Lee, Rice and Anderson, in their monumental paper, have proved the existence of a collective mode describing the coupled motion of electron density and phonons in one-dimensional incommensurate charge density wave (CDW) in the Peierls state. This mod
e, which represents the coherent sliding motion of electrons and lattice distortions and affects low energy transport properties, is described by the phase of the complex order parameter of the Peierls condensate, leading to Frohlich superconductivity in pure systems. Once spatial disorder is present, however, phason is pinned and system is transformed into an insulating ground state: a dramatic change. Since phason can be considered as an ultimate of phonon drag effect, it is of interest to see its effects on thermoelectricity, which has been studied in the present paper based linear response theory of Kubo and Luttinger. The result indicates that a large absolute value of Seebeck coefficient proportional to the square root of resistivity is expected at low temperatures k_B T/Delta <<1 (Delta: Peierls gap) with opposite sign to the electronic contributions in the absence of Peierls gap.
The orbital susceptibility for graphene is calculated exactly up to the first order with respect to the overlap integrals between neighboring atomic orbitals. The general and rigorous theory of orbital susceptibility developed in the preceding paper
is applied to a model for graphene as a typical two-band model. It is found that there are contributions from interband, Fermi surface, and occupied states in addition to the Landau--Peierls orbital susceptibility. The relative phase between the atomic orbitals on the two sublattices related to the chirality of Dirac cones plays an important role. It is shown that there are some additional contributions to the orbital susceptibility that are not included in the previous calculations using the Peierls phase in the tight-binding model for graphene. The physical origin of this difference is clarified in terms of the corrections to the Peierls phase.
Orbital susceptibility for Bloch electrons is calculated for the first time up to the first order with respect to overlap integrals between the neighboring atomic orbitals, assuming single-band models. A general and rigorous theory of orbital suscept
ibility developed in the preceding paper is applied to single-band models in two-dimensional square and triangular lattices. In addition to the Landau-Peierls orbital susceptibility, it is found that there are comparable contributions from the Fermi surface and from the occupied states in the partially filled band called intraband atomic diamagnetism. This result means that the Peierls phase used in tight-binding models is insufficient as the effect of magnetic field.
We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Greens functions. The obtained formula contains four contributions: (1) Landau-Peierls s
usceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time.
Based on the Phase Hamiltonian, two types of solitons are found to exist in the crossover region between band insulator and Mott insulator in one-dimension. Both of these solitons have fractional charges but with different spins, zero and 1/2, respec
tively. The results are in accord with the experimental results by Kanoda et al. for TTF-Chloranil under pressure.
A new mechanism for superconductivity in the newly discovered Co-based oxide is proposed by using charge fluctuation. A single-band extended Hubbard model on the triangular lattice is studied within random phase approximation. $f$-wave triplet superc
onductivity is stabilized in the vicinity of charge-density-wave instability, which is in sharp contrast with the square-lattice case. The physical origin of the realization of the $f$-wave triplet state as well as the relevance to experiments are discussed.
The two-dimensional t-J model on a frustrating lattice is studied using mean-field variational theories with Gutzwiller approximation. We find that a superconducting state with broken time-reversal symmetry (d+id state) is realized in the parameter r
egion close to the triangular lattice. The frustration enlarges the region of superconductivity when $t<0$ for the hole-doped case, which is equivalent to $t>0$ for electron doping. We also discuss the SU(2) degeneracy at half-filling. The d+id state probably corresponds to the spin gap state at half-filling.
It is shown that the energy $(varepsilon)$ and momentum $(k)$ dependences of the electron self-energy function $ Sigma (k, varepsilon + i0) equiv Sigma^{R}(k, varepsilon) $ are, $ {rm Im} Sigma^{R} (k, varepsilon) = -avarepsilon^{2}|varepsilon - xi_{
k}|^{- gamma (k)} $ where $a$ is some constant, $xi_{k} = varepsilon(k)-mu, varepsilon(k)$ being the band energy, and the critical exponent $ gamma(k) $, which depends on the curvature of the Fermi surface at $ k $, satisfies, $ 0 leq gamma(k) leq 1 $. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of $ varepsilon, xi_{k} rightarrow 0 $ but for $ xi_{k} eq 0 $ has a split one-particle spectra as in the Tomonaga-Luttinger liquid.
