Ginzburg-Landau Equations for Coexistent States of Superconductivity and Antiferromagnetism in t-J model

Ginzburg-Landau (GL) equations for the coexistent state of superconductivity and antiferromagnetism are derived microscopically from the t-J model with extended transfer integrals. GL equations and the GL free energy, which are obtained based on the slave-boson mean-field approximation, reflect the electronic structure of the microscopic model, especially the evolution of the Fermi surface due to the change of the doping rate. Thus they are suitable for studying the material dependence of the coexistent states in high-$T_C$ cuprate superconductors.Comment: 12 page

Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model

Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the non-interacting) Hamiltonian. We describe such a renormalized perturbation expansion for interacting Fermi systems, which treats Fermi surface shifts and superconductivity with an arbitrary gap function via additive counterterms. The expansion is formulated explicitly for the Hubbard model to second order in the interaction. Numerical soutions of the self-consistency condition determining the Fermi surface and the gap function are calculated for the two-dimensional case. For the repulsive Hubbard model close to half-filling we find a superconducting state with d-wave symmetry, as expected. For Fermi levels close to the van Hove singularity a Pomeranchuk instability leads to Fermi surfaces with broken square lattice symmetry, whose topology can be closed or open. For the attractive Hubbard model the second order calculation yeilds s-wave superconductivity with a weakly momentum dependent gap, whose size is reduced compared to the mean-field result.Comment: 18 pages incl. 6 figure

Charge Ordering in Organic ET Compounds

The charge ordering phenomena in quasi two-dimensional 1/4-filled organic compounds (ET)_2X (ET=BEDT-TTF) are investigated theoretically for the $\theta$ and $\alpha$-type structures, based on the Hartree approximation for the extended Hubbard models with both on-site and intersite Coulomb interactions. It is found that charge ordered states of stripe-type are stabilized for the relevant values of Coulomb energies, while the spatial pattern of the stripes sensitively depends on the anisotropy of the models. By comparing the results of calculations with the experimental facts, where the effects of quantum fluctuation is incorporated by mapping the stripe-type charge ordered states to the S=1/2 Heisenberg Hamiltonians, the actual charge patterns in the insulating phases of $\theta$-(ET)_2MM'(SCN)_4 and $\alpha$-(ET)_2I_3 are deduced. Furthermore, to obtain a unified view among the $\theta$, $\alpha$ and $\kappa$-(ET)_2X families, the stability of the charge ordered state in competition with the dimeric antiferromagnetic state viewed as the Mott insulating state, which is typically realized in $\kappa$-type compounds, and with the paramagnetic metallic state, is also pursued by extracting essential parameters.Comment: 35 pages, 27 figures, submitted to J. Phys. Soc. Jp

High-Tc Superconductivity and Antiferromagnetism in Multilayered Copper Oxides - A New Paradigm of Superconducting Mechanism -

High-temperature superconductivity (HTSC) in copper oxides emerges on a layered CuO2 plane when an antiferromagnetic Mott insulator is doped with mobile hole carriers. We review extensive studies of multilayered copper oxides by site-selective nuclear magnetic resonance (NMR), which have uncovered the intrinsic phase diagram of antiferromagnetism (AFM) and HTSC for a disorder-free CuO2 plane with hole carriers. We present our experimental findings such as the existence of the AFM metallic state in doped Mott insulators, the uniformly mixed phase of AFM and HTSC, and the emergence of d-wave SC with a maximum Tc just outside a critical carrier density, at which the AFM moment on a CuO2 plane disappears. These results can be accounted for by the Mott physics based on the t-J model. The superexchange interaction J_in among spins plays a vital role as a glue for Cooper pairs or mobile spin-singlet pairs, in contrast to the phonon-mediated attractive interaction among electrons established in the Bardeen-Cooper-Schrieffer (BCS) theory. We remark that the attractive interaction for raising the $T_c$ of HTSC up to temperatures as high as 160 K is the large J_in (~0.12 eV), which binds electrons of opposite spins to be on neighboring sites, and that there are no bosonic glues. It is the Coulomb repulsive interaction U(> 6 eV) among Cu-3d electrons that plays a central role in the physics behind high-Tc phenomena. A new paradigm of the SC mechanism opens to strongly correlated electron matter.Comment: 20 pages, 25 figures, Special topics "Recent Developments in Superconductivity" in J. Phys. Soc. Jpn., Published December 26, 201

Fermi-liquid instabilities at magnetic quantum phase transitions

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.Comment: 62 pages, 29 figs, review article for Rev. Mod. Phys; (v2) discussion extended, refs added; (v3) shortened; final version as publishe

Gapped collective charge excitations and interlayer hopping in cuprate superconductors

We use resonant inelastic x-ray scattering (RIXS) to probe the propagation of plasmons in the electron-doped cuprate superconductor Sr$_{0.9}$La$_{0.1}$CuO$_2$ (SLCO). We detect a plasmon gap of $\sim$~120 meV at the two-dimensional Brillouin zone center, indicating that low-energy plasmons in SLCO are not strictly acoustic. The plasmon dispersion, including the gap, is accurately captured by layered $t$-$J$-$V$ model calculations. A similar analysis performed on recent RIXS data from other cuprates suggests that the plasmon gap is generic and its size is related to the magnitude of the interlayer hopping $t_z$. Our work signifies the three-dimensionality of the charge dynamics in layered cuprates and provides a new method to determine $t_z$.Comment: 17 pages, 10 figures, includes Supplemental Material. Accepted for publication in Physical Review Letter

High-T_c Superconductivity with T_c = 52 K under Antiferromagnetic Order in Five-layered Cuprate Ba_2Ca_4Cu_5O_10(F,O)_2 with T_N = 175 K: 19F- and Cu-NMR Studies

We report on the observation of high-T_c superconductivity (SC) emerging with the background of an antiferromagnetic (AFM) order in the five-layered cuprate Ba_2Ca_4Cu_5O_10(F,O)_2 through 19F-NMR and zero-field Cu-NMR studies. The measurements of spectrum and nuclear spin-lattice relaxation rates 19(1/T_1) of 19F-NMR give convincing evidence for the AFM order taking place below T_N = 175 K and for the onset of SC below T_c = 52 K, hence both coexisting. The zero-field Cu-NMR study has revealed that AFM moments at Cu sites are 0.14 mu_B at outer CuO_2 layers and 0.20 mu_B at inner ones. We remark that an intimate coupling exists between the AFM state and the SC order parameter below T_c = 52 K; the spin alignment in the AFM state is presumably changed in the SC-AFM mixed state.Comment: 4 pages, 4 figures, to be published in Journal of the Physical Society of Japan, Vol.80, No.

Evolution of plasmon excitations across the phase diagram of the cuprate superconductor La2−x_{2-x}Srx_{x}CuO4_4

We use resonant inelastic x-ray scattering (RIXS) at the O $K$- and Cu $K$-edges to investigate the doping- and temperature dependence of low-energy plasmon excitations in La$_{2-x}$Sr$_{x}$CuO$_4$. We observe a monotonic increase of the energy scale of the plasmons with increasing doping $x$ in the underdoped regime, whereas a saturation occurs above optimal doping $x \gtrsim 0.16$ and persists at least up to $x = 0.4$. Furthermore, we find that the plasmon excitations show only a marginal temperature dependence, and possible effects due to the superconducting transition and the onset of strange metal behavior are either absent or below the detection limit of our experiment. Taking into account the strongly correlated character of the cuprates, we show that layered $t$-$J$-$V$ model calculations accurately capture the increase of the plasmon energy in the underdoped regime. However, the computed plasmon energy continues to increase even for doping levels above $x \gtrsim 0.16$, which is distinct from the experimentally observed saturation, and reaches a broad maximum around $x = 0.55$. We discuss whether possible lattice disorder in overdoped samples, a renormalization of the electronic correlation strength at high dopings, or an increasing relevance of non-planar Cu and O orbitals could be responsible for the discrepancy between experiment and theory for doping levels above $x = 0.16$.Comment: 19 pages, 11 figure

Dual Nature of the Electronic Structure of the Stripe Phase

High resolution angle-resolved photoemission measurements have been carried out on (La_1.4-xNd_0.6Sr_x)CuO_4, a model system with static stripes, and (La_1.85Sr_0.15)CuO_4, a high temperature superconductor (T_c=40K) with dynamic stripes. In addition to the straight segments near (pi, 0) and (0, pi) antinodal regions, we have identified the existence of nodal spectral weight and its associated Fermi surface in the electronic structure of both systems. The ARPES spectra in the nodal region show well-defined Fermi cut-off, indicating a metallic character of this charge-ordered state. This observation of nodal spectral weight, together with the straight segments near antinodal regions, reveals dual nature of the electronic structure of the stripes due to the competition of order and disorder

Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity

This article will give an overview on both theoretical and experimental developments concerning states with lattice symmetry breaking in the cuprate high-temperature superconductors. Recent experiments have provided evidence for states with broken rotation as well as translation symmetry, and will be discussed in terms of nematic and stripe physics. Of particular importance here are results obtained using the techniques of neutron and x-ray scattering and scanning tunneling spectroscopy. Ideas on the origin of lattice-symmetry-broken states will be reviewed, and effective models accounting for various experimentally observed phenomena will be summarized. These include both weak-coupling and strong-coupling approaches, with a discussion on their distinctions and connections. The collected experimental data indicate that the tendency toward uni-directional stripe-like ordering is common to underdoped cuprates, but becomes weaker with increasing number of adjacent CuO_2 layers.Comment: Review article prepared for Adv. Phys., 66 pg, 22 figs. Comments welcome, (v2) extensions and clarifications, added references, final version to be publishe