Phasons and excitations in skyrmion lattice

Excitations of two-dimensional skyrmion lattice are theoretically studied based on a collective coordinate description. Starting from the representation of skyrmion lattice in terms of three helices, we identify the canonical coordinates describing low energy excitations as phasons. The phason excitation spectra turn out to have one gapless mode with a quadratic dispersion and one massive mode, in agreement with previous studies. We will show that there is another collective mode governing the topological nature and the stability of skyrmion lattice and that the fluctuation of this mode leads to a screening of the topological charge of the lattice. Experimental implications of the screening effect in microwave absorption, topological Hall effect and depinning threshold current in metals are discussed

Solitons in the Crossover between Band Insulator and Mott Insulator: Application to TTF-Chloranil under Pressure

Based on the Phase Hamiltonian, two types of solitons are found to exist in the crossover region between band insulator and Mott insulator in one-dimension. Both of these solitons have fractional charges but with different spins, zero and 1/2, respectively. The results are in accord with the experimental results by Kanoda et al. for TTF-Chloranil under pressure.Comment: Submitted to J. Phys. Soc. Japan, 8 pages, 4 figure

Backward Scattering and Coexistent State in Two-Dimensional Electron System

The results of the mean field studies on the effects of the backward scattering with large momentum transfer in a two-dimensional electron system are extended to the case with various types of the Fermi surface and coupling constants. It is found that the coexistent state of d-wave superconductivity, antiferromagnetism and $\pi$-triplet pair can be stabilized quite generally near half filling.Comment: 16 pages, LaTeX, 16 figures included, revised in April 199

Orbital Magnetism of Bloch Electrons I. General Formula

We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Green's functions. The obtained formula contains four contributions: (1) Landau-Peierls susceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time.Comment: 18 pages, 2 figure

Bipolar thermoelectric effects in semiconducting carbon nanotubes: Description in terms of one-dimensional Dirac electrons

The thermoelectric effects in semiconducting single-walled carbon nanotubes (SWCNTs) are investigated based on the linear response theory combined with the thermal Green's function method. It is shown that the electronic states near the lowest conduction band minimum and the highest valence band maximum can be effectively described in terms of one-dimensional (1D) Dirac electrons to which a theoretical scheme is developed to describe the thermoelectric responses making it possible to study the effects of inter-band impurity scattering and in-gap states. Using the proposed scheme, the bipolar thermoelectric effects (i.e., the sign inversion of the Seebeck coefficient) in semiconducting SWCNTs observed in recent experiments are explained. Moreover, the temperature dependence of the Seebeck coefficient of semiconducting SWCNTs at low temperature is clarified.Comment: 14 pages, 16 figure

Effects of the Backward Scattering in Two-Dimensional Electron System

Effects of the backward scattering with large momentum transfer are examined in two-dimensional electron system with a special emphasis on electrons around ($\pi$,0), (0,$\pi$). The phase diagram is shown in the plane of temperature $T$ and hole doping $\delta$ in the mean field approximation and it is found that d-wave superconductivity, antiferromagnetism and $\pi$-triplet pair can coexist near half filling.Comment: 7 pages, LaTeX, 5 figures, uses jpsj.st

Analytical Solutions for the Surface States of Bi1−x_{1-x}Sbx_x (0≤x≲0.10\le x \lesssim 0.1)

Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the semi-infinite system, there are three types of SS solutions: (I-a) linearly crossing SSs in the direct bulk band gap, (I-b) SSs with linear dispersions entering the bulk conduction or valence bands away from the band edge, and (II) SSs with nearly flat dispersions entering the bulk state at the band edge. For the finite-thickness system, a gap opens in the SS of solution I-a. Numerical solutions for the SS are also obtained based on the tight-binding model of Liu and Allen [Phys. Rev. B, 52, 1566 (1995)] for Bi$_{1-x}$Sb$_x$ ($0\le x \le 0.1$). A perfect correspondence between the analytic and numerical solutions is obtained around the $\bar{M}$ point including their thickness dependence. This is the first time that the character of the SS numerically obtained is identified with the help of analytical solutions. The size of the gap for I-a SS can be larger than that of bulk band gap even for a "thick" films ($\lesssim 200$ bilayers $\simeq 80$ nm) of pure bismuth. Consequently, in such a film of Bi$_{1-x}$Sb$_x$, there is no apparent change in the SSs through the band inversion at $x\simeq 0.04$, even though the nature of the SS is changed from solution I-a to I-b. Based on our theoretical results, the experimental results on the SS of Bi$_{1-x}$Sb$_x$ ($0\le x \lesssim 0.1$) are discussed.Comment: 11 pages, 12 figure

Possible High Thermoelectric Power in Semiconducting Carbon Nanotubes ~A Case Study of Doped One-Dimensional Semiconductors~

We have theoretically investigated the thermoelectric properties of impurity-doped one-dimensional semiconductors, focusing on nitrogen-substituted (N-substituted) carbon nanotubes (CNTs), using the Kubo formula combined with a self-consistent $t$-matrix approximation. N-substituted CNTs exhibit extremely high thermoelectric power factor ($PF$) values originating from a characteristic of one-dimensional materials where decrease in the carrier density increase both the electrical conductivity and the Seebeck coefficient in the low-N regime. The chemical potential dependence of the $PF$ values of semiconducting CNTs has also been studied as a field-effect transistor and it turns out that the $PF$ values show a noticeable maximum in the vicinity of the band edges. This result demonstrates that "band-edge engineering" will be crucial for solid development of high-performance thermoelectric materials.Comment: 11 pages, 11 figure

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Bismuth crystal is known for its remarkable properties resulting from particular electronic states, e. g., the Shubnikov-de Haas effect and the de Haas-van Alphen effect. Above all, the large diamagnetism of bismuth had been a long-standing puzzle soon after the establishment of quantum mechanics, which had been resolved eventually in 1970 based on the effective Hamiltonian derived by Wolff as due to the interband effects of a magnetic field in the presence of a large spin-orbit interaction. This Hamiltonian is essentially the same as the Dirac Hamiltonian, but with spatial anisotropy and an effective velocity much smaller than the light velocity. This paper reviews recent progress in the theoretical understanding of transport and optical properties, such as the weak-field Hall effect together with the spin Hall effect, and ac conductivity, of a system described by the Wolff Hamiltonian and its isotropic version with a special interest of exploring possible relationship with orbital magnetism. It is shown that there exist a fundamental relationship between spin Hall conductivity and orbital susceptibility in the insulating state on one hand, and the possibility of fully spin-polarized electric current in magneto-optics. Experimental tests of these interesting features have been proposed.Comment: 22 pages, 23 figures, submitted to J. Phys. Soc. Jp

Spin-Hall Effect and Diamagnetism of Anisotropic Dirac Electrons in Solids

Spin-Hall conductivity $\sigma_{{\rm s}xy}$ and orbital susceptibility $\chi$ are investigated for the anisotropic Wolff Hamiltonian, which is an effective Hamiltonian common to Dirac electrons in solids. It is found that, both for $\sigma_{{\rm s}xy}$ and $\chi$, the effect of anisotropy appears only in the prefactors, which is given as the Gaussian curvature of the energy dispersion, and their functional forms are equivalent to those of the isotropic Wolff Hamiltonian. As a result, it is revealed that the relationship between the spin Hall conductivity and the orbital susceptibility in the insulating state, $\sigma_{{\rm s}xy}=(3mc^2/\hbar e)\chi$, which was firstly derived for the isotropic Wolff Hamiltonian, is also valid for the anisotropic Wolff Hamiltonian. Based on this theoretical finding, the magnitude of spin-Hall conductivity is estimated for bismuth and its alloys with antimony by that of orbital susceptibility, which has good correspondence between theory and experiments. The magnitude of spin-Hall conductivity turns out to be as large as $e\sigma_{{\rm s}xy} \sim 10^4 {\Omega}^{-1}{\rm cm}^{-1}$, which is about 100 times larger than that of Pt.Comment: 11 pages, 5 figure