Two-Band-Type Superconducting Instability in MgB2

Using the tight-binding method for the $\pi$-bands in MgB$_2$, the Hubbard on-site Coulomb interaction on two inequivalent boron $p_z$-orbitals is transformed into expressions in terms of $\pi$-band operators. For scattering processes relevant to the problemin which a wave vector {\bf q} is parallel to $\hat{z}$, it is found to take a relatively simple form consisting of intra-band Coulomb scattering, interband pair scattering etc. with large constant coupling constants. This allows to get a simple expression for the amplitude of interband pair scattering between two $\pi$-bands, which diverges if the interband polarization function in it becomes large enough.The latter was approximately evaluated and found to be largely enhanced in the band structure in MgB$_2$. These results lead to a divergent interband pair scattering, meaning two-band-type superconducting instability with enhanced $T_c$. Adding a subsidiary BCS attractive interaction in each band into consideration, a semi-quantitative gap equation is given, and $T_c$ and isotope exponent $\alpha$ are derived. The present instability is asserted to be the origin of high $T_c$ in MgB$_2$.Comment: 4 pages, to be published in J. Phys. Soc. Jpn. vol. 70, No.

Composite-Fermion Theory for Pseudogap, Fermi Arc, Hole Pocket, and Non-Fermi-Liquid of Underdoped Cuprate Superconductors

We propose that an extension of the exciton concept to doped Mott insulators offers a fruitful insight into challenging issues of the copper oxide superconductors. In our extension, new fermionic excitations called cofermions emerge in conjunction to generalized excitons. The cofermions hybridize with conventional quasiparticles. Then a hybridization gap opens, and is identified as the pseudogap observed in the underdoped cuprates. The resultant Fermi-surface reconstruction naturally explains a number of unusual properties of the underdoped cuprates, such as the Fermi arc and/or pocket formation.Comment: 9 pages, 8 figure

Quantum Monte Carlo diagonalization for many-fermion systems

In this study we present an optimization method based on the quantum Monte Carlo diagonalization for many-fermion systems. Using the Hubbard-Stratonovich transformation, employed to decompose the interactions in terms of auxiliary fields, we expand the true ground-state wave function. The ground-state wave function is written as a linear combination of the basis wave functions. The Hamiltonian is diagonalized to obtain the lowest energy state, using the variational principle within the selected subspace of the basis functions. This method is free from the difficulty known as the negative sign problem. We can optimize a wave function using two procedures. The first procedure is to increase the number of basis functions. The second improves each basis function through the operators, $e^{-\Delta\tau H}$, using the Hubbard-Stratonovich decomposition. We present an algorithm for the Quantum Monte Carlo diagonalization method using a genetic algorithm and the renormalization method. We compute the ground-state energy and correlation functions of small clusters to compare with available data

Sign reversals of the Quantum Hall Effect in quasi-1D conductors

The sign reversals of the Quantum Hall Effect observed in quasi-one-dimensional conductors of the Bechgaard salts family are explained within the framework of the quantized nesting model. The sequence of reversals is driven by slight modifications of the geometry of the Fermi surface. It is explained why only even phases can have signign reversals and why negative phases are less stable than positive ones.Comment: 4 LaTex pages, 3 Postscript figure

Nuclear fission: The "onset of dissipation" from a microscopic point of view

Semi-analytical expressions are suggested for the temperature dependence of those combinations of transport coefficients which govern the fission process. This is based on experience with numerical calculations within the linear response approach and the locally harmonic approximation. A reduced version of the latter is seen to comply with Kramers' simplified picture of fission. It is argued that for variable inertia his formula has to be generalized, as already required by the need that for overdamped motion the inertia must not appear at all. This situation may already occur above T=2 MeV, where the rate is determined by the Smoluchowski equation. Consequently, comparison with experimental results do not give information on the effective damping rate, as often claimed, but on a special combination of local stiffnesses and the friction coefficient calculated at the barrier.Comment: 31 pages, LaTex, 9 postscript figures; final, more concise version, accepted for publication in PRC, with new arguments about the T-dependence of the inertia; e-mail: [email protected]

Ground state of the three-band Hubbard model

The ground state of the two-dimensional three-band Hubbard model in oxide superconductors is investigated by using the variational Monte Carlo method. The Gutzwiller-projected BCS and spin- density wave (SDW) functions are employed in the search for a possible ground state with respect to dependences on electron density. Antiferromagnetic correlations are considerably enhanced near half-filling. It is shown that the d-wave state may exist away from half-filling for both the hole and electron doping cases. The overall structure of the phase diagram obtained by the calculations qualitatively agrees with experimental indications. The superconducting condensation energy is in reasonable agreement with the experimental value obtained from specific heat and critical magnetic field measurements for optimally doped samples. The inhomogeneous SDW state is also examined near 1/8-hole doping.Comment: 10 pages, 17 figure

Green's-function theory of the Heisenberg ferromagnet in a magnetic field

We present a second-order Green's-function theory of the one- and two-dimensional S=1/2 ferromagnet in a magnetic field based on a decoupling of three-spin operator products, where vertex parameters are introduced and determined by exact relations. The transverse and longitudinal spin correlation functions and thermodynamic properties (magnetization, isothermal magnetic susceptibility, specific heat) are calculated self-consistently at arbitrary temperatures and fields. In addition, exact diagonalizations on finite lattices and, in the one-dimensional case, exact calculations by the Bethe-ansatz method for the quantum transfer matrix are performed. A good agreement of the Green's-function theory with the exact data, with recent quantum Monte Carlo results, and with the spin polarization of a $\nu=1$ quantum Hall ferromagnet is obtained. The field dependences of the position and height of the maximum in the temperature dependence of the susceptibility are found to fit well to power laws, which are critically analyzed in relation to the recently discussed behavior in Landau's theory. As revealed by the spin correlation functions and the specific heat at low fields, our theory provides an improved description of magnetic short-range order as compared with the random phase approximation. In one dimension and at very low fields, two maxima in the temperature dependence of the specific heat are found. The Bethe-ansatz data for the field dependences of the position and height of the low-temperature maximum are described by power laws. At higher fields in one and two dimensions, the temperature of the specific heat maximum linearly increases with the field.Comment: 9 pages, 9 figure

Quantum Monte Carlo study of the pairing correlation in the Hubbard ladder

An extensive Quantum Monte Carlo calculation is performed for the two-leg Hubbard ladder model to clarify whether the singlet pairing correlation decays slowly, which is predicted from the weak-coupling theory but controversial from numerical studies. Our result suggests that the discreteness of energy levels in finite systems affects the correlation enormously, where the enhanced pairing correlation is indeed detected if we make the energy levels of the bonding and anti-bonding bands lie close to each other at the Fermi level to mimic the thermodynamic limit.Comment: 10 pages, RevTeX, 5 figures in PostScript file

Spin-Density-Wave Phase Transitions in Quasi-One-Dimensional Dimerized Quarter-Filled Organic Conductors

We have studied spin density wave (SDW) phase transitions in dimerized quarter-filled Hubbard chains weakly coupled via interchain one-particle hopping, $t_{b0}$. It is shown that there exists a critical value of $t_{b0}$, $t_{b}^\ast$, between the incoherent metal regime ($t_{b0}<t_{b}^\ast$) and the Fermi liquid regime ($t_{b0}>t_{b}^\ast$) in the metallic phase above the SDW transition temperature. By using the 2-loop perturbative renormalization-group approach together with the random-phase-approximation, we propose a SDW phase diagram covering both of the regimes. The SDW phase transition from the incoherent metal phase for $t_{b0}<t_{b}^\ast$ is caused by growth of the intrachain electron-electron umklapp scattering toward low temperatures, which is regarded as preformation of the Mott gap. We discuss relevance of the present result to the SDW phase transitions in the quasi-one-dimensional dimerized quarter-filled organic conductors, (TMTTF)$_2$X and (TMTSF)$_2$X.Comment: 19 pages, 13 eps figures, uses jpsj.sty, corrected typo in the text and figures, no changes to the paper, to appear in J. Phys. Soc. Jpn. 68, No.8 (1999