Theory of Kondo lattices and its application to high-temperature superconductivity and pseudo-gaps in cuprate oxides

A theory of Kondo lattices is developed for the t-J model on a square lattice. The spin susceptibility is described in a form consistent with a physical picture of Kondo lattices: Local spin fluctuations at different sites interact with each other by a bare intersite exchange interaction, which is mainly composed of two terms such as the superexchange interaction, which arises from the virtual exchange of spin-channel pair excitations of electrons across the Mott-Hubbard gap, and an exchange interaction arising from that of Gutzwiller's quasi-particles. The bare exchange interaction is enhanced by intersite spin fluctuations developed because of itself. The enhanced exchange interaction is responsible for the development of superconducting fluctuations as well as the Cooper pairing between Gutzwiller's quasi-particles. On the basis of the microscopic theory, we develop a phenomenological theory of low-temperature superconductivity and pseudo-gaps in the under-doped region as well as high-temperature superconductivity in the optimal-doped region. Anisotropic pseudo-gaps open mainly because of d\gamma-wave superconducting low-energy fluctuations: Quasi-particle spectra around (\pm\pi/a,0) and (0,\pm\pi/a), with a the lattice constant, or X points at the chemical potential are swept away by strong inelastic scatterings, and quasi-particles are well defined only around (\pm\pi/2a,\pm\pi/2a) on the Fermi surface or line. As temperatures decrease in the vicinity of superconducting critical temperatures, pseudo-gaps become smaller and the well-defined region is extending toward X points. The condensation of d\gamma-wave Cooper pairs eventually occurs at low enough temperatures when the pair breaking by inelastic scatterings becomes small enough.Comment: 15 pages, 14 figure

Frustrated electron liquids in the Hubbard model

The ground state of the Hubbard model is studied within the constrained Hilbert space where no order parameter exists. The self-energy of electrons is decomposed into the single-site and multisite self-energies. The calculation of the single-site self-energy is mapped to a problem of self-consistently determining and solving the Anderson model. When an electron reservoir is explicitly considered, it is proved that the single-site self-energy is that of a normal Fermi liquid even if the multisite self-energy is anomalous. Thus, the ground state is a normal Fermi liquid in the supreme single-site approximation (S^3A). In the strong-coupling regime, the Fermi liquid is stabilized by the Kondo effect in the S^3A and is further stabilized by the Fock-type term of the superexchange interaction or the resonating-valence-bond (RVB) mechanism beyond the S^3A. The stabilized Fermi liquid is frustrated as much as an RVB spin liquid in the Heisenberg model. It is a relevant unperturbed state that can be used to study a normal or anomalous Fermi liquid and an ordered state in the whole Hilbert space by Kondo lattice theory. Even if higher-order multisite terms than the Fock-type term are considered, the ground state cannot be a Mott insulator. It can be merely a gapless semiconductor even if the multisite self-energy is so anomalous that it is divergent at the chemical potential. A Mott insulator is only possible as a high temperature phase.Comment: 11 pages, no figur

Magnetic and charge structures in itinerant-electron magnets: Coexistence of multiple SDW and CDW

A theory of Kondo lattices is applied to studying possible magnetic and charge structures of itinerant-electron antiferromagnets. Even helical spin structures can be stabilized when the nesting of the Fermi surface is not sharp and the superexchange interaction, which arises from the virtual exchange of pair excitations across the Mott-Hubbard gap, is mainly responsible for magnetic instability. Sinusoidal spin structures or spin density waves (SDW) are only stabilized when the nesting of the Fermi surface is sharp enough and a novel exchange interaction arising from that of pair excitations of quasi-particles is mainly responsible for magnetic instability. In particular, multiple SDW are stabilized when their incommensurate ordering wave-numbers $\pm{\bf Q}$ are multiple; magnetizations of different $\pm{\bf Q}$ components are orthogonal to each other in double and triple SDW when magnetic anisotropy is weak enough. Unless $\pm 2{\bf Q}$ are commensurate, charge density waves (CDW) with $\pm 2{\bf Q}$ coexist with SDW with $\pm{\bf Q}$. Because the quenching of magnetic moments by the Kondo effect depends on local numbers of electrons, the phase of CDW or electron densities is such that magnetic moments are large where the quenching is weak. It is proposed that the so called stipe order in cuprate-oxide high-temperature superconductors must be the coexisting state of double incommensurate SDW and CDW.Comment: 10 pages, no figure

Thermal conductivity of the thermoelectric layered cobalt oxides measured by the Harman method

In-plane thermal conductivity of the thermoelectric layered cobalt oxides has been measured using the Harman method, in which thermal conductivity is obtained from temperature gradient induced by applied current. We have found that the charge reservoir block (the block other than the CoO$_2$ block) dominates the thermal conduction, where a nano-block integration concept is effective for material design. We have further found that the thermal conductivity shows a small but finite in-plane anisotropy between $a$ and $b$ axes, which can be ascribed to the misfit structure.Comment: 4 pages, 4 figures, J. Appl. Phys. (scheduled on July 1, 2004

Opening of a pseudogap in a quasi-two dimensional superconductor due to critical thermal fluctuations

We examine the role of the anisotropy of superconducting critical thermal fluctuations in the opening of a pseudogap in a quasi-two dimensional superconductor such as a cuprate-oxide high-temperature superconductor. When the anisotropy between planes and their perpendicular axis is large enough and its superconducting critical temperature T_c is high enough, the fluctuations are much developed in its critical region so that lifetime widths of quasiparticles are large and the energy dependence of the selfenergy deviates from that of Landau's normal Fermi liquids. A pseudogap opens in such a critical region because quasiparticle spectra around the chemical potential are swept away due to the large lifetime widths. The pseudogap never smoothly evolves into a superconducting gap; it starts to open at a temperature higher than T_c while the superconducting gap starts to open just at T_c. When T_c is rather low but the ratio of varepsilon_G(0)/k_BT_c, with varepsilon_G(0) the superconducting gap at T=0K and k_B the Boltzmann constant, is much larger than a value about 4 according to the mean-field theory, the pseudogap must be closing as temperature T approaches to the low T_c because thermal fluctuations become less developed as T decreases. Critical thermal fluctuations cannot cause the opening of a prominent pseudogap in an almost isotropic three dimensional superconductor, even if its T_c is high.Comment: 25 pages, 5 figures (14 subfigures

Rashba spin splitting in biased semiconductor quantum wells

Rashba spin splitting (RSS) in biased semiconductor quantum wells is investigated theoretically based on the eight-band envelope function model. We find that at large wave vectors, RSS is both nonmonotonic and anisotropic as a function of in-plane wave vector, in contrast to the widely used linear and isotropic model. We derive an analytical expression for RSS, which can correctly reproduce such nonmonotonic behavior at large wave vectors. We also investigate numerically the dependence of RSS on the various band parameters and find that RSS increases with decreasing band gap and subband index, increasing valence band offset, external electric field, and well width. Our analytical expression for RSS provides a satisfactory explanation to all these features.Comment: 5 pages, 4 figures, author names corrected, submitted to Phys. Rev.

Spin-Valley Kondo Effect in Multi-electron Silicon Quantum Dots

We study the spin-valley Kondo effect of a silicon quantum dot occupied by $\mathcal{N}$ electrons, with $\mathcal{N}$ up to four. We show that the Kondo resonance appears in the $\mathcal{N}=1,2,3$ Coulomb blockade regimes, but not in the $\mathcal{N}=4$ one, in contrast to the spin-1/2 Kondo effect, which only occurs at $\mathcal{N}=$ odd. Assuming large orbital level spacings, the energy states of the dot can be simply characterized by fourfold spin-valley degrees of freedom. The density of states (DOS) is obtained as a function of temperature and applied magnetic field using a finite-U equation-of-motion approach. The structure in the DOS can be detected in transport experiments. The Kondo resonance is split by the Zeeman splitting and valley splitting for double- and triple-electron Si dots, in a similar fashion to single-electron ones. The peak structure and splitting patterns are much richer for the spin-valley Kondo effect than for the pure spin Kondo effect.Comment: 8 pages, 4 figures, in PRB format. This paper is a sequel to the paper published in Phys. Rev. B 75, 195345 (2007

Theory of itinerant-electron ferromagnetism

A theory of Kondo lattices or a $1/d$ expansion theory, with $d$ spatial dimensionality, is applied to studying itinerant-electron ferromagnetism. Two relevant multi-band models are examined: a band-edge model where the chemical potential is at one of band-edges, the top or bottom of bands, and a flat-band model where one of bands is almost flat or dispersionless and the chemical potential is at the flat band. In both the models, a novel ferromagnetic exchange interaction arises from the virtual exchange of pair excitations of quasiparticles; it has two novel properties such as its strength is in proportion to the effective Fermi energy of quasiparticles and its temperature dependence is responsible for the Curie-Weiss law. When the Hund coupling $J$ is strong enough, the superexchange interaction, which arises from the virtual exchange of pair excitations of electrons across the Mott-Hubbard gap, is ferromagnetic. In particular, it is definitely ferromagnetic for any nonzero $J>0$ in the large limit of band multiplicity. Ferromagnetic instability occurs, when the sum of the two exchange interactions is ferromagnetic and it overcomes the quenching of magnetic moments by the Kondo effect or local quantum spin fluctuations and the suppression of magnetic instability by the mode-mode coupling among intersite spin fluctuations.Comment: 14 pages, 4 figure

Size Dependence In The Disordered Kondo Problem

We study here the role randomly-placed non-magnetic scatterers play on the Kondo effect. We show that spin relaxation effects (with time $\tau_s^o$)in the vertex corrections to the Kondo self-energy lead to an exact cancellation of the singular temperature dependence arising from the diffusion poles. For a thin film of thickness $L$ and a mean-free path $\ell$, disorder provides a correction to the Kondo resistivity of the form $\tau_s^o/(k_FL\ell^2)\ln T$ that explains both the disorder and sample-size depression of the Kondo effect observed by Blachly and Giordano (PRB {\bf 51}, 12537 (1995)).Comment: 11 pages, LaTeX, 2 Postscript figure

Kondo effect in two-dimensional disordered electron systems

We investigate the Kondo effect in two-dimensional disordered electron systems using a finite-temperature quantum Monte Carlo method. Depending on the position of a magnetic impurity, the local moment is screened or unscreened by the spin of the conduction electron. On the basis of the results, we show that the distribution of the Kondo temperature becomes wide and the weight at $T_K=0$ becomes large as randomness increases. The average susceptibility shows a weak power-law or logarithmic divergence at low temperature, indicating a non-Fermi-liquid behavior.Comment: 2 pages, 2 figures, to be published in supplement of J. Phys. Soc. Japan, Proceedings of Localisation 2002, (Tokyo, Japan, 2002