Superconductivity in the Alkali-Doped Fullerides: Competition of Phonon-Mediated Attractions with Coulomb Repulsions in Polaron Pairing

Yasutami Takada and Takashi Hotta

Int. J. Mod. Phys. B 12, 3042-3051 (1998)

The mechanism of superconductivity in the alkali-metal-doped fullerides is investigated theoretically based on the Hubbard-Holstein model. Salient observed features such as the anomalous $^{13}$C isotope effect on the critical temperature $T_c$ for 50\% molecular substitution, the rapid decrease of $T_c$ with the deviation of electron number from half-filling, and the difference in the relation of $T_c$ with the lattice constant $a_0$ between fcc and sc structures are explained from a unified viewpoint of polaron pairings originating from the competition between phonon-mediated attractions and Coulomb repulsions.

Role of the Berry Phase in the Formation of Stripes in Manganese Oxides

Takashi Hotta, Yasutami Takada, and Hiroyasu Koizumi

Int. J. Mod. Phys. B 12,  3437-3455 (1998) [Invited Review Paper]

In order to gain an insight into the formation of paired Jahn-Teller (JT) stripes, we have investigated the electronic and vibronic structures in the manganese oxides by paying due attention to the effect of the Berry phase associated with the JT distortions on the band motion of an $e_g$ electron. In terms of a band-insulator picture, we have succeeded in obtaining the JT stripes and the stabilization mechanism of the $CE$-type antiferromagnetism in agreement with experiment.

Exchange and correlation effects in the 3D electron gas in strong magnetic fields and application to graphite

Yasutami Takada and Hiroki Goto

J. Physics: Condensed Matter 10, 11315-11325 (1998)

The self-consistent theory for obtaining the spin-dependent local-field correction $G_{\pm}({\bf q})$ due to Singwi, Toi, Land, and Sj\"olander is extended to investigate the exchange and correlation effects in the three-dimensional electron gas in strong magnetic fields. We find that $G_{\pm}({\bf q})$ barely changes with $H$ as long as it is weak enough for the ratio of $\ell$, the magnetic length, to $r_0$, the average interelectron spacing, to be larger than about 0.7. With this information, we calculate the self-energy in a self-consistent way to obtain the electronic structure of graphite in strong magnetic fields. The result obtained is in agreement with experiment.

High-Density Expansion of Correlation Energy and its Extrapolation to the Metallic Density Region

T. Endo, M. Horiuchi, Y. Takada, and H. Yasuhara

Phys. Rev. B 59, 7367-7372 (1999)

The $r_s$ expansion of the correlation energy per electron for an electron liquid is completed exactly up to order $r_s$ in units of Rydberg. A simple but accurate fitting formula for the correlation energy, which is a smooth extrapolation of the $r_s$ expansion to the region of metallic densities is presented.

Stripe Structures and the Berry-Phase Connection: Concept of Geometric Energy

Yasutami Takada, Takashi Hotta, and Hiroyasu Koizumi

Int. J. Mod. Phys. B 13, 3778-3782 (1999) (Plenary Talk at New3SC-2): cond-mat/9906128

Electronic states of an $e_g$ electron are calculated in the system composed of two MnO$_6$ octahedra with the inclusion of the Berry phase acquired by parallel transport. Based on this calculation, a comment is made on the controversy between ``Wigner-crystal'' and ``paired-stripe'' models for the the insulating charge-ordered manganese oxides.

Topological Scenario for Stripe Formation in Manganese Oxides

Takashi Hotta, Yasutami Takada, Hiroyasu Koizumi, and Elbio Dagotto

Phys. Rev. Lett. 84, 2477-2480 (2000)

The spin-charge-orbital complex structures of manganites are studied using topological concepts. The key quantity is the ``winding number'' $w$ associated with the Berry-phase connection of an $e_g$ electron parallel-transported through Jahn-Teller centers, along zigzag one-dimensional paths in an antiferromagnetic environment of $t_{2g}$ spins. From these concepts, it is shown that the ``bi-stripe'' and ``Wigner-crystal'' states observed experimentally have different $w$'s. Predictions for the spin structure of the charge-ordered states for heavily doped manganites are discussed.

Effective Mass of the $E\otimes e$ Jahn-Teller Polaron in Comparison with the Holstein Polaron

Yasutami Takada

Phys. Rev. B 61, 8631-8634 (2000)

Based on an exact expression for the self-energy of the Jahn-Teller polaron, we find that symmetry of pseudospin rotation makes the vertex correction much less effective than that for the Holstein polaron. This ineffectiveness brings about a smaller effective mass $m^*$ and a quantitatively differenent large-to-small polaron crossover, as examined by exact diagonalization in a two-site system. In the strong-coupling and antiadiabatic region, a rigorous analytic expression is found for $m^*$.

Effect of Electron Correlation on the Bragg Reflection

Yasutami Takada and Manabu Kido

J. Phys. Soc. Jpn. 70, 21-24 (2001)

We study the effect of correlation on the Bragg reflection in the 3D electron gas, the 1D Luttinger liquid, and the 1D Hubbard model in an alternating periodic potential at half-filling. In the last system, we suggest a Luttinger-liquid-type quasi-metallic state in the crossover region from the band insulator to the Mott insulator. We explain the appearance of this state in terms of the incompatibility of the Bragg reflection with the concept of Luttinger liquids.

Stripes in Manganites

T. Hotta, E. Dagotto, H. Koizumi, and Y. Takada

Int. J. Mod. Phys. B 14, 3494-3499 (2000)

Topological aspects of the stripe structure in manganese oxides are discussed in terms of the "winding number" w associated with the Berry-phase connection for eg orbitals acquired by the parallel transport through the periodic array of Jahn-Teller centers. For La1-xCaxMnO3, w is shown to characterize both the three-dimensional spin-charge-orbital structures in the antiferromagnetic phase for x > 1/2 and the charge-orbital stripes in the two-dimensional ferromagnetic phase for x < 1/2.

Self-Energy Revision Operator Theory for the Many-Body Problem: Application to Dynamic Properties of the Electron Gas

Yasutami Takada

Int. J. Mod. Phys. B 15, 2595-2610 (2001) (Plenary Talk at SCES-Y2K)

An approximation scheme is proposed for implementing the algorithm to obtain the exact self-energy in the many-body problem [Phys. Rev. B {\bf 52}, 12708 (1995)]. This scheme relates the self-energy revision operator ${\cal F}$, the key quantity in the algorithm, with $f_{xc}(q,\omega)$ the frequency-dependent exchange-correlation kernel appearing in the time-dependent density functional theory. We illustrate this scheme by applying it to the calculation of dynamic properties of the electron gas at metallic densities.

Concluding Remarks on CMR and Related Problems

Y. Takada and T. Hotta

Int. J. Mod. Phys. B 15, 4267-4270 (2001) (Summary Talk at SCES-Y2K)

We review the talks on the colossal mangetoresistance (CMR) and its related subjects addressed at the Conference, together with a very brief explanation of our recent work. We also suggest some problems left in the future.

Comment on "Charge-Orbital Stripe Structure in La1-xCaxMnO3 (x=1/2,2/3)"

T. Hotta, E. Dagotto, H. Koizumi, and Y. Takada

Phys. Rev. Lett. 86, 2478 (2001)

Comments on the paper by T. Mutou and H. Kontani [Phys. Rev. Lett. 83, 3685 (1999)].

Structural phase transition at high temperatures in solid molecular hydrogen and deuterium

T. Cui, Y. Takada, Q. Cui, Y. Ma, and G. Zou

Phys. Rev. B 64, 024108: 1-7 (2001)

We study the effect of temperature up to 1000K on the structure of dense molecular para-hydrogen (p-H$_{2}$) and {ortho-deuterium (o-D$_{2}$), using the path-integral Monte Carlo method. We find a structural phase transition from orientationally disordered hexagonal close packed (hcp) to an orthorhombic structure of Cmca symmetry before melting. The transition is basically induced by thermal fluctuations, but quantum fluctuations of protons (deuterons) are important in determining the transition temperature through effectively hardening the intermolecular interaction. We estimate the phase line between hcp and Cmca phases as well as the melting line of the Cmca solid.

Polaron in the Jahn-Teller system and its superconductivity

Y. Takada

Physica C 364-365, 71-73 (2001) (Plenary Talk at New3SC-3)

We approach superconductivity in a crystal composed of the $E \otimes e$ Jahn-Teller centers from the weak-coupling region. We find that the vertex correction is less important in this system than in the usual electron-phonon coupled systems due to the presence of rotational symmetry in the pseudospin space representing twofold degeneracy. This ineffectiveness of the vertex correction results in the expansion of the applicable range of the conventional Migdal-Eliashberg theory.

Inclusion of Vertex Corrections in the Self-Consistent Calculation of Quasiparticles in Metals

Y. Takada

Phys. Rev. Lett. 87, 226402: 1-4  (2001)

Based on the Bethe-Salpeter equation and the Ward identity derived from it, we provide a scheme for constructing the vertex function in the self-consistent iteration loop to determine the electron self-energy. The scheme is implemented in the homogeneous electron gas at the sodium density.

Geometric Phase Current in Solids:Derivation in a Path-Integral Approach

H. Koizumi and Y. Takada

Phys. Rev. B 65, 153104: 1-4  (2002)

We consider a path-integral representation for the propagator of a Bloch electron with band crossings. The geometric phase arising from the crossings is included through the modification of the matrix element for the unitary transformation from Bloch to Wannier bases. We adopt the semiclassical approximation to the path integral to obtain a fundamental expression for the electron velocity, based on which we derive an anomalous current, named geometric phase current, of Bloch electrons induced by the geometric phase connection in k-space.

Dynamical Structure Factor of the Homogeneous Electron Liquid: Its Accurate Shape and the Interpretation of Experiments on Aluminum

Y. Takada and H. Yasuhara

Phys. Rev. Lett. 89, 216402: 1-4  (2002)

Based on a highly self-consistent theory maintaining the exact functional relations between the self-energy and the vertex part, we evaluate the dynamical structure factor S(q,w) of the electron liquid. We find striking deviations from S(q,w) in the RPA for |q| larger than the Fermi wave number; besides a broad peak in the one-pair excitation region as seen in the RPA, a clear shoulder appears along a steepened slope at low w due to electron-hole multiple scattering and a flattened structure follows due to inseparable interference between one- and multi-pair excitations. Our result agrees with experiments on Al on the whole. The remaining discrepancy is ascribed to the band-structure-induced effect.

Possibility of a Metallic Phase in the CDW-SDW Crossover Region in the One-Dimensional Hubbard-Holstein Model at Half Filling

Y. Takada and A. Chatterjee

Phys. Rev. B 67, 081102 (R) : 1-4  (2003)

The Hubbard-Holstein model is studied at half-filling in one dimension using a variational method based on the variable-displacement Lang-Firsov canonical transformation and the exact solution to the Hubbard model due to Lieb and Wu. It is usually believed that the system undergoes a direct insulator-to-insulator transition from charge-density wave (CDW) to spin-density wave (SDW) with the increase of the on-site Coulomb repulsion $U$ for a given strength of the electron-phonon coupling. Here we show indications that, at least in the antiadiabatic region, an intervening metallic state may exist in the crossover region of the CDW-SDW transition.

Quantum Fluctuations in a Four-Body Coulomb System and Breakdown of the Adiabatic Approximation

Y. Takada and T. Cui

J. Phys. Soc. Jpn. 67, 081102 (2003)

Accuracy of the Born-Oppenheimer adiabatic approximation to the ground state of a hydrogenlike molecule (M+M+m-m-) is examined in comparison with the exact results obtained by diffusion Monte Carlo simulations, fully incorporating quantum fluctuations. For the mass ratio m/M<0.1, the relative error in the ground-state energy is found to be less than 1%. We discuss the change in nature of the binding mechanism of this system with the increase of m/M from the usual chemical bonding at m/M << 1 to the one in which nonadiabatic effects such as the retardation of electron response to proton motion play a crucial role.

The Hubbard-Holstein Model with Anharmonic Phonons in One Dimension

A. Chatterjee and Y. Takada

J. Phys. Soc. Jpn. 67, 081102 (2004)

Effects of cubic and quartic anharmonic phonons on the polaronic properties are investigated in the one-dimensional Hubbard-Holstein model at half filling, using the variable-displacement Lang-Firsov canonical transformation and the exact solution of Lieb and Wu. Although the quartic anharmonicity always reduces the effect of the Coulomb repulsion U, the cubic one mainly responsible for the thermal expansion of lattice brings about the effect of strong asymmetric nature in the sign of the electron-phonon coupling constant g; it enhances the effect of U for positive  g, while it suppresses for negative g. As a result, the overall features of the anharmonic system are basically similar to those in the harmonic one for positive g, but even in the range of the realistic magnitudes for those anharmonicities, they may become qualitatively so different for negative g as to provide a first-order phase transition.

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