Single-Particle Pseudogap in Two-Dimensional Electron Systems

We investigate pseudogap phenomena in the 2D electron system. Based on the mode-mode coupling theory of antiferromagnetic (AFM) and $d_{x^2-y^2}$-wave superconducting ($d$SC) fluctuations, single-particle dynamics is analyzed. For the parameter values of underdoped cuprates, pseudogap structure grows in the single-particle spectral weight $A(k,\omega)$ around the wave vector $(\pi,0)$ and $(0,\pi)$ below the pseudo-spin-gap temperature \TPG signaled by the reduction of dynamical spin correlations in qualitative agreement with the experimental data. The calculated results for the overdoped cuprates also reproduce the absence of the pseudogap in the experiments. We also discuss limitations of our weak-coupling approach.Comment: 6 pages with 4 figures, submitted to J. Phys. Soc. Jp

Operator Projection Theory for Electron Differentiation in Underdoped Cuprate Superconductors

Metals approaching the Mott insulator generate a new hierarchy in the electronic structure accompanied by a momentum dependent electron differentiation, beyond the Mott-Hubbard, Brinkman-Rice and Slater pictures of the Mott transition. To consider such nonlinear phenomenon, we develop an analytic nonperturbative theory based on operator projections combined with a self-consistent treatment of the low-energy excitations. This reproduces the formation of the Hubbard bands, Mott gap, spin fluctuations, mass divergence, diverging charge compressibility, and strongly renormalized flat and damped dispersion similar to angle-resolved photoemission data in high-T_c cuprates. Main structures in electronic spectra show a remarkable similarity to numerical results.Comment: 11 pages, presented at ``Spectroscopies of Novel Superconductors 2001'

Type-IV Superconductivity: Cooper Pairs with Broken Inversion and Time-Reversal Symmetries in Conventional Superconductors

Vortex phase in a singlet superconductor in the absence of impurities is shown to be absolutely unstable with respect to the appearance of a triplet component which breaks both inversion and time-reversal symmetries of Cooper pairs. Symmetry breaking paramagnetic effects are demonstrated to be of the order of unity if the orbital upper critical field, Hc2(0), is of the order of Clogston paramagnetic limiting field, Hp. We suggest a generic phase diagram of such type-IV superconductor, which is singlet one at H=0 and characterized by mixed singlet-triplet order parameter with broken time-reversal symmetry in vortex phase. A possibility to observe type-IV superconductivity in clean organic, high-Tc, MgB2, and other superconductors is discussed.Comment: 10 pages, 2 figures (Talk at PPHMF-V conference, August 5, 2005, Tallahasse

Electronic structure of underdoped cuprates

We consider a two-dimensional Fermi liquid coupled to low-energy commensurate spin fluctuations. At small coupling, the hole Fermi surface is large and centered around $Q =(\pi,\pi)$. We show that as the coupling increases, the shape of the quasiparticle Fermi surface and the spin-fermion vertex undergo a substantial evolution. At strong couplings, $g \gg \omega_0$, where $\omega_0$ is the upper cutoff in the spin susceptibility, the hole Fermi surface consists of small pockets centered at $(\pm \pi/2, \pm \pi/2)$. Simultaneously, the full spin-fermion vertex is much smaller than the bare one, and scales nearly linearly with $|q-Q|$, where $q$ is the momentum of the susceptibility. At intermediate couplings, there exist both, a large hole Fermi surface centered at $(\pi,\pi)$, and four hole pockets, but the quasiparticle residue is small everywhere except for the pieces of the pockets which face the origin of the Brillouin zone. The relevance of these results for recent photoemission experiments in $YBCO$ and $Bi2212$ systems is discussed.Comment: 19 pages, RevTeX, 15 figures embedded in the text, submitted to Phys. Rep., ps-file is also available at http://lifshitz.physics.wisc.edu/www/morr/morr_homepage.htm

Effect of Magnetic field on the Pseudogap Phenomena in High-Tc Cuprates

We theoretically investigate the effect of magnetic field on the pseudogap phenomena in High-Tc cuprates. The obtained results well explain the experimental results including their doping dependences. In our previous paper (J. Phys. Soc. Jpn. 68 (1999) 2999.), we have shown that the pseudogap phenomena observed in High-Tc cuprates are naturally understood as a precursor of the strong coupling superconductivity. On the other hand, there is an interpretation for the recent high field NMR measurements to be an evidence denying the pairing scenarios for the pseudogap. In this paper, we investigate the magnetic field dependence of NMR $1/T_{1}T$ on the basis of our formalism and show the interpretation to be inappropriate. The results indicate that the value of the characteristic magnetic field $B_{{\rm ch}}$ is remarkably large in case of the strong coupling superconductivity, especially near the pseudogap onset temperature $T^{*}$. Therefore, the magnetic field dependences can not be observed and $T^{*}$ does not vary when the strong pseudogap anomaly is observed. On the other hand, $B_{{\rm ch}}$ is small in the comparatively weak coupling case and $T^{*}$ varies when the weak pseudogap phenomena are observed. These results properly explain the high magnetic field NMR experiments continuously from under-doped to over-doped cuprates. Moreover, we discuss the transport phenomena in the pseudogap phase. The behaviors of the in-plane resistivity, the Hall coefficient and the c-axis resistivity in the pseudogap phase are naturally understood by considering the d-wave pseudogap

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

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