Topological Defects and Morphology of Graphitic Carbon Materials: An Approach Based on Differential Geometry

It has been known that pentagons and heptagons in hexagonal graphitic network give rise to a certain amount of curvature in the three dimensional structure of graphitic carbon materials. The amount of curvature is quantized due to the symmetry of graphite and, as a result, the structure formed by the network is also restricted. We clarify the effects of curvature quantization on the forms of graphitic carbon materials, employing the knowledge of differential geometry, especially the Gauss-Bonnet theorem.Comment: 8 pages, 9 figure

A Numerical Formulation to Calculate the Conductance of Mesoscopic Conductors Using Singular Value Decomposition

We present a new formulation to calculate the electric conductance of mesoscopic conductors by utilizing the singular value decomposition, which is a mathematical technique to manipulate matrices. Our formulation is useful in treating conductors with rather complicated atomic structures, for which naive recursion formula is cumbersome. It also has an advantage in scaling up the calculation by using parallel computation, which potentially allows us the real-scale calculations at the atomic level. On the other hands, the effects of electron-electron interactions are hard to be treated within this framework, since it depends crucially on the linearity of the system. In this paper, we study graphene nanoribbons with external leads for a simple example.Comment: 9 pages, 5 figures; Some changes have been made in DIscussion and Appendices. Several errors have been correcte

Spectral Flow and Quantum Theory of Dissipation in the Vortex Core of BCS superconductors

The dissipation process in two dimensional BCS superconductor due to the quasiparticles in the core of moving vortex is studied from a quantum mechanical point of view, especially paying attention to the spectral flow of the bound state energies in the vortex core. In order to clarify the nature of the spectral flow, we performed a numerical study of a finite system and, by extending the analysis to include the effect of impurities, we discuss the quantum mechanical origin of the dissipation in the vortex core.Comment: 4 pages, 5 figures. Some grammatical changes were made and new references were adde

Spectral Flow and the Dynamics of Dislocations in Charge Density Waves

The spectral flow in the cores of moving dislocations is found to play an important role in the dynamics and transport of charge density wave (CDW) by significantly modifying the hydrodynamic effective action of the condensate. The analogy of spectral flow in CDW with the baryogenesis in the early universe is pointed out.Comment: 5 pages, 2 figure

On the Ginzburg-Landau Free Energy of Charge Density Waves with a Three-Dimensional Order

The effective free energy of a charge density wave (CDW) with a three-dimensional order is derived from a microscopic model (Fr\"olich model) based on the path integral method. Electron hoping and Coulomb interaction between chains are taken into account perturbatively, leading to an elastic interchain coupling of the CDW ordered state.Comment: 8 pages, Revtex format, no figure

Superconductivity on a M\"obius strip: numerical studies on order parameter and quasiparticles

Superconducting states of an anisortopic s-wave superconductor on a M\"obius strip are studied numerically based on the Ginzburg-Landau theory and the Bogoliubov-de Gennes theory. In both, the equations are solved numerically on discitized lattice and the nonlinearity and the self-consistency are fully taken into account. First, we study the superconducting states on the M\"obius strip in the presence of the Aharonov-Bohm flux threading the ring by employing the Ginzburg-Landau theory, and confirm the phase diagram previously proposed by Hayashi and Ebisawa [J. Phys. Soc. Jpn. {\bf 70}, 3495 (2002)]. The metastable states as well as the equilibrium energy state are studied and the nonequiriblium processes when the magnetic field is varied at a fixed temperature are discussed. Next, we study the microscopic superconducting states on the M\"obius strip based on the Bogoliubov-de Gennes theory, especially focusing on the state with a real-space node in the superconducting gap, which is expected to appear when the flux threading the ring is half the superconducting flux quantum. The local density of states in this {\it nodal state} is calculated in detail and the existence of the zero-energy bound states is shown.Comment: 7 pages, 8 figure

Time-dependent Ginzburg-Landau equation and Boltzmann transport equation for charge-density-wave conductors

The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for one-dimensional charge-density-wave (CDW) conductors are derived from a microscopic model by applying the Keldysh Green's function approach under a quasiclassical approximation. The effects of external electric field and impurity pinning of the CDW are fully taken into account without relying on a phenomenological argument. These equations simultaneously describe spatiotemporal dynamics of both the CDW and quasiparticles, so they serve as a powerful tool to analyze various nonequilibrium phenomena, such as the current conversion between the CDW condensate and quasiparticles mediated by phase slips. It is shown that, in typical situations, the equations correctly describe the nonlinear behavior of electric conductivity in a simpler manner.Comment: 8 page

Theory of Antiferromagnetic Order in High-Tc Oxides: An Approach Based on Ginzburg-Landau Expansion

The mean-field phase diagram of antiferromagnetic order in t-J model has been examined, using the free energy obtained by Ginzburg-Landau (GL) expansion. We extended the usual GL theory in two ways: First, we have included higher order terms with respect to the spatial derivative (or wave number) to incorporate the incommensurate antiferromagnetic order. Second, we have also included higher order terms with respect to the order parameter amplitude, in order to treat the first order phase transition between paramagnetic and antiferromagnetic phase, which appears at some doping rates. We found the possibility of tricritical point and critical endpoint in the magnetic phase diagram of the high-Tc oxides associated with the commensurate and incommensurate antiferromagnetic order. The possible effects of thermal fluctuations and randomness (spin glass) are also discussed qualitatively based on the GL free energy.Comment: 7 pages, 3 figure

Planetary System Formation in Protoplanetary Disk around HL Tauri

We re-process the Atacama Large Millimeter/Submillimeter Array (ALMA) long-baseline science verification data taken toward HL Tauri. As shown by the previous work, we confirm that the high spatial resolution (~ 0."019, corresponding to ~ 2.7 AU) dust continuum images at \lambda = 0.87, 1.3, and 2.9 mm exhibit a multiple ring-like gap structure in the circumstellar disk. Assuming that the observed gaps are opened up by currently forming, unseen bodies, we estimate the mass of such hypothetical bodies based on following two approaches; the Hill radius analysis and a more elaborated approach developed from the angular momentum transfer analysis in gas disks. For the former, the measured gap widths are used for calibrating the mass of the bodies, while for the latter, the measured gap depths are utilized. We show that their masses are likely comparable to or less than the mass of Jovian planets, and then discuss an origin of the observed gap structure. By evaluating Toomre's gravitational instability (GI) condition and cooling effect, we find that the GI might be a possible mechanism to form the bodies in the outer region of the disk. As the disk might be gravitationally unstable only in the outer region of the disk, inward planetary migration would be needed to construct the current architecture of the hypothetical bodies. We estimate the gap-opening mass and show that type II migration might be able to play such a role. Combining GIs with inward migration, we conjecture that all of the observed gaps may be a consequence of bodies that might have originally formed at the outer part of the disk, and have subsequently migrated to the current locations. While ALMA's unprecedented high spatial resolution observations can revolutionize our picture of planet formation, more dedicated observational and theoretical studies are needed in order to fully understand the HL Tau images.Comment: 12 pages, 5 figure

Phase-Sensitive Flux-Flow resistivity in Unconventional Superconductors

We theoretically investigate the magnetic-field-angle dependence of the flux-flow resistivity $\rho_{\rm f}$ in unconventional superconductors. Two contributions to $\rho_{\rm f}$ are considered: one is the quasiparticle (QP) relaxation time $\tau(\bm{k}_{\rm F})$ and the other is $\omega_0(\bm{k}_{\rm F})$, which is a counterpart to the interlevel spacing of the QP bound states in the quasiclassical approach. Here, $\bm{k}_{\rm F}$ denotes the position on a Fermi surface. Numerical calculations are conducted for a line-node s-wave and a d-wave pair potential with the same anisotropy of their amplitudes, but with a sign change only for a d-wave one. We show that the field-angle dependence of $\rho_{\rm f}$ differs prominently between s-wave and d-wave pairs, reflecting the phase of the pair potentials. We also discuss the case where $\tau$ is constant and compare it with the more general case where $\tau$ depends on $\bm{k}_{\rm F}$.Comment: 4 pages, 3 figures; Proc. of LT2