Publications by topics

Electrical Conduction in Graphene
  1. Interface Landau levels in graphene monolayer-bilayer junction ,
    Mikito Koshino, Takeshi Nakanishi and Tsuneya Ando,
    Phys. Rev. B, Vol. 82 No. 20 (2010) 205436
    arXiv:1008.4679 || Abstract+PDF[APS]
    Electronic structure of graphene monolayer-bilayer junction in a magnetic field is studied within an effective-mass approximation. The energy spectrum is characterized by interface Landau levels, i.e., the locally flat bands appearing near the boundary region, resulting in a series of characteristic peaks in the local density of states. Their energies are independent of boundary types such as zigzag or armchair. In the atomic scale, the local density of states shows a Kekul{e} pattern due to the valley mixing in the armchair boundary, while does not in the zigzag boundary.

  2. Transmission through a boundary between monolayer and bilayer graphen ,
    Takeshi Nakanishi, Mikito Koshino and Tsuneya Ando,
    Phys. Rev. B, Vol. 82 No. 12 (2010) 125428.
    PDF(preprint) ||arXiv:1008.4450 || Abstract+PDF[APS]
    The electron transmission between monolayer and bilayer graphene is theoretically studied for zigzag and armchair boundaries within an effective-mass scheme. Due to the presence of an evanescent wave in the bilayer graphene, traveling modes are well connected to each other. The transmission through the boundary is strongly dependent on the incident angle and the dependence is opposite between the K and K' points, leading to valley polarization of transmitted wave.

  3. Role of evanescent wave in valley polarization through junction of mono- and bi-layer graphenes ,
    Takeshi Nakanishi, Mikito Koshino and Tsuneya Ando
    J. Phys.: Conf. Ser., Vol. 302 (2011) 012021.
    PDF(preprint) || Abstract+PDF[IOP]
    The origin of strong valley polarization of electron wave transmitted through boundary between mono- and bi-layer graphenes can be ascribed to an evanescent wave in the bilayer graphene. The valley polarization is further enhanced across a ribbon-like region formed by partially overlapping of two monolayer graphenes.

  4. Valley polarization in transmission through boundary between mono- and bi-layer graphene ,
    Takeshi Nakanishi and Tsuneya Ando,
    AIP Conference Proceedings, Vol. 1399 (2011) 835.
    Abstract+PDF[AIP]
    The electron transmission between monolayer and bilayer graphene is theoretically studied within an effective‐mass scheme. The transmission through the boundary is strongly dependent on the incident angle and the dependence is opposite between the K and K′ points, leading to valley polarization of transmitted wave.

  5. Even-odd oscillation and valley polarization of transmission between multilayer graphenes ,
    Takeshi Nakanishi and Tsuneya Ando,
    AIP Conference Proceedings, Vol. 1566 (2013) 113.
    Abstract+PDF[AIP]
    Electron transmission through a boundary between multi-layer graphenes with Bernal stacking consisting of different number of layers is studied. A valley polarization in transmission probability appears as in monolayer and bilayer systems, exhibits considerable oscillation depending of even or odd layer numbers, and its amplitude gradually decreases with the layer number. The total transmission shows oscillation with much smaller amplitude.

  6. Electronic states and analytic solutions of graphene nanoribbons ,
    Katsunori Wakabayashi, Ken-ichi Sasaki, Takeshi Nakanishi and Toshiaki Enoki,
    Sci. Tech. Adv. Mat., Vol. 11 No. 5 (2010) 054504
    Abstract+PDF[IOP]
    Graphene is a carbon sheet with a thickness of one atom, and the lowenergy electronic states of graphene are described by the massless Dirac fermion. The orientation of the edge in graphene determines the energy spectrum of the pi-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this paper, we introduce the nanoscale effect on the physical properties of graphene nanoribbons and clarify the role of the edge boundary. We also provide analytic solutions of electronic dispersion and corresponding wavefunction for graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete in accordance with the edge boundary condition analogous to the case of carbon nanotubes. Because in zigzag nanoribbons the transverse wavenumber depends on not only the ribbon width but also the longitudinal wavenumber, the simple analogy of carbon nanotubes cannot be applied to zigzag nanoribbons. The quantization rule of electronic conductance and the magnetic instability of edge states due to the electron-electron interaction are briefly discussed.

  7. Honeycomb superperiodic pattern and its fine structure near the armchair edge of graphene observed by low-temperature scanning tunneling microscopy,
    Ken-ichi Sakai, Kazuyuki Takai, Ken-ichi Fukui, Takeshi Nakanishi and Toshiaki Enoki,
    Phys. Rev. B, Vol. 81 No. 23 (2010) 235417.
    Abstract+PDF[APS]
    The local electronic structure near a graphene edge was investigated by scanning tunneling microscopy (STM) at low temperature. In addition to the presence of (\sqrt{3}\times\sqrt{3}) R30^\circ and honeycomb superperiodic pat- terns, a fine structure with threefold symmetry was discovered on the individual bright sites in the honeycomb pattern. Electron wave scattering occurring at an armchair edge was confirmed to be responsible for the honeycomb pattern. The fine structure in the honeycomb pattern can be explained by spatial distribution of the local density of states and the following overlap between the atomic orbital of carbon atom and that of STM-tip-end atom, resulting in the threefold-symmetric spatial variation in the tunneling current.

Electrical Conduction in Carbon Nanotubes

    Antenna Effects

  1. Optical response of finite-length carbon nanotubes,
    Takeshi Nakanishi and Tsuneya Ando,
    Journal of the Physical Society of Japan, Vol. 78, No. 11 (2009) 114708.
    PDF(preprint) || Abstract+PDF[JPSJ] || arXiv:0909.1908
    Optical response of finite-length metallic carbon nanotubes is calculated including effects of induced edge charges in a self-consistent manner. The results show that the main resonance corresponding to excitation of the fundamental plasmon mode with wave vector $\pi/l$ with $l$ being the tube length is quite robust and unaffected. This arises because the strong electric field associated with edge charges is screened and decays rapidly inside the nanotube. For higher-frequency resonances, the field starts to be mixed and tends to shift resonances to higher frequencies.

    STM

  2. Conductance between Two Scanning-Tunneling-Microscopy Probes in Carbon Nanotubes,
    Takeshi Nakanishi and Tsuneya Ando,
    Journal of the Physical Society of Japan, Vol. 77, No. 2 (2008) 024703.
    PDF ||PDF(preprint) || Abstract+PDF[JPSJ]
    The conductance image between two probes of scanning-tunneling-microscopy (STM) is calculated in an armchair carbon nanotube within a tight-binding model and a realistic model for STM probes. A Kekulé - type pattern usually appears due to interference of states at K and K' points except in special cases.

  3. Kekulé pattern on conductance images between two STM probes,
    Takeshi Nakanishi and Tsuneya Ando,
    physica status solidi (b), Vol. 245, No. 10 (2008) 2173-2176.
    PDF(preprint) || Abstract+PDF[Wiley]
    The conductance image between two probes of scanning-tunneling-microscopy (STM) is calculated in a zigzag carbon nanotube within a tight-binding model and a realistic model for STM probes. A Kekulé - type pattern usually appears due to interference of states at K and K' points.

  4. Conductance images between two STM probes in graphene,
    Takeshi Nakanishi and Tsuneya Ando,
    Physica E, Vol. 42, No. 4 (2010) 726-728.
    PDF(preprint) || Abstract+PDF[Elsevier]
    The conductance image between two probes of scanning-tunneling-microscopy (STM) is calculated in a graphene within a tight-binding model and a realistic model for STM probes. A Kekulé-type pattern appears due to interference of states at K and K' points.

    Peapod Nanotubes

  5. Optical Band Gap Modification of Single-Walled Carbon Nanotubes by Encapsulated Fullerenes,
    T. Okazaki, S. Okubo, T. Nakanishi, S.-K. Joung, T. Saito, M. Otani, S. Okada, S. Bandow and S. Iijima ,
    J. Am. Chem. Soc., Vol. 130 (2008) 4122-4128.
    PDF || Abstract+PDF[ACS]
    We report optical band gap modifications of single-walled carbon nanotubes upon C60 insertions by using photoluminescence and the corresponding excitation spectroscopy. The shifts in optical transition energies strongly depend on the tube diameter (dt) and the "2n + m" family type, which can be explained by the local strain and the hybridization between the nanotube states and the C60 molecular orbitals. The present results provide possible design rules for nanotube-based heterostructures having a specific type of electronic functionality.

  6. Diameter-Dependent Band Gap Modification of Single-Walled Carbon Nanotubes by Encapsulated Fullerenes,
    S. Okubo, T. Okazaki, N. Kishi, S.-K. Joung, T. Nakanishi, S. Okada and S. Iijima ,
    Journal of Physical Chemistry C, Vol. 113 (2009) 571-575.
    PDF||Abstract+PDF[ACS]
    Band gap photoluminescence (PL) of single-walled carbon nanotubes (SWCNTs) encapsulating C60 fullerenes (nanopeapods) is examined over a wide range of diameters (1.25−1.55 nm). The encapsulated fullerenes induce characteristic PL peak shifts that strongly depend on the tube diameter (dt) and the “2n + m” family type {type I [mod(2n + m, 3) = 1] and type II [mod(2n + m, 3) = 2]}. This behavior can be explained by the strain-induced band gap shifts due to the C60 insertion and the hybridization between the electronic states of SWCNTs and C60. The present results provide significant insights into band gap engineering of SWCNTs in future nanodevices.

  7. Host–guest interactions in azafullerene (C59N)-single-wall carbon nanotube (SWCNT) peapod hybrid structures,
    Yoko Iizumi, Toshiya Okazaki, Zheng Liu, Kazu Suenaga, Takeshi Nakanishi, Sumio Iijima, Georgios Rotas, and Nikos Tagmatarchis,
    Chem. Commun. Vol. 46 (2010) 1293-1295.
    Abstract+PDF[RSC]
    The effect of azafullerene encapsulation on the electronic states of single-wall carbon nanotubes (SWCNTs) is investigated; UV-vis-NIR absorption and photoluminescence spectroscopy shows that the interaction between SWCNTs and the encapsulated azafullerenes is originated from the weak intermolecular forces, which suggests a lack of strong doping effect such as electron transfer between them.

    AB effects

  8. Conductivity in Carbon Nanotubes with Aharonov-Bohm Flux,
    Takeshi Nakanishi and Tsuneya Ando,
    Journal of the Physical Society of Japan, (2005) Vol. 74, No. 11, pp. 3027-3034.
    PDF(preprint) || PDF || Abstract+PDF[JPSJ]
    The Boltzmann conductivity is calculated for carbon nanotubes in the presence of an Aharonov-Bohm magnetic flux. Effects of impurity scattering are considered at low temperatures and those of electron-phonon scattering are considered at room temperature. Effects of strains and curvature manifest themselves as a prominent conductivity peak as a function of the flux. The appearance of the peak corresponds to the absence of backscattering in metallic linear bands.

  9. Aharonov-Bohm effects on conductivity in carbon nanotubes: A tool for determination of a gap due to strain and curvature,
    Takeshi Nakanishi and Tsuneya Ando,
    physica status solidi (b) Vol. 243, No. 13 (2006) pp. 3370-3374.
    PDF(preprint) ||Abstract+PDF[WILEY] ||
    The Boltzmann conductivity is calculated for carbon nanotubes in the presence of an Aharonov-Bohm magnetic flux. Effects of strain or curvature manifest themselves as a prominent conductivity peak as a function of the flux. The appearance of the peak corresponds to the absence of backscattering in metallic linear bands and makes it possible to determine a gap due to curvature and strain.

    Application

  10. Logic circuits with carbon nanotube transistors,
    Adrian Bachtold, Peter Hadley, Takeshi Nakanishi and Cees Dekker,
    Science, (2001) Vol. 294, pp. 1317-1320; Science express (http://www.sciencexpress.org) 4 October 2001.
    PDF|| Abstruct+PDF [Science]
    We demonstrate logic circuits with field-effect transistors based on single carbon nanotubes. Our device layout features local gates that provide an excellent capacitive coupling between the gate and the nanotube, enabling strong electrostatic doping of the nanotube from p-doping to n-doping and the study of the non-conventional long-range screening of the charge along the one-dimensional nanotubes. The transistors show favorable device characteristics such as a high gain (>10), a large on-off ratio (>10$^5$), and room-temperature operation. Importantly, the local-gate layout allows for integration of multiple devices on a single chip. Indeed, we demonstrate one-, two-, and three-transistor circuits that exhibit a range of digital logic operations such as an inverter, a logic NOR, a static random-access memory cell, and an ac ring oscillator.

  11. Transport through the Interface between a Semiconducting Carbon Nanotube and a Metal Electrode,
    Takeshi Nakanishi, Adrian Bachtold, and Cees Dekker,
    Physical Review B, (2002) Vol. 66, p. 073307
    Abstruct+PDF [APS]||cond-mat/0206436
    We report a numerical study of the tunnel conductance through the Schottky barrier at the contact between a semiconducting carbon nanotube and a metal electrode. In a planar gate model the asymmetry between the p--doped and the n--doped region is shown to depend mainly on the difference between the electrode Fermi level and the band gap of carbon nanotubes. We quantitatively show how the gate/nanotube distance is important to get large on--off ratios. We explain the bend of the current versus gate voltage as the transition from a thermal--activation region to a tunneling region. A good agreement is obtained with experimental results for carbon nanotubes field--effect transistors.

  12. Logic circuits based on carbon nanotubes,
    Adrian Bachtold, Peter Hadley, Takeshi Nakanishi, Cees Dekker,
    Physica E Vol. 16, (2003) pp. 42-46.
    Abstruct+PDF [Elsevier]
    We demonstrate logic circuits with field-effect transistors based on single carbon nanotubes. A new technique is used for achieving local gates in nanotube field-effect transistors that provide excellent capacitive coupling between the gate and nanotube, enabling strong electrostatic doping of the nanotube from p-doping to n-doping. The transitors show favorable device characteristics such as a high gain, a large on-off ratio, and room-temperature operation. Importantly, it also allows for the integration of multiple devices on a single chip. Indeed, we demonstrate 1-, 2-, and 3-transistor circuits that exhibit a wide range of digital logic operations such as an inverter, a logic NOR, and an ac ring oscillator.

  13. Logic circuits with carbon nanotubes,
    Adrian Bachtold, Peter Hadley, Takeshi Nakanishi, Cees Dekker,
    AIP Conf. Proc. 633 (2002) 502.
    Abstruct+PDF [AIP]
    A new technique is used for achieving field-effect transistors based on a single semiconducting nanotube and with a gate that is local and that provides an excellent capacitive coupling with the nanotube. Transconductance measurements are reported that show the possible injection of either p- and n-type carriers. Importantly, we demonstrate circuits that exhibit digital logic operations such as an inverter and an ac ring oscillator.

    Crossed Carbon Nanotubes

  14. Conductance of Crossed Carbon Nanotubes,
    Takeshi Nakanishi and Tsuneya Ando,
    Journal of the Physical Society of Japan, (2001) Vol. 70, No. 6, pp. 1647-1658.
    Abstruct+PDF [JPSJ]||PDF|| PDF(preprint)
    The effective Hamiltonian for two crossed nanotubes is derived in a {\mb k}$\cdot${\mb p} scheme and the conductance between them is calculated in the Born approximation. The conductance is found to depend strongly on the crossing angle with large maxima at commensurate stacking of lattices of two nanotubes. In a magnetic field perpendicular to both nanotubes, these two maxima exhibit a field dependence completely different to each other.

  15. Electrical Transport through Crossed Carbon Nanotube Junctions,
    Takeshi Nakanishi and Tsuneya Ando,
    Fullerenes, Nanotubes, and Related Systems ed. by S. Saito, T. Ando, Y. Iwasa, K. Kikuchi, M. Kobayashi, and Y. Saito, AIP Conference Proceedings, (2001) Vol. 590, pp. 149-152.
    (Proceedings of International Symposium on Nanonetwork Materials: Fullerenes, Nanotubes, and Related Systems ISNM 2001)
    PDF(preprint)||Abstruct+PDF [AIP]
    The conductance between two crossed nanotubes is calculated in a tight-binding model and found to depend strongly on the crossing angle with large maxima at commensurate stacking of lattices of two nanotubes. The results are in good agreement with those calculated in the lowest Born approximation in an effective-mass scheme.

    Contact

  16. Contact between Carbon Nanotube and Metallic Electrode,
    Takeshi Nakanishi and Tsuneya Ando,
    Journal of the Physical Society of Japan, (2000) Vol. 69, No. 7, pp. 2175-2181.
    Abstruct+PDF [JPSJ]||PDF|| PDF(preprint)
    Effects of a contact between a carbon nanotube and metallic electrode are studied in a tight-binding model. A model of dirty contact is introduced and discussed for electrode weakly coupled to a carbon nanotube. Measurements of a perfect transmission in two-terminal measurement may be possible by the using of the contact with both weak coupling and large area.

  17. Perfect Transmission from Dirty Electrode to Carbon Nanotube,
    Takeshi Nakanishi and Tsuneya Ando,
    Proceedings of the 25th International Conference on the Physics of Semiconductors, World Scientific, Singapore, ed. by N. Miura and T. Ando, (2001) Vol. 2, pp. 1641-1642.
    PDF(preprint)
    A contact resistance between a carbon nanotube and metallic electrode is studied in a tight-binding model. A model of dirty contact is employed for electrode weakly coupled to the carbon nanotube. Both weak coupling and large contact area make perfect transmission possible in two-terminal measurement.

    Point Defects

  18. Conductance of Carbon Nanotubes with a Vacancy,
    Masatsura Igami, Takeshi Nakanishi, and Tsuneya Ando,
    Journal of the Physical Society of Japan, (1999) Vol. 68, No. 3, pp. 716-719.
    Abstruct+PDF [JPSJ]
    The conductance of carbon nanotubes with a vacancy is studied in a tight-binding model. We examine the Fermi energy $\epsilon$ dependence of the conductance and show it is quantized into zero, one, and two times of the conductance quantum $e^2/\pi\hbar$ depending on the type of the vacancy in the half filled case, i.e, $epsilon\!=\!0$. In the presence of a magnetic field, the conductance is scaled by the component of the magnetic field in the direction of the vacancy.

  19. Numerical Study of Transport in Carbon Nanotubes with Lattice Vacancy,
    Masatsura Igami, Takeshi Nakanishi, and Tsuneya Ando,
    Journal of the Physical Society of Japan, (1999) Vol. 68, No. 10, pp. 3146-3149.
    Abstruct+PDF [JPSJ]|| PDF(preprint)
    The conductance is calculated for approximately $1.6\!\times\!10^5$ armchair carbon nanotubes (CN's) with a different lattice vacancy in a tight-binding model using a multi-channel Landauer's formula. When the vacancy is much smaller than the circumference of CN, the conductance is quantized into zero, one, and two times the conductance quantum $e^2/\pi\hbar depending only on the site-number difference between removed A and B sublattice sites.

  20. Effective-Mass Theory of Carbon Nanotubes with Vacancy,
    Tsuneya Ando, Takeshi Nakanishi, and Masatsura Igami,
    Journal of the Physical Society of Japan, (1999) Vol. 68, No. 12, pp. 3994-4008.
    Abstruct+PDF [JPSJ]|| PDF(preprint)
    Effects of impurities with a strong and short-range potential are studied in carbon nanotubes within a {\mb k}$\cdot${\mb p} scheme. The calculated conductance approaches those obtained for nanotubes with a lattice vacancy when the strength of the potential is sufficiently large. The conductance at $\epsilon\!=\!0$ is analytically shown to be quantized into zero, one, and two times of the conductance quantum $e^2/\pi\hbar$ depending on the difference in the number of vacancies at A and B sublattices in nanotubes with a sufficiently large diameter.

  21. Effective-Mass Theory of Carbon Nanotubes with Vacancies in Magnetic Fields,
    Masatsura Igami, Takeshi Nakanishi, and Tsuneya Ando,
    Journal of the Physical Society of Japan, (2001) Vol. 70, No. 2, pp. 481-491.
    Abstruct+PDF [JPSJ]||PDF
    An effective-mass theory is developed on transport of non-doped carbon nanotubes with local and short-range impurities in the presence of a magnetic field. The conductance is shown to be scaled completely by the field component in the direction of impurities. In a weak-field regime, the conductance strongly depends on strength of potential and the difference in the number of impurities at A and B sublattices $\Delta N_{AB}$. In a strong-field limit, the conductance is reduced to $e^2/\pi\hbar$ if impurities exist only on A or B sublattices and vanishes in all other cases. These results are intuitively understood by localized charge distribution of the wave function in magnetic fields.

  22. Conductance Quantization in the Presence of Huge and Short-Range Potential in Carbon Nanotubes,
    Takeshi Nakanishi, Masatsura Igami, and Tsuneya Ando,
    Physica E, (2000) Vol. 6, Nos. 1-4, pp. 872-875.
    Abstruct+PDF[Elsevier]
    Conductance of carbon nanotubes (CNs) with a pair of impurities having a huge and short-range potential is studied within a tight-binding model. When a pair occupies different sublattices, the conductance is given by 2$e^2/\pi\hbar$ same as in ideal CNs for a small distance and approaches either $e^2/\pi\hbar$ or 0 with the increase of the distance depending on types of their sites. When a pair occupies same sublattice points, the conductance is either $e^2/\pi\hbar$ or 0 independent of the distance.

  23. Effect of Lattice Vacancy on Conductance of Carbon Nanotubes,
    Masatsura Igami, Takeshi Nakanishi, and Tsuneya Ando,
    Physica B, (2000) Vol. 284-288, pp. 1746-1747.
    Abstruct+PDF [Elsevier]
    Conductance of carbon nanotubes with a lattice vacancy in the presence or absence of a magnetic field is studied within a tight-binding model. In the absence of a magnetic field, it is quantized into zero, one, or two times of $e^2/\pi\hbar$ depending on the type of the vacancy if its size is much smaller than the circumference. This strong dependence on kinds of vacancies prevails even in a magnetic field perpendicular to the axis.

  24. Effects of Lattice Vacancy in Carbon Nanotubes - Conductance Quantization -,
    Masatsura Igami, Takeshi Nakanishi, and Tsuneya Ando,
    Mol. Cryst. Liq. Cryst., (2000) Vol. 340, pp. 719-724.
    PDF(preprint)||Abstruct+PDF
    Conductance of carbon nanotubes (CN's) with a lattice vacancy or strong and short-range impurity potential is studied within a tight-binding model. The conductance is quantized into zero, one, or two times the conductance quantum $e^2/\pi\hbar$ depending on the type of the vacancy if its size is much smaller than the circumference of CN.

    Absence of Back Scattering

  25. Impurity Scattering in Carbon Nanotubes -Absence of Back Scattering -,
    Tsuneya Ando and Takeshi Nakanishi,
    Journal of the Physical Society of Japan, (1998) Vol. 67, No. 5, pp. 1704-1713.
    Abstruct+PDF [JPSJ]|| PDF(preprint)
    The effective potential of an impurity in a k$\cdot$p scheme is derived in two-dimensional graphite sheet. When the potential range is smaller than the lattice constant, it has an off-diagonal matrix element between K and K' points comparable to the diagonal element. With the increase of the range, this off-diagonal element decreases rapidly and the diagonal element for envelopes at A and B sites becomes identical. The crossover between these two regimes occurs around the range smaller than the lattice constant. In the latter regime, back scattering between states with +k and -k vanishes identically for the bands crossing the Fermi level in the absence of a magnetic field, leading to an extremely large conductivity. The absence of the back scattering disappears in magnetic fields, giving rise to a huge positive magnetoresistance.

  26. Berrys's Phase and Absence of Back Scattering in Carbon Nanotubes,
    Tsuneya Ando, Takeshi Nakanishi and Riichiro Saito,
    Journal of the Physical Society of Japan, (1998) Vol. 67, No. 8, pp. 2857-2863.
    Abstruct+PDF [JPSJ]|| PDF(preprint)
    The absence of back scattering in carbon nanotubes is shown to be ascribed to Berry's phase which corresponds to a sign change of the wave function under a spin rotation of a neutrino-like particle in a two-dimensional graphite. Effects of trigonal warping of the bands appearing in a higher order k$\cdot$p approximation are shown to give rise to a small probability of back scattering.

  27. Numerical Study of Impurity Scattering in Carbon Nanotubes,
    Takeshi Nakanishi and Tsuneya Ando,
    Journal of the Physical Society of Japan, (1999) Vol. 68, No. 2, pp. 561-566.
    Abstruct+PDF [JPSJ]|| PDF(preprint)
    The transmission and reflection coefficients of a carbon nanotube with a scatterer are calculated in a tight-binding model. The result obtained in a {\mb k}$\cdot${\mb p} scheme is shown to be essentially valid, including the complete absence of back scattering for scatterers with range larger than the lattice constant, unless the strength of the potential becomes comparable to the band width. When the potential strength is comparable to the band width, a resonant enhancement of back scattering appears and the result becomes completely different from that in the {\mb k}$\cdot${\mb p} scheme.

  28. Conductance Quantization in Carbon Nanotubes: Neutrionos on Cylinder Surface,
    Tsuneya Ando, Takeshi Nakanishi, and Riichiro Saito,
    Microelectronics Engineering, (1999) Vol. 47, pp. 421-423.
    Abstruct+PDF [Elsevier]
    Effects of impurity scattering in carbon nanotubes (CN's) are studied and the complete absence of back scattering is demonstrated for scatterers with range larger than the lattice constant.

  29. Carobn Nanotubes as a Perfect Conductor,
    Takeshi Nakanishi and Tsuneya Ando,
    Proceedings of the 24st International Conference on the Physics of Semiconductors, World Scientific, Singapore, ed. by D. Gershoni, (1999) X. A. 2 (CD-ROM).
    PDF(preprint)
    Effects of impurity scattering in carbon nanotubes (CN's) are studied in a {\bf k}$\cdot${\bf p} scheme and in a tight-binding model. The result obtained in a {\bf k}$\cdot${\bf p} scheme is shown to be essentially valid, including the complete absence of back scattering for scatterers with range larger than the lattice constant, unless the strength of the potential becomes comparable to the band width.

    Topological Defects

  30. Conductance of Carbon Nanotube Junctions in Magnetic Fields,
    Takeshi Nakanishi and Tsuneya Ando,
    Journal of the Physical Society of Japan, (1997) Vol. 66, No.10, pp. 2973-2976.
    Abstruct+PDF [JPSJ]|| PDF
    The conductance of a junction connecting two carbon nanotubes of differing diameter is calculated in magnetic fields perpendicular to the tube axis. The relative importance of mixing between different valleys exhibits a characteristic change depending on the effective strength of the magnetic field in the two tubes. The conductance depends only on the component of the magnetic field in the direction of the pentagonal and heptagonal rings.

  31. Scattering by Topological Disorder in Connected Carbon Nanotubes in Magnetic Fields,
    Takeshi Nakanishi and Tsuneya Ando,
    Physica B, (1998) Vol. 249-251, pp. 136-139.
    Abstruct+PDF[Elsevier]
    he conductance of connected zig-zag carbon nanotubes with a pair of topological defects is calculated in magnetic fields perpendicular to the tube axis. The conductance exhibits essentially the same magnetic-field dependence as that for armchair nanotubes, demonstrating a universality in magnetic fields. Some deviations can be understood in terms of small corrections due to a warping of the band in a graphite sheet.

  32. Theory of Ballistic Transport in Carbon Nanotubes,
    Tsuneya Ando, Hajime Matsumura, and Takeshi Nakanishi,
    Physica B Vol. 323 (2002) pp. 44-50.
    Abstruct+PDF[Elsevier]
    A brief review is given of electronic and transport properties of carbon nanotubes mainly from a theoretical point of view. The topics include an effective-mass description of electronic states, the absence of backward scattering except for scatterers with a potential range smaller than the lattice constant, a conductance quantization in the presence of lattice vacancies, junction systems, and effects of Stone-Wales defects.

    Short Review (Japanese)

Thermoelectric power in a quantum dot
  1. Thermopower of a Quantum Dot in a Coherent Regime,
    Takeshi Nakanishi and Takeo Kato,
    Journal of the Physical Society of Japan, Vol. 76 No. 3 (2007) 034715.
    PDF(preprint) ||PDF||cond-mat/0611538 || Abstract+PDF[JPSJ]
    Thermoelectric power due to coherent electron transmission through a quantum dot is theoretically studied. In addition to the known features related to resonant peaks, we show that a novel significant structure appears between the peaks. This structure arises from the so-called transmission zero, which is characteristic of coherent transmission through several quantum levels. Because of sensitivity to the phase-breaking effect in quantum dots, this novel structure indicates the degree of coherency in the electron transmission.
  2. Thermoelectric power in coherent transport as a tool for transmission-phase measurement,
    Takeshi Nakanishi and Takeo Kato,
    American Institute of Physics Conference Proceedings 893, "Twenty-eighth International Conference on the Physics of Semiconductors" (CD-ROM) ,
    AIP, ed. by W. Jantsch and F. Schaffler, (2007) pp. 841-842.
    PDF(preprint) ||Abstract+PDF[AIP]
    Thermoelectric power of a quantum dot is studied in a coherent region. Pronounced peaks are shown in the thermoelectric power, corresponding to a transmission zero in the conductance. Phase information of wavefunction in the quantum dot can be extracted from peak-and-dip structures of the thermoelectric power without the use of a magnetic field.

Fano effects in an Aharonov-Bohm ring with a quantum dot
  1. Theory of Fano effects in an Aharonov-Bohm ring with a quantum dot,
    Takeshi Nakanishi, Kiyoyuki Terakura, and Tsuneya Ando,
    Physical Review B 69 (2004) 115307.
    PDF(preprint) ||Abstruct+PDF [APS]
    Using a realistic model of a quantum dot embedded in an Aharonov-Bohm ring with several current-carrying channels, we demonstrate phase persistence in the Fano and Aharonov-Bohm effects as has been observed in experiments. The phase persistence arises because most of states contributing to the Coulomb oscillation of the conductance are weakly coupled to ring states through a small number of states giving a major contribution to the conductance under off-resonant conditions.

  2. Fano Effects and Wave Functions in a Quantum Dot,
    Takeshi Nakanishi, Kiyoyuki Terakura, and Tsuneya Ando,
    IPAP Conference Series, Vol. 5, (2004) 51-56.
    PDF(preprint)||Title+PDF[IPAP]
    The analysis of wave functions shows that states in a quantum dot embedded in an Aharonov-Bohm ring are classified into two groups, a large number of weekly coupled states and a small number of strongly coupled states. Coexistence of these states leads to a phase persistence in the Fano and Aharonov-Bohm effects, which has been observed in experiments.

  3. Persistence of Fano and Aharonov-Bohm Phases in an Interferometer with a Quantum Dot,
    Takeshi Nakanishi, Kiyoyuki Terakura, and Tsuneya Ando,
    International Journal of Modern Physics B, Vol. 18, Nos. 27-29 (2004) 3493-3498.
    PDF(preprint) ||Abstruct+PDF [WorldScientific]
    Using a realistic model of an Aharonov-Bohm ring with a quantum dot in one arm and a control gate in the other, we demonstrate phase persistence in the Fano and Aharonov-Bohm effects as has been observed in experiments. The Fano effects in the conductance is examined by changing the states in the Aharonov-Bohm ring by the control gate.

Fermi-Edge Singularity in a Lateral Periodic Potential
  1. Fermi-Edge Singularities in Photoluminescence Spectra of n-type Modulation-Doped Quantum Wells with a Lateral Periodic Potential,
    Shintaro Nomura, Takeshi Nakanishi, and Yoshinobu Aoyagi,
    Physical Review B, (2001) Vol. 63, pp. 165330-165335.
    Abstruct+PDF [APS]||PDF
    We demonstrate that a many-body effect between electrons and a finite-mass hole can be modulated externally by lateral periodic potentials in a n-type modulation-doped GaAs-Ga$_{1-x}$Al$_x$As quantum-well structure. A peculiar asymmetric peak is observed in the photoluminescence spectra 2.5 meV below the Fermi energy when a weak lateral periodic potential is applied, whereas no significant feature is observed without any lateral potential. The asymmetric peak is shown to be due to the recombination of the electrons at the Fermi surface and a hole, by investigating the oscillations of the energy positions and the intensity of the emission spectrum as a function of the magnetic field.

  2. Controlling Fermi-Edge Singularities by a Periodic External Potential,
    Shintaro Nomura, Takeshi Nakanishi, and Yoshinobu Aoyagi,
    Proceedings of the 25th International Conference on the Physics of Semiconductors, World Scientific, Singapore, ed. by N. Miura and T. Ando, (2001) Vol. 1, pp. 459-460.

Numerical Study of Quantum Transport Using Equation-of-Motion Method
  1. Dephasing by time-dependent random potentials,
    Takeshi Nakanishi, Tomi Ohtsuki, and Tohru Kawarabayashi,
    Journal of the Physical Society of Japan, (1997) Vol. 66, No.4, pp. 949-952.
    Abstruct+PDF [JPSJ] (Errata PDF [JPSJ]), cond-mat/9702240
    Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. The correction to the conductivity due to inelastic scatterings by oscillating potentials is shown to be a universal function of the frequency $\omega$, which is consistent with the weak localization prediction $\frac{e^2}{3\pi^2\hbar} \log \omega$.

  2. Numerical Study of Inelastic Scatterings by Time-Dependent Random Potentials in Two-Dimensional Systems,
    Takeshi Nakanishi and Tomi Ohtsuki,
    Physica B, (1998) Vol. 249-251, pp. 801-804.
    Abstruct+PDF[Elsevier]|| cond-mat/9710107
    Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. In the absence of spin-orbit scattering, the conductivity shows universal weak localization correction. In the presence of it, however, the correction to the conductivity depends weakly on the strength of disorder, and becomes vanishingly small close to the metal-insulator transition point.

Quantum Transport in Antidot Lattices
  1. Quantum Interference Effects in Antidot Lattices in Magnetic Fields,
    Takeshi Nakanishi and Tsuneya Ando
    Physical Review B, (1996) Vol. 54, No. 11, pp. 8021-8027.
    Abstruct+PDF [APS]|| PDF
    A numerical study is performed on quantum interference effects in antidot lattices in a weak magnetic field with the use of a recursive Green's function technique. An irregular Aharonov-Bohm (AB)-type oscillation varying sensitively with antidot diameters and periods is dominant in ideal antidot lattices. The AB-type oscillation disappears and an Al'tshuler, Aranov, and Spivak (AAS) oscillation manifests itself in the presence of fluctuations in the size or position of antidots. The AAS oscillation is much stronger in hexagonal lattices than in square lattices, in good agreement with experiments.

  2. AAS Oscillations on Antidot Lattices,
    Takeshi Nakanishi and Tsuneya Ando,
    Physica B, (1996) Vol. 227, pp. 127-130.
    Abstruct+PDF[Elsevier]
    Quantum-interference effects on the conductance of antidot lattices are studied with the use of a recursive Green's function technique. It is shown that Aharonov-Bohm (AB) type oscillations varying sensitively with the antidot diameter and period are dominant in the ideal case. The AB oscillations disappear and an AAS oscillation manifests itself in the presence of fluctuations in the size or position of the antidots.

  3. Quantum Transport in Antidot Lattices,
    Tsuneya Ando, Seiji Uryu, Satoshi Ishizaka, and Takeshi Nakanishi,
    Chaos, Solitons & Fractals, (1997) Vol. 8, No. 7/8, pp. 1057-1083.
    Abstruct [Elsevier]

Variational Monte Carlo Calculation in Two-Dimensional Hubbard Model
  1. Variational Monte Carlo Indications of d-Wave Superconductivity in the Two-Dimensional Hubbard Model,
    Takeshi Nakanishi, Kunihiko Yamaji, and Takashi Yanagisawa,
    Journal of the Physical Society of Japan, (1997) Vol. 66, No.2, pp. 294-297.
    Abstruct+PDF [JPSJ]
    The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6$\times$6 and 10$\times$10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d-wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.

  2. Variational Monte Carlo study on the superconductivity in the two-dimensional Hubbard model,
    Kunihiko Yamaji, Takaashi Yanagisawa, Takeshi Nakanishi and Soh Koike,
    Physica C, (1998) Vol. 304, Nos.3-4, pp. 225-238.
    Abstruct+PDF[Elsevier]|| cond-mat/9806210
    The possibility of superconductivity (SC) in the ground state of the two-dimensional (2D) Hubbard model was investigated by means of the variational Monte Carlo method. The energy gain of the d-wave SC state, obtained as the difference of the minimum energy with a finite gap and that with zero gap, was examined with respect to dependences on U, electron density and next nearest neighbor transfer t' mainly on the 10$\times$10 lattice. It was found to be maximized around U=8 (the energy unit is nearest neighbor transfer t). It was shown to sharply increase for negative values of t' and have a broad peak for t'$\sim$-0.10. For these value of t' the energy gain was a smooth increasing function of almost independent of the shell structure in the region starting from $\sim$0.76 up to the upper bound of investigation 0.92. This clearly indicates that the result is already close to the value in the bulk limit. For t'=0, the energy gain depended on the electronic shell state. This suggests the 10$\times$10 lattice is not sufficiently large for this case, although it is highly plausible that the bulk limit value is finite. Competition between the SC and the commensurate SDW states was also investigated. When t'=0, the ground state is SDW in the range of $\geq$0.84. The SC region slightly extends up to $\sim$0.87 for t'$\sim$-0.10. Consequently the present results strongly support an assertion that the 2D Hubbard model with t'$\sim$-0.1 drives SC by itself in the region from $\sim$0.76 to $\sim$0.87. The above features are in a fair agreement with the phase diagram of the optimally and overly hole-doped cuprates. The energy gain in the SC state with suitable parameters is found to be in reasonable agreement with the condensation energy in the SC state of YBa$_2$Cu$_3$O$_7$. The corresponding t-J model proves to give an order-of-magnitude larger energy gain, which questions its validity.

  3. Strong indications of d-wave superconductivity in the two-dimensional Hubbard model obtained by the variational Monte Carlo calculations,
    Kunihiko Yamaji, Takeshi Nakanishi, and Takashi Yanagisawa,
    Physica C, (1997) Vol. 282-287, pp. 1767-1768.
    Abstruct+PDF[Elsevier]
    The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6$\times$6 and 10$\times$ 10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d-wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.

Stark Ladder in Superlattices
  1. Two-Dimensional Tight-Binding Electrons in Electric and Magnetic Fields,
    Takeshi Nakanishi, Tomi Ohtsuki, and Motohiko Saitoh,
    Journal of the Physical Society of Japan, (1995) Vol. 64, No.6, pp. 2092-2099.
    Abstruct+PDF [JPSJ]
    Electronic states of a two-dimensional tight-binding lattice with finite size in the presence of both uniform electric and magnetic fields are studied. Numerical solutions for eigenenergies are presented. The magnetic subbands at zero electric field known as the Hofstadter butterfly are modified by the electric field and the eigenenergies for high electric fields are represented by the Stark ladder states associated with each of the magnetic subbands. When the electric potential drop across the system becomes comparable to the bandwidth of zero field, the density of states becomes the pyramid shape with steps, the steps being induced by the finiteness of the lattice. The influence on the density of states by the change of the direction of the electric field is also discussed.

  2. The Ballistic Transport in Crossed Electric and Magnetic Fields,
    Takeshi Nakanishi, Tomi Ohtsuki, and Motohiko Saitoh,
    Proceedings of the 11th International Conference on the High Magnetic Fields in Semiconductor Physics, World Scientific, Singapore, ed. by D. Heiman, (1995) pp. 516-519.

  3. Stark Ladders in a Two-Dimensional Tight-Binding Lattice,
    Takeshi Nakanishi, Tomi Ohtsuki, and Motohiko Saitoh,
    Journal of the Physical Society of Japan, (1993) Vol. 62, No. 8, pp. 2773-2782.
    Abstruct+PDF [JPSJ]
    Electronic states of a two-dimensional tight-binding model in a uniform electric field are studied. Numerical solutions for eigenenergies and eigenfunctions are presented as functions of the angle between the electric field and the symmetry axis of the lattice. When the direction of the electric field is [M, N], where M and N are mutually prime each other and MN$\neq$0, the eigenenergies are shown to be quantized with an interval equal to the potential drop between the nearest neighbor net lines. Though the level separation varies discontinuously with the change of the direction, the density of states is shown to be independent of the direction of the electric field, except for the direction [1 0] where the motions parallel and perpendicular to the electric field directions are separable. Unexpected gaps open near the band edges for appropriate electric fields, the magnitudes and the positions of which are smooth functions of the angle for a fixed electric field. The effects of the system edges are also discussed.

  4. Electronic States of a Two-Dimensional Tight-Binding Model in Electric and Magnetic Fields,
    Takeshi Nakanishi, Tomi Ohtsuki, and Motohiko Saitoh,
    Physica B, (1993) Vol. 184, pp. 310-313.
    Abstruct+PDF[Elsevier]

  5. Stark Ladders in a Two Dimensional Tight-Binding Model,
    Takeshi Nakanishi, Tomi Ohtsuki, and Motohiko Saitoh,
    Proceedings of the 21st International Conference on the Physics of Semiconductors, World Scientific, Singapore, ed. by P. Jiang and H. -Z. Zheng, (1993) Vol. 1, pp. 741-744.


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