A factorization of a super-conformal map

A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a meromorphic function. Analogs of the Liouville theorem, the Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem, the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and branch points of a super-conformal map are obtained.Comment: 21 page

Superconductivity and Pseudogap in Quasi-Two-Dimensional Metals around the Antiferromagnetic Quantum Critical Point

Spin fluctuations (SF) and SF-mediated superconductivity (SC) in quasi-two-dimensional metals around the antiferrromagnetic (AF) quantum critical point (QCP) are investigated by using the self-consistent renormalization theory for SF and the strong coupling theory for SC. We introduce a parameter y0 as a measure for the distance from the AFQCP which is approximately proportional to (x-xc), x being the electron (e) or hole (h) doping concentration to the half-filled band and xc being the value at the AFQCP. We present phase diagrams in the T-y0 plane including contour maps of the AF correlation length and AF and SC transition temperatures TN and Tc, respectively. The Tc curve is dome-shaped with a maximum at around the AFQCP. The calculated one-electron spectral density shows a pseudogap in the high-density-of-states region near (pi,0) below around a certain temperature T* and gives a contour map at the Fermi energy reminiscent of the Fermi arc. These results are discussed in comparison with e- and h-doped high-Tc cuprates.Comment: 5 pages, 3 figure

Ru-NMR Studies and Specific Heat Measurements of Bi3Ru3O11 and La4Ru6O19

Specific heats measurements and Ru-NMR studies have been carried out for Bi3Ru3O11 and La4Ru6O19, which commonly have three-dimensional linkages of edge-sharing pairs of RuO6 octahedra. The Knight shifts, the nuclear spin-lattice relaxation rates 1/T1 and the electronic specific heats Cel of these systems exhibit anomalous temperature (T) dependence at low temperatures, as was pointed out by Khalifah et al. [Nature 411 (2001) 660.] for the latter system based on their experimental data of the resistivity, magnetic susceptibility and electronic specific heat. Ratios of 1/T1T to the square of the spin component of the isotropic Knight shift, Kspin estimated for these systems at low temperatures suggest that they have antiferromagnetic (AF) spin fluctuations. It is confirmed by the fact that the T-dependences of 1/T1T and Cel/T of the present systems can be explained by the self-consistent renormalization theory for three dimensional itinerant electron systems with AF spin fluctuations. All these results suggest that the AF fluctuations are the primary origin of the characteristics of their low temperature physical behavior.Comment: 9 pages, 8 figures, 2 Tables, submitted to J. Phys. Soc. Jp

Comparing pertinent effects of antiferromagnetic fluctuations in the two and three dimensional Hubbard model

We use the dynamical vertex approximation (D$\Gamma$A) with a Moriyaesque $\lambda$ correction for studying the impact of antiferromagnetic fluctuations on the spectral function of the Hubbard model in two and three dimensions. Our results show the suppression of the quasiparticle weight in three dimensions and dramatically stronger impact of spin fluctuations in two dimensions where the pseudogap is formed at low enough temperatures. Even in the presence of the Hubbard subbands, the origin of the pseudogap at weak-to-intermediate coupling is in the splitting of the quasiparticle peak. At stronger coupling (closer to the insulating phase) the splitting of Hubbard subbands is expected instead. The $\mathbf{k}$-dependence of the self energy appears to be also much more pronounced in two dimensions as can be observed in the $\mathbf{k}$-resolved D$\Gamma$A spectra, experimentally accessible by angular resolved photoemission spectroscopy in layered correlated systems.Comment: 10 pages, 12 figure

Low energy magnetic excitation spectrum of the unconventional ferromagnet CeRh3_{3}B2_{2}

The magnetic excitation spectrum of the unconventional ferromagnet CeRh$_{3}$B$_{2}$ was measured by inelastic neutron scattering on single crystal sample in the magnetically ordered and paramagnetic phases. The spin-wave excitation spectrum evidences high exchange interaction along the c-axis about two orders of magnitude higher than the ones in the basal plane of the hexagonal structure. Both strong out of plane and small in plane anisotropies are found. This latter point confirms that considering the $J$=5/2 multiplet alone is not adequate for describing the ground state of CeRh$_{3}$B$_{2}$. Quasielastic scattering measured above $T_{Curie}$ is also strongly anisotropic between the basal plane and the c-axis and suggests localized magnetism.Comment: 8 Figure

Origin and roles of a strong electron-phonon interaction in cuprate oxide superconductors

A strong electron-phonon interaction arises from the modulation of the superexchange interaction by phonons. As is studied in Phys. Rev. B 70, 184514 (2004), Cu-O bond stretching modes can be soft around (pm pi/a, 0) and (0, pm pi/a), with a the lattice constant of CuO_2 planes. In the critical region of SDW, where antiferromagnetic spin fluctuations are developed around nesting wave numbers Q of the Fermi surface, the stretching modes can also be soft around 2Q. Almost symmetric energy dependences of the 2Q component of the density of states, which are observed in the so called stripe and checker-board states, cannot be explained by CDW with 2Q following the complete softening of the 2Q modes, but they can be explained by a second-harmonic effect of SDW with Q. The strong electron-phonon interaction can play no or only a minor role in the occurrence of superconductivity.Comment: 5 pages, 1 fugur

Superconductivity in CeCoIn5-xSnx: Veil Over an Ordered State or Novel Quantum Critical Point?

Measurements of specific heat and electrical resistivity in magnetic fields up to 9 T along [001] and temperatures down to 50 mK of Sn-substituted CeCoIn5 are reported. The maximal -ln(T) divergence of the specific heat at the upper critical field H_{c2} down to the lowest temperature characteristic of non-Fermi liquid systems at the quantum critical point (QCP), the universal scaling of the Sommerfeld coefficient, and agreement of the data with spin-fluctuation theory, provide strong evidence for quantum criticality at H_{c2} for all x < 0.12 in CeCoIn5-xSnx. These results indicate the "accidental" coincidence of the QCP located near H_{c2} in pure CeCoIn5, in actuality, constitute a novel quantum critical point associated with unconventional superconductivity.Comment: 12 pages, 4 figure

Antiferromagnetic Spin Fluctuation above the Superconducting Dome and the Full-Gaps Superconducting State in LaFeAsO1-xFx Revealed by 75As-Nuclear Quadrupole Resonance

We report a systematic study by 75As nuclear-quadrupole resonance in LaFeAsO1-xFx. The antiferromagnetic spin fluctuation (AFSF) found above the magnetic ordering temperature TN = 58 K for x = 0.03 persists in the regime 0.04 < x < 0.08 where superconductivity sets in. A dome-shaped x-dependence of the superconducting transition temperature Tc is found, with the highest Tc = 27 K at x = 0.06 which is realized under significant AFSF. With increasing x further, the AFSF decreases, and so does Tc. These features resemble closely the cuprates La2-xSrxCuO4. In x = 0.06, the spin-lattice relaxation rate (1/T1) below Tc decreases exponentially down to 0.13 Tc, which unambiguously indicates that the energy gaps are fully-opened. The temperature variation of 1/T1 below Tc is rendered nonexponential for other x by impurity scattering.Comment: 5 pages, 5 figures, more references adde

Quantum Lifshitz point in the infinite dimensional Hubbard model

We show that the Gutzwiller variational wave function is surprisingly accurate for the computation of magnetic phase boundaries in the infinite dimensional Hubbard model. This allows us to substantially extend known phase diagrams. For both the half-hypercubic and the hypercubic lattice a large part of the phase diagram is occupied by an incommensurate phase, intermediate between the ferromagnetic and the paramagnetic phase. In case of the hypercubic lattice the three phases join at a new quantum Lifshitz point at which the order parameter is critical and the stiffness vanishes.Comment: 4 pages, 3 figure

Doping driven magnetic instabilities and quantum criticality of NbFe2_{2}

Using density functional theory we investigate the evolution of the magnetic ground state of NbFe$_{2}$ due to doping by Nb-excess and Fe-excess. We find that non-rigid-band effects, due to the contribution of Fe-\textit{d} states to the density of states at the Fermi level are crucial to the evolution of the magnetic phase diagram. Furthermore, the influence of disorder is important to the development of ferromagnetism upon Nb doping. These findings give a framework in which to understand the evolution of the magnetic ground state in the temperature-doping phase diagram. We investigate the magnetic instabilities in NbFe$_{2}$. We find that explicit calculation of the Lindhard function, $\chi_{0}(\mathbf{q})$, indicates that the primary instability is to finite $\mathbf{q}$ antiferromagnetism driven by Fermi surface nesting. Total energy calculations indicate that $\mathbf{q}=0$ antiferromagnetism is the ground state. We discuss the influence of competing $\mathbf{q}=0$ and finite $\mathbf{q}$ instabilities on the presence of the non-Fermi liquid behavior in this material.Comment: 8 pages, 7 figure