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Electronic Band Structure of Graphene Based on the Rectangular 4-Atom Unit Cell

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Journal of Modern Physics 2017年第4期8卷 607-621页

作者： Akira Suzuki Masashi Tanabe shigeji fujita Department of Physics Faculty of Science Tokyo University of Science Tokyo Japan Department of Physics University at Buffalo State University of New York Buffalo NY USA

The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.

关键词： Graphene Rectangular 4-Atom Unit Cell Model Primitive Orthogonal Basis Vector Bloch Electron (Wave Packet) Dynamics k-Vector Dirac Points Linear Dispersion Relation

Theory of Conductivity in Semiconducting Single-Wall Carbon Nanotubes

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Journal of Modern Physics 2012年第10期3卷 1550-1555页

作者： shigeji fujita Salvador Godoy Akira Suzuki Departamento de Física Facultad de Ciencias Universidad Nacional Autónoma de México Mexico City Mexico Department of Physics Faculty of Science Tokyo University of Science Shinjuku-ku Japan Department of Physics University at Buffalo Buffalo USA

The conduction of a single-wall carbon nanotube depends on the pitch. If there are an integral number of carbon hexagons per pitch, then the system is periodic along the tube axis and allows “holes” (not “electrons”) to move inside the tube. This case accounts for a semiconducting behavior with the activation energy of the order of around 3 meV. There is a distribution of the activation energy since the pitch and the circumference can vary. Otherwise nanotubes show metallic behaviors (significantly higher conductivity). “Electrons” and “holes” can move in the graphene wall (two dimensions). The conduction in the wall is the same as in graphene if the finiteness of the circumference is disregarded. Cooper pairs formed by the phonon exchange attraction moving in the wall is shown to generate a temperature-independent conduction at low temperature (3 - 20 K).

关键词： Semiconducting SWNT Cartesian Unit Cell Model Cooper Pair Bloch Electron Dynamics

Theory of Zero-Resistance States Generated by Radiation in GaAs/AlGaAs

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Journal of Modern Physics 2012年第7期3卷 546-552页

作者： shigeji fujita Kei Ito Akira Suzuki Department of Physics Faculty of Science Tokyo University of Science Shinjuku-ku Tokyo Japan Department of Physics University at Bu_alo SUNY Bu_alo NY USA Research Division National Center for University Entrance Examinations Meguro-ku Tokyo Japan

Mani observed zero-registance states similar to those quantum-Hall-effect states in GaAs/AlGaAs but without the Hall resistance plateaus upon the application of radiations [R. G. Mani, Physica E 22, 1 (2004)]. An interpretation is presented. The applied radiation excites “holes”. The condensed composite (c)-bosons formed in the excited channel create a superconducting state with an energy gap. The supercondensate suppresses the non-condensed c-bosons at the higher energy, but it cannot suppress the c-fermions in the base channel, and the small normal current accompanied by the Hall field yeilds a B-linear Hall resistivity.

关键词： Superconducting (Zero-Resistance) States Composite-Boson (Fermion) B-Linear Hall Resistivity Phonon (Fluxon) Exchange

Theory of Low- and High-Field Transports in Metallic Single-Wall Nanotubes

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Journal of Modern Physics 2013年第6期4卷 886-897页

作者： shigeji fujita Hung-Cheuk Ho Akira Suzuki Department of Physics Faculty of Science Tokyo University of Science Tokyo Japan Department of Physics University at Buffalo Buffalo USA Sincere Learning Centre Hong Kong China

Individual metallic single-wall carbon nanotubes show unusual non-Ohmic transport behaviors at low and high bias fields. For low-resistance contact samples, the differential conductance increases with increasing bias, reaching a maximum at ~100 mV. As the bias increases further, drops dramatically [1]. The higher the bias, the system behaves in a more normal (Ohmic) manner. This low-bias anomaly is temperature-dependent (50 - 150 K). We propose a new interpretation. Supercurrents run in the graphene wall below ~150 K. The normal hole currents run on the outer surface of the wall, which are subject to the scattering by phonons and impurities. The currents along the tube length generate circulating magnetic fields and eventually destroy the supercurrent in the wall at high enough bias, and restore the Ohmic behavior. If the prevalent ballistic electron model is adopted, then the temperature-dependent scattering effects cannot be discussed. For the high bias (0.3 - 5 V), (a) the I-V curves are temperature-independent (4 - 150 K), and (b) the currents (magnitudes) saturate. The behavior (a) arises from the fact that the neutral supercurrent below the critical temperature is not accelerated by the electric field. The behavior (b) is caused by the limitation of the number of quantum-states for the “holes” running outside of the tube.

关键词： Metallic SWNT Orthogonal Unit Cell Model Supercurrent Cooper Pair (Pairon) Bloch Electron Dynamics

Theory of Seebeck Coefficient in Multi-Walled Carbon Nanotubes

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Journal of Modern Physics 2013年第5期4卷 628-637页

作者： shigeji fujita James McNabb III Akira Suzuki Department of Physics Faculty of Science Tokyo University of Science Tokyo Japan Department of Physics State University of New York Buffalo USA

Based on the idea that different temperatures generate different conduction electron densities and the resulting carrier diffusion generates the thermal electromotive force (emf), a new formula for the Seebeck coefficient (thermopower) S is obtained: S=(2/3)ln2(qn)-1εFkBD0, where kB is the Boltzmann constant, and q, n, εF, D0 are charge, carrier density, Fermi energy, density of states at εF, respectively. Ohmic and Seebeck currents are fundamentally different in nature, and hence, cause significantly different behaviors. For example, the Seebeck coefficient S in copper (Cu) is positive, while the Hall coefficient is negative. In general, the Einstein relation between the conductivity and the diffusion coefficient does not hold for a multicarrier metal. Multi-walled carbon nanotubes are superconductors. The Seebeck coefficient S is shown to be proportional to the temperature T above the superconducting temperature Tc based on the model of Cooper pairs as carriers. The S follows a temperature behavior, , where Tg ’= constant, at the lowest temperatures.

关键词： Thermoelectric Power (Seebeck Coefficient) Multi-Walled Carbon Nanotubes The Model of Cooper Pairs

Electron Dynamics in Solids

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Journal of Modern Physics 2015年第6期6卷 733-748页

作者： shigeji fujita James McNabb III Akira Suzuki Department of Physics University at Buffalo State University of New York Buffalo USA Department of Physics Faculty of Science Tokyo University of Science Tokyo Japan

Following Ashcroft and Mermin, the conduction electrons (“electrons” or “holes”) are assumed to move as wave packets. Dirac’s theorem states that the quantum wave packets representing massive particles always move, following the classical mechanical laws of motion. It is shown here that the conduction electron in an orthorhombic crystal moves classical mechanically if the primitive rectangular-box unit cell is chosen as the wave packet, the condition requiring that the particle density is constant within the cell. All crystal systems except the triclinic system have k-vectors and energy bands. Materials are conducting if the Fermi energy falls on the energy bands. Energy bands and gaps are calculated by using the Kronig-Penny model and its 3D extension. The metal-insulator transition in VO2 is a transition between conductors having three-dimensional and one-dimensional k-vectors.

关键词： Electron Dynamics Dirac’s Theorem Primitive Rectangular-Box Unit Cell Wave Packet k-Vector

On the Heisenberg and Schrodinger Pictures

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Journal of Modern Physics 2014年第5期5卷 171-176页

作者： shigeji fujita James MacNabb III Akira Suzuki Department of Physics University at BuffaloState University of New YorkBuffaloUSA Department of Physics Faculty of ScienceTokyo University of ScienceTokyoJapan

A quantum theory for a one-electron system can be developed in either Heisenberg picture or Schrodinger picture. For a many-electron system, a theory must be developed in the Heisenberg picture, and the indistinguishability and Pauli’s exclusion principle must be incorporated. The hydrogen atom energy levels are obtained by solving the Schrodinger energy eigenvalue equation, which is the most significant result obtained in the Schrodinger picture. Both boson and fermion field equations are nonlinear in the presence of a pair interaction.

关键词： Heisenberg and Schrodingier Pictures Many-Particle Systems Indistinguishability Second Quantization Pauli’s Exclusion Principle

On Nernst’s Theorem and Compressibilities

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Journal of Modern Physics 2017年第5期8卷 839-843页

作者： James R. McNabb III shigeji fujita Akira Suzuki Department of Physics University at Buffalo SUNY Buffalo USA Department of Physics Tokyo University of Science Tokyo Japan

The unattainability of the absolute zero of temperature is proved by using Carnot’s theorem. Hence this unattainability is distinct from the Planck-Fer-mi statement of the Third Law of Thermodynamics that the entropy vanishes at ?T=0. It is shown that the isothermal compressibility KT is in general larger than the adiabatic compressibility Ks and the difference KT?−?Ks?vanishes in the low temperature limit.

关键词： Nernst’s Theorem Carnot’s Theorem Adiabatic Compressibility Isothermal Compressibility: The Third Law of Thermodynamics

Lattice Stability and Reflection Symmetry

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Journal of Modern Physics 2015年第5期6卷 691-697页

作者： shigeji fujita James R. McNabb III Hung-Cheuk Ho Akira Suzuki Department of Physics University at Buffalo SUNY Buffalo USA Sincere Learning Centre Kowloon Hong Kong China Department of Physics Faculty of Science Tokyo University of Science Tokyo Japan

Reflection symmetry properties play important roles for the stability of crystal lattices in which electrons and phonons move. Based on the reflection symmetry properties, cubic, tetragonal, orthorhombic, rhombohedral (trigonal) and hexagonal crystal systems are shown to have three-dimensional (3D) k-spaces for the conduction electrons (“electrons”, “holes”). The basic stability condition for a general crystal is the availability of parallel material planes. The monoclinic crystal has a 1D k-space. The triclinic has no k-vectors for electrons, whence it is a true insulator. The monoclinic (triclinic) crystal has one (three) disjoint sets of 1D phonons, which stabilizes the lattice. Phonons’ motion is highly directional;no spherical phonon distributions are generated for monoclinic and triclinic crystal systems.

关键词： k-Vectors Conduction Electron Reflection Symmetry Crystal Structure Lattice Stability