Kaori Tanaka

Superconductive sodalite-like clathrate calcium hydride at high pressures

Hydrogen-rich compounds hold promise as high-temperature superconductors under high pressures. Recent theoretical hydride structures on achieving high-pressure superconductivity are composed mainly of H2 fragments. Through a systematic investigation of Ca hydrides with different hydrogen contents using particle-swam optimization structural search, we show that in the stoichiometry CaH6 a body-centered cubic structure with hydrogen that forms unusual “sodalite” cages containing enclathrated Ca stabilizes above pressure 150 GPa. The stability of this structure is derived from the acceptance by two H2 of electrons donated by Ca forming an “H4” unit as the building block in the construction of the three-dimensional sodalite cage. This unique structure has a partial occupation of the degenerated orbitals at the zone center. The resultant dynamic Jahn–Teller effect helps to enhance electron–phonon coupling and leads to superconductivity of CaH6. A superconducting critical temperature (Tc) of 220–235 K at 150 GPa obtained from the solution of the Eliashberg equations is the highest among all hydrides studied thus far.

Superconductivity in high-pressure SiH4

A combination of static and dynamical first-principles electronic calculations of silane, SiH4, at high pressure has revealed a novel monoclinic structure with C2/c symmetry. This high-pressure phase is metallic and composed of layers of SiH4 bridged by H bonds. Perturbative linear response calculations at 90 and 125 GPa predict large electron-phonon couplings yielding an electron-phonon coupling parameter λ close to 0.9. The application of McMillan equation gives a superconducting critical temperature (Tc) between 45 and 55 K.

Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lame equation as classified in 1940 by Ince. In Hamiltonians with C2v symmetry, they occur alternatingly as Lame functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lame equation. We also show that the two pairs of orbits created at period-doubling bifurcations of island-chain type are given by two different linear combinations of algebraic Lame functions with period 8K.

Transcritical bifurcations in nonintegrable Hamiltonian systems.

We report on transcritical bifurcations of periodic orbits in nonintegrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties using a recent mathematical description of transcritical bifurcations in families of symplectic maps. We then present numerical examples of transcritical bifurcations in a class of generalized Hénon-Heiles Hamiltonians and illustrate their stabilities and unfoldings under various perturbations of the Hamiltonians. We demonstrate that for Hamiltonians containing straight-line librating orbits, the transcritical bifurcation of these orbits is the typical case which occurs also in the absence of any discrete symmetries, while their isochronous pitchfork bifurcation is an exception. We determine the normal forms of both types of bifurcations and derive the uniform approximation required to include transcritically bifurcating orbits in the semiclassical trace formula for the density of states of the quantum Hamiltonian. We compute the coarse-grained density of states in a specific example both semiclassically and quantum mechanically and find excellent agreement of the results.

Theory of vortices in hybridized ballistic/diffusive-band superconductors

We study the electronic structure in the vicinity of a vortex in a two-band superconductor in which the quasiparticle motion is ballistic in one band and diffusive in the other. This study is based on a model appropriate for such a case, that we have introduced recently Tanaka et al., Phys. Rev. B 73, 220501R 2006. We argue that in the two-band superconductor MgB2, such a case is realized. Motivated by the experimental findings on MgB2, we assume that superconductivity in the diffusive band is “weak,” i.e., mostly induced. We examine intriguing features of the order parameter, the current density, and the vortex core spectrum in the “strong” ballistic band under the influence of hybridization with the “weak” diffusive band. Although the order parameter in the diffusive band is induced, the characteristic length scales in the two bands differ due to Coulomb interactions. The current density in the vortex core is dominated by the contribution from the ballistic band, while outside the core the contribution from the diffusive band can be substantial, or even dominating. The current density in the diffusive band has strong temperature dependence, exhibiting the Kramer-Pesch effect when hybridization is strong. A particularly interesting feature of our model is the possibility of additional bound states near the gap edge in the ballistic band, that are prominent in the vortex center spectra. This contrasts with the single band case, where there is no gap-edge bound state in the vortex center. We find the above-mentioned unique features for parameter values relevant for MgB2.

Phonon-mediated superconductivity in quasi-1D Sc3CoC4

The mechanism for the superconductivity observed in quasi-1D Sc3CoC4 has been investigated with density functional theory. No evidence supporting a charge density wave distortion in the superconducting state was found. Instead, the conventional phonon-mediated theory was shown to be valid. Solutions to Eliashberg equations for partitioned vibrational modes permit the characterization of important electron-phonon processes. The superconducting state is the result of interactions between the electronic structure with the lattice vibrations and the dicarbo-C2 librations.

Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator

The spectrum of a particle in a rotating two-dimensional harmonic oscillator is studied as a function of the cranking frequency. The occurrence of energy gaps is linked to classical periodic orbits. Special attention is paid to the Farey fan pattern generated beyond the Landau limit.