Effect of Band Structure on the Symmetry of Superconducting States

Effects of the band structure on the symmetry of superconducting (SC) states are studied. For a square lattice system with a nearest-neighbor attractive interaction, SC states with various symmetries are found by changing the band structure, or, the shape of the Fermi surface. The spin-triplet ($(p_x + ip_y)$-wave) and spin-singlet ($d$- or s-wave) SC states, and states with their coexistence ($d + ip_y$, $s + ip_y$) can be stabilized within the same type of interaction. The stability of interlayer-pairing states with line nodes is also examined, and its relation to the SC state of Sr$_2$RuO$_4$ is discussed.Comment: 4 pages, 4 figure

The Mixed State of Charge-Density-Wave in a Ring-Shaped Single Crystals

Charge-density-wave (CDW) phase transition in a ring-shaped crystals, recently synthesized by Tanda et al. [Nature, 417, 397 (2002)], is studied based on a mean-field-approximation of Ginzburg-Landau free energy. It is shown that in a ring-shaped crystals CDW undergoes frustration due to the curvature (bending) of the ring (geometrical frustration) and, thus, forms a mixed state analogous to what a type-II superconductor forms under a magnetic field. We discuss the nature of the phase transition in the ring-CDW in relation to recent experiments.Comment: 6 pages, 4 figure

Ginzburg-Landau Equations for Coexistent States of Superconductivity and Antiferromagnetism in t-J model

Ginzburg-Landau (GL) equations for the coexistent state of superconductivity and antiferromagnetism are derived microscopically from the t-J model with extended transfer integrals. GL equations and the GL free energy, which are obtained based on the slave-boson mean-field approximation, reflect the electronic structure of the microscopic model, especially the evolution of the Fermi surface due to the change of the doping rate. Thus they are suitable for studying the material dependence of the coexistent states in high-$T_C$ cuprate superconductors.Comment: 12 page

Microscopic derivation of Ginzburg-Landau equations for coexistent states of superconductivity and magnetism

Ginzburg-Landau (GL) equations for the coexistent states of superconductivity and magnetism are derived microscopically from the extended Hubbard model with on-site repulsive and nearest-neighbor attractive interactions. In the derived GL free energy a cubic term that couples the spin-singlet and spin-triplet components of superconducting order parameters (SCOP) with magnetization exists. This term gives rise to a spin-triplet SCOP near the interface between a spin-singlet superconductor and a ferromagnet, consistent with previous theoretical studies based on the Bogoliubov de Gennes method and the quasiclassical Green's function theory. In coexistent states of singlet superconductivity and antiferromagnetism it leads to the occurrence of pi-triplet SCOPs.Comment: 18 page

Dynamic spin Jahn-Teller effect in small magnetic clusters

We study the effect of spin-phonon coupling in small magnetic clusters, concentrating on a S=1/2 ring of 4 spins coupled antiferromagnetically. If the phonons are treated as classical variables, there is a critical value of the spin-phonon coupling above which a static distortion occurs. This is a good approximation if the zero point energy is small compared to the energy gain due to the distortion, which is true for large exchange interactions compared to the phonons energy ($J\gg\hbar\omega$). In the opposite limit, one can integrate out the phonon degrees of freedom and get an effective spin hamiltonian. Using exact diagonalizations to include the quantum nature of both spins and phonons, we obtain the spectrum in the whole range of parameters and explicit the crossover between the classical and quantum regimes. We then establish quantitatively the limits of validity of two widely used approaches (one in the quantum and one in the classical limits) and show that they are quite poor for small magnetic clusters. We also show that upon reducing $\hbar\omega/J$ the first excitation of a 4-site cluster becomes a singlet, a result that could be relevant for Cu$_2$Te$_2$O$_5$Br$_2$

Geometrically Frustrated Crystals: Elastic Theory and Dislocations

Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is pointed out and the phase diagram of the ring-crystal, which depends on radius and thickness, is discussed.Comment: 4 pages, 3 figure

Ground state of an S=1/2S=1/2 distorted diamond chain - model of Cu3Cl6(H2O)2⋅2H8C4SO2\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2

We study the ground state of the model Hamiltonian of the trimerized $S=1/2$ quantum Heisenberg chain $\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2$ in which the non-magnetic ground state is observed recently. This model consists of stacked trimers and has three kinds of coupling constants between spins; the intra-trimer coupling constant $J_1$ and the inter-trimer coupling constants $J_2$ and $J_3$. All of these constants are assumed to be antiferromagnetic. By use of the analytical method and physical considerations, we show that there are three phases on the $\tilde J_2 - \tilde J_3$ plane ($\tilde J_2 \equiv J_2/J_1$, $\tilde J_3 \equiv J_3/J_1$), the dimer phase, the spin fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists the excitation gap between the two-fold degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in $\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2$. We also obtain the phase diagram on the $\tilde J_2 - \tilde J_3$ plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.Comment: LaTeX2e, 15 pages, 21 eps figures, typos corrected, slightly detailed explanation adde

Dynamical Induction of s-wave Component in d-wave Superconductor Driven by Thermal Fluctuations

We investigated the mutual induction effects between the d-wave and the s-wave components of order parameters due to superconducting fluctuation above the critical temperatures and calculated its contributions to paraconductivity and excess Hall conductivity based on the two-component stochastic TDGL equation. It is shown that the coupling of two components increases paraconductivity while it decreases excess Hall conductivity compared to the cases when each component fluctuates independently. We also found the singular behavior in the paraconductivity and the excess Hall conductivity dependence on the coupling parameter which is consistent with the natural restriction among the coefficients of gradient terms.Comment: 10 pages, 4 figures included, submitted to J.Phys.Soc.Jp

On the Bloch Theorem Concerning Spontaneous Electric Current

We study the Bloch theorem which states absence of the spontaneous current in interacting electron systems. This theorem is shown to be still applicable to the system with the magnetic field induced by the electric current. Application to the spontaneous surface current is also examined in detail. Our result excludes the possibility of the recently proposed $d$-wave superconductivity having the surface flow and finite total current.Comment: 12 pages, LaTeX, 3 Postscript figure