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

Valley Splitting Theory of SiGe/Si/SiGe Quantum Wells

We present an effective mass theory for SiGe/Si/SiGe quantum wells, with an emphasis on calculating the valley splitting. The theory introduces a valley coupling parameter, $v_v$, which encapsulates the physics of the quantum well interface. The new effective mass parameter is computed by means of a tight binding theory. The resulting formalism provides rather simple analytical results for several geometries of interest, including a finite square well, a quantum well in an electric field, and a modulation doped two-dimensional electron gas. Of particular importance is the problem of a quantum well in a magnetic field, grown on a miscut substrate. The latter may pose a numerical challenge for atomistic techniques like tight-binding, because of its two-dimensional nature. In the effective mass theory, however, the results are straightforward and analytical. We compare our effective mass results with those of the tight binding theory, obtaining excellent agreement.Comment: 13 pages, 7 figures. Version submitted to PR

Resonant X-Ray Scattering from the Quadrupolar Ordering Phase of CeB_6

We theoretically investigate the origin of the resonant x-ray scattering (RXS) signal near the Ce $L_{III}$ absorption edge in the quadrupolar ordering phase of CeB$_6$, considering the intersite interaction between the $\Gamma_8$ states in the initial state. The anisotropic charge distribution of the $4f$ states modulates the $5d$ states through the intra-atomic Coulomb interaction and thereby generates a large RXS superlattice intensity. The temperature and magnetic field dependence indicates that the induced dipolar and octupolar orders have little influence on the RXS spectra, in good agreement with the recent experiment.Comment: 4 pages, 4 figure

Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB6_6

A minimal model for multipole orders in CeB$_6$ shows that degeneracy of the quadrupole order parameters and strong spin-orbit coupling lead to peculiar temperature and magnetic-field dependences of the X-ray reflection intensity at superlattice Bragg points. Furthermore, the intensity depends sensitively on the surface direction. These theoretical results explain naturally recent X-ray experiments in phases II and III of CeB$_6$. It is predicted that under weak magnetic field perpendicular to the (111) surface, the reflection intensity should change non-monotonically as a function of temperature.Comment: 4 pages, 5 figure

Fluctuation Effects on the Quadrupolar Ordering in Magnetic Field

Effects of magnetic field on the quadrupolar ordering are investigated with inclusion of fluctuation of order parameters. For the simplest model with the nearest-neighbor quadrupolar interaction, the transition temperature and the specific heat are derived by the use of the recently proposed effective medium theory. It is shown that magnetic field H has two competing effects on the quadrupolar ordering; one is to encourage the ordering by suppressing the fluctuation among different components of order parameters, and the other is to block the ordering as in antiferromagnets. The former is found to be of order H^2 and the latter of order H^4. Hence the fluctuation is suppressed for weak fields, and the transition temperature increases with magnetic field. The fluctuation effect is so strong that the entropy released at the quadrupolar ordering is only about half of the full value ln 4 even without the Kondo effect.Comment: 10 pages including 3 Postscript figure

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

Resonant X-Ray Scattering from CeB6_{6}

We calculate the resonant x-ray scattering (RXS) spectra near the Ce $L_{\rm III}$ absorption edge in CeB$_6$, on the basis of a microscopic model that the $4f$ states of Ce are atomic while the $5d$ states form an energy band with a reasonable density of states. In the initial state, we employ an effective Hamiltonian of Shiina {\it et al}. in the antiferro-quadrupole (AFQ) ordering phase, while we construct the wave function consistent with the neutron scattering experiment in the magnetic ground state. In the intermediate state, we take full account of the intra-atomic Coulomb interaction. Without assuming any lattice distortion, we obtain sufficient RXS intensities on the AFQ superlattice spot. We obtain the spectral shape, the temperature and magnetic field dependences in good agreement with the experiment, thus demonstrating the mechanism that the intensity is brought about by the modulation of $5d$ states through the anisotropic term of the $5d$-$4f$ Coulomb interaction. In the magnetic ground state, a small pre-edge peak is found by the $E_2$ process. On the magnetic superlattice spot, we get a finite but considerably small intensity. The magnetic form factor is briefly discussed.Comment: Latex, 10 pages, 12 figures. To be published in J. Phys. Soc. Jpn., Vol.71, No. 7 (2002

Valley splitting of Si/SiGe heterostructures in tilted magnetic fields

We have investigated the valley splitting of two-dimensional electrons in high quality Si/Si$_{1-x}$Ge$_x$ heterostructures under tilted magnetic fields. For all the samples in our study, the valley splitting at filling factor $\nu=3$ ($\Delta_3$) is significantly different before and after the coincidence angle, at which energy levels cross at the Fermi level. On both sides of the coincidence, a linear density dependence of $\Delta_3$ on the electron density was observed, while the slope of these two configurations differs by more than a factor of two. We argue that screening of the Coulomb interaction from the low-lying filled levels, which also explains the observed spin-dependent resistivity, is responsible for the large difference of $\Delta_3$ before and after the coincidence.Comment: REVTEX 4 pages, 4 figure

Phase diagram of YBa2_2Cu3_3O7−y_{7-y} at T<<Tc_c based on Cu(2) transverse nuclear relaxation

Two maxima in transverse relaxation rate of Cu(2) nuclei in YBa$_2$Cu$_3$O$_{7-y}$ are observed, at T = 35 K and T = 47 K. Comparison of the $^{63}$Cu(2) and $^{65}$Cu(2) rates at T = 47 K indicates the magnetic character of relaxation. The enhancement at T = 47 K of fluctuating local magnetic fields perpendicular to the CuO$_2$ planes is connected with the critical fluctuations of orbital currents. Maximum at T = 35 K is connected with the appearance of inhomogeneous supeconducting phase. Together with data published to date, our experimental results allow to suggest a qualitatively new phase diagram of the superconducting phase.Comment: 4 LaTEX pages + 3 figures in *.ps forma

Strong-coupling Superconductivity in the Cuprate Oxide

Superconductivity in the cuprate oxide is studied by Kondo-lattice theory based on the t-J model with the el-ph interaction arising from the modulation of the superexchange interaction by phonons. The self-energy of electrons is decomposed into the single-site and multisite ones. It is proved by using the mapping of the single-site one in the t-J model to its corresponding one in the Anderson model that the single-site self-energy is that of a normal Fermi liquid, even if a superconducting (SC) order parameter appears or the multisite one is anomalous. The electron liquid characterized by the single-site self-energy is a normal Fermi liquid. The Fermi liquid is further stabilized by the RVB mechanism. The stabilized Fermi liquid is a relevant unperturbed state that can be used to study superconductivity and anomalous Fermi-liquid behaviors. The so-called spin-fluctuation-mediated exchange interaction, which includes the superexchange interaction as a part, is the attractive interaction that binds d-wave Cooper pairs. An analysis of the spin susceptibility implies that, because of the el-ph interaction, the imaginary part of the exchange interaction has a sharp peak or dip at \pm\omega^*, where \omega^*\simeq \omega_ph in the normal state and \epsilon_G/2 \lessim \omega^* \lessim \epsilon_G /2+ \omega_ph in the SC state, where \omega_ph is the energy of relevant phonons and \epsilon_G is the SC gap. If the imaginary part has a sharp peak or dip at \pm\omega^*, the dispersion relation of quasi-particles has kink structures near \pm\omega^* above and below the chemical potential, the density of states has dip-and-hump structures near \pm \omega^* outside the coherence peaks in the SC state, and the anisotropy of the gap deviates from the simple d-wave anisotropy.Comment: 19 pages, 12 figure