen, Phys. Rev. B 48, 11260 (1993)]. Variation of the offset charge may change the Coulomb gap and thus shift the exact voltage at which the discrete levels of the tube appear in the I-V measurements. In fact, switching of offset charges was observed in some of our line scans. This effect is irrelevant for the observations reported here, which are the periodic oscillations in the differential conductance of discrete energy levels.
21. The total wave function is in fact defined by the atomic lattice potential modulated with a standing wave profile resulting from the confinement in the length direction. Because the STM tip follows the atomic corrugation by scanning in constant-current mode at a high bias voltage, the lattice periodicity is largely compensated so that the standing waves can be resolved in the spectroscopy measurements for several discrete states at low bias.
22. A. Rubio, E. Artacho, P. Ordejon, P. D. Sanchez-Portal, D. J. Soler, in preparation.
23. We thank R. E. Smalley and co-workers for supplying the nanotube material and A. Rubio for sharing results before publication. Supported in part by the Dutch Foundation for Fundamental Research of Matter (FOM). L.P.K. is supported by the Royal Dutch Acadamy of Sciences and Art (KNAW).