HIGHLIGHTS IN CONDENSED MATTER PHYSICS

Phonon‐assisted strong Cooper pair interaction in highly correlated cuprate systems
View Description Hide DescriptionThe dispersion of the in‐plane CuO bond stretching LO phonon mode in the high‐T_{C} cuprate superconductors shows strong softening with the optimum doped samples near the zone boundary, but the overdoped samples with zero T_{C} does not show the anomalous softening. This fact suggests that the phonon is closely related to the mechanism of the high‐T_{C} superconductivity. The softening can be described with a negative electronic dielectric function that results in overscreening of the inter‐site Coulomb interaction in the highly correlated cuprate systems. We propose that such a strong electron‐phonon coupling of specific modes can form basis for phonon mechanism of high‐temperature superconductivity. On the basis of the model, with the Eliashberg theory using the experimentally determined electron dispersion and dielectric function, we demonstrate the possibility of superconductivity with the order parameter of the symmetry and the transition temperature well in excess of 100K.

Aspects of unconventional density waves
View Description Hide DescriptionRecently many people discuss unconventional density waves (i.e. unconventional charge density waves (UCDW) and unconventional spin density waves (USDW)). Unlike in conventional density waves, the quasiparticle spectrum in these systems is gapless. Also these systems remain metallic. Indeed it appears that there are many candidates for UDW. The low temperature phase of α‐(BEDT‐TTF)_{2}KHg(SCN)_{4}, the antiferromagnetic phase in URu_{2}Si_{2}, the CDW in transition metal dichalcogenite NbSe_{2}, the pseudogap phase in high T_{c} cuprate superconductors, the glassy phase in organic superconductor κ‐(BEDT‐TTF)_{2}Cu[N(CN)_{2}]Br. After a brief introduction on UCDW and USDW, we shall discuss some of the above systems, where we believe we have evidence for unconventional density waves.

Superconductors as giant atoms: Qualitative aspects
View Description Hide DescriptionWhen the Fermi level is near the top of a band the carriers (holes) are maximally dressed by electron‐ion and electron‐electron interactions. The theory of hole superconductivity predicts that only in that case can superconductivity occur, and that it is driven by undressing of the carriers at the Fermi energy upon pairing. Indeed, experiments show that dressed hole carriers in the normal state become undressed electron carriers in the superconducting state. This leads to a description of superconductors as giant atoms, where undressed time‐reversed electrons are paired and propagate freely in a uniform positive background. The pairing gap provides rigidity to the wavefunction, and electrons in the giant atom respond to magnetic fields the same way as electrons in diamagnetic atoms. We predict that there is an electric field in the interior of superconductors and that the charge distribution is inhomogeneous, with higher concentration of negative charge near the surface; that the ground state of superconductors has broken parity and possesses macroscopic spin currents, and that negative charge spills out when a body becomes superconducting.

High temperature superconductors: Experimental implications of a variational theory of the superconducting state
View Description Hide DescriptionWe review recent work on the properties of a d‐wave superconducting state in which strong Coulomb interactions suppress double occupancy. We find that pairing and phase coherence show qualitatively different trends as a function of doping: the pairing scale decreases monotonically with hole doping x while the order parameter shows a non‐monotonic “dome”. We obtain detailed results for the doping‐dependences of various quantities including the momentum distribution, nodal quasiparticle weights and dispersions, optical spectral weight, and superfluid density. Our results are in remarkable agreement with existing data on the high T_{c} cuprates and some of our predictions have been recently verified.

Critical temperature of high‐T_{c} superconductors in the bipolaron model
View Description Hide DescriptionThe extension of the BCS theory to the strong‐coupling regime with small bipolarons numerically accounts for high superconducting critical temperatures and isotope effects, of many high‐T_{c} superconductors.

Polarons: Recent developments
View Description Hide DescriptionIn this presentation three recent contributions to the theory of continuum (or “Fröhlich”‐) polarons are discussed. (i) Using a generalization of the Jensen‐Feynman variational principle within the path‐integral formalism for identical particles, the ground‐state energy of a confined N‐polaron system is studied as a function of N and of the electron‐phonon coupling strength. (ii) Cyclotron‐resonance (CR) spectra of a gas of interacting polarons in a GaAs/AlAs quantum well are theoretically investigated taking into account the magnetoplasmon‐phonon mixing and the band non‐parabolicity. The calculated CR spectra are in a good agreement with experimental data. The theory explains that, for a high‐density polaron gas, anticrossing of the CR spectra occurs near the GaAs TO‐phonon frequency rather than near the GaAs LO‐frequency. (iii) A theoretical investigation of the optical properties of stacked quantum dots is presented, which is based on the non‐adiabatic approach.

Charge dynamics of t‐J model and anomalous bond‐stretching phonons in cuprates
View Description Hide DescriptionThe density response of a doped Mott‐Hubbard insulator is discussed starting from the t‐J model in a slave boson 1/N representation. In leading order O(1) the density fluctuation spectra N(q, ω) are determined by an undamped collective mode at large momentum transfer, in striking disagreement with results obtained by exact diagonalization, which reveal a very broad dispersive peak, reminescent of strong spin‐charge coupling. The 1/N corrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resulting N(q, ω) captures all features observed in diagonalization studies, fulfills the appropriate sum rules, and apart from the broadening of the collective mode shows a new low energy feature at the energy χJ + δt related to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in (π, 0) direction, describes the strong renormalization and anomalous damping of the highest bond‐stretching phonons in La_{2−x }Sr_{ x }CuO_{4}.

Tools for Studying Quantum Emergence near Phase Transitions
View Description Hide DescriptionWe review recent studies on developing tools for quantum complex phenomena. The tools have been applied for clarifying the perspective of the Mott transitions and the phase diagram of metals, Mott insulators and magnetically ordered phases in the two‐dimensional Hubbard model. The path‐integral renormalization‐group (PIRG) method has made it possible to numerically study correlated electrons even with geometrical frustration effects without biases . It has numerically clarified the phase diagram at zero temperature, T = 0, in the parameter space of the onsite Coulomb repulsion, the geometrical frustration amplitude and the chemical potential. When the bandwidth is controlled at half filling, the first‐order transition between insulating and metallic phases is evidenced. In contrast, the filling‐control transition shows diverging critical fluctuations for spin and charge responses with decreasing doping concentration. Near the Mott transition, a nonmagnetic spin‐liquid phase appears in a region with large frustration effects. The phase is characterized remarkably by gapless spin excitations and the vanishing dispersion of spin excitations. Magnetic orders quantum mechanically melt through diverging magnon mass. The correlator projection method (CPM) is formulated as an extension of the operator projection theory. This method also allows an extension of the dynamical mean‐field theory (DMFT) with systematic inclusion of the momentum dependence in the self‐energy. It has enabled determining the phase diagram at T > 0, where the boundary surface of the first‐order metal‐insulator transition at half filling terminates on the critical end curve at T = T_{c} . The critical end curve is characterized by the diverging compressibility. The single particle spectra show strong renormalization of low‐energy spectra, generating largely momentum dependent and flat dispersion. The results of two tools consistently suggest that the strong competitions of various phases with underlying diverging compressibility can induce an emergence near a new type of quantum criticality distinguished from the conventional and simple quantum critical phenomena.

Antiferromagnetic exchange and spin‐fluctuation pairing mechanisms in cuprates
View Description Hide DescriptionSuperconducting pairing mediated by antiferromagnetic (AFM) exchange and spin‐fluctuations is considered within the effective two‐band Hubbard model for a copper‐oxide plane. It is proved that retardation effects for the AFM exchange induced by interband hopping are unimportant that results in pairing of all the carries in the conduction band and high T_{c} proportional to the Fermi energy. The kinematic interaction induced by intraband hopping gives an additional spin‐fluctuation contribution to the d‐wave pairing. T_{c} dependence on pressure and oxygen isotope effect are explained.

Magnetic fluctuations and resonant peak in doped antiferromagnets
View Description Hide DescriptionA theory of the dynamical spin susceptibility is presented, relevant for the normal‐state magnetic response and the resonant magnetic peak in superconducting (SC) cuprates. The analysis is based on the equations of motion for spins within the t‐J model and on the memory‐function representation of magnetic response. An evidence from numerical studies of the model confirms that the damping of the spin collective model is large in the normal state being due to the decay into fermionic degrees of freedom. Assuming the saturation of equal‐time correlations at low T this leads to the anomalous ω/T scaling, explaining neutron scattering experiments on cuprates at low doping. In the SC phase a d‐wave SC gap leads to a sharp resonant peak with reduced intensity and downward dispersion.

A criterion for the transition of a three dimensional Bravais lattice from bulk to molecular behaviour
View Description Hide DescriptionThis paper addresses the question of “how large is large enough for a crystallite to be a three dimensional Bravais lattice?” Based on the premise that the ratio of the bulk volume to that of the volume of the unit cell for a given material should determine the transition to a large molecule, it is proposed that for values of the ratio < 10^{6} crystallites can be considered as large molecules. The universality of this criterion has been established by examples from magnetism, optics, ferroelectrics and superconductivity. It is expected, due to the wide variety of materials considered, that other classes of inorganic materials would also obey this rule leading to a quantitative definition for a nanocrystal or nanostructure.

Bose‐Einstein Condensation in Thermo Field Dynamics
View Description Hide DescriptionIn the development of Thermo Field Dynamics (the quantum field theory at finite temperature and density), Prof. Mancini acted as one of the originators and played the important role for its birth through the work of superconductivity. Recent development of the Bose‐Einstein condensation in the dilute alkaline atomic gas enables us to investigate deeply the quantum coherence in bose and fermi particle systems, and gives us a plenty of experimental data even for the problem in nonequilibrium formation of the condensate. There the relaxation time is reasonably slow to make the laboratory observation possible. In this talk, we will show that Thermo Field Dynamics gives us a reasonable approximation scheme to describe time‐dependent ordered states with spatial inhomogeniety by use of a single‐time quasi‐particle field equation, which contains the information of the spatial and temporal dependent order parameter, particle energy and particle distribution.

Coherent structures of Bose‐Einstein condensates in optical lattices
View Description Hide DescriptionWe propose to employ the phenomenon of modulational instability in order to create regularly arranged localized excitations in arrays of Bose‐Einstein condensates. These excitations are narrow tubes in 2D and small hollows in 3D arrays filled in with the condensed atoms of much greater density compared to surrounding array sites. As the regions with high atomic concentration develop due to the modulational instability, they can be preserved by increasing the strength of the optical lattice. Theoretical model, based on the multiple scale expansion, describes the main features of the phenomenon. Analytical predictions are confirmed by numerical simulations of the Gross‐Pitaevskii equation.

Multifractal Analysis of Various PDF in Turbulence based on Generalized Statistics: A Way to Tangle in Superfluid He
View Description Hide DescriptionBy means of the multifractal analysis (MFA), the expressions of the probability density functions (PDFs) are unified in a compact analytical formula which is valid for various quantities in turbulence. It is shown that the formula can explain precisely the experimentally observed PDFs both on log and linear scales. The PDF consists of two parts, i.e., the tail part and the center part. The structure of the tail part of the PDFs, determined mostly by the intermittency exponent, represents the intermittent large deviations that is a manifestation of the multifractal distribution of singularities in physical space due to the scale invariance of the Navier‐Stokes equation for large Reynolds number. On the other hand, the structure of the center part represents small deviations violating the scale invariance due to thermal fluctuations and/or observation error.

Combinatorial aspects of exclusion and parastatistics
View Description Hide DescriptionCombinatorial aspects of all statistics based on the permutation group are analyzed by imposing the requirements of indistinguishability in the permutation group sense on the Hilbert space describing N identical particles. Compact expressions for the grand canonical partition functions are given wherever possible. The theory of symmetric functions is found to play a significant role in this development. An analysis of the semion statistics of Haldane is also presented from this perspective together with some recent developments in the field of exclusion statistics.

Charge and Phase Dynamics in a Stack of Intrinsic Josephson Junctions
View Description Hide DescriptionOur recent studies for the intrinsic Josephson effect are reviewed. We propose a simple phenomenological model based on the time‐dependent Ginzburg‐Landau model at T = 0K for describing the phase dynamics of a stack of intrinsic Josephson junctions. In this model the capacitive and the inductive couplings between junctions dominate the dynamics of the gauge‐invariant phase differences. It is shown that our model well explains the intrinsic Josephson effects observed in strongly anisotropic layered high‐T_{c} superconductors.

Self‐Consistent Mean‐Field Theory for Frustrated Josephson Junction Arrays
View Description Hide DescriptionWe review the self‐consistent mean‐field theory for charge‐frustrated Josephson junction arrays. Using 〈cosφ〉 (φ is the phase of the superconducting wavefunction) as order parameter and imposing the self‐consistency condition, we compute the phase boundary line between the superconducting region (〈cosφ〉 ≠ 0) and the insulating one (〈cosφ〉 = 0). For a uniform offset charge q = e the superconducting phase increases with respect to the situation in which q = 0. We generalize the self‐consistent mean‐field theory to include the effects induced by a random distribution of offset charges and/or of diagonal self‐capacitances. We find results in agreement with the ones obtained in studies using the path‐integral approach.

Magnetic Interactions in Transition Metal Oxides with Orbital Degrees of Freedom
View Description Hide DescriptionWe review the frustrated magnetic interactions in spin‐orbital models which describe superexchange in transition metal oxides with orbital degeneracy, and analyze the reasons for the symmetry breaking in cubic perovskites. The superexchange in e_{g} systems is dominated by orbital interactions responsible for the orbital ordering, and the A‐type antiferromagnetic ordering follows at lower temperatures. Instead, a generic tendency towards dimerization, found already in the degenerate Hubbard model, occurs in t _{2g } systems. In this case the quantum orbital fluctuations may stabilize orbital liquid states along one directions even in some undoped t _{2g } systems, leading to the C‐type antiferromagnetic order. The orbital liquid in manganites is triggered by doping. The present understanding of the spectroscopic parameters provides reliable information on the magnetic interactions, as shown on the example of magnons in ferromagnetic cubic and bilayer manganites.

Orbital Physics versus Spin Physics
View Description Hide DescriptionTo elucidate the similarities and differences between the physics displayed by orbital and spin degrees of freedom, we analyze an orbital‐Hubbard model with two orbital flavors, corresponding to pseudospin 1/2, and contrast its behavior with that of the familiar (spin‐1/2) Hubbard model. The orbital‐Hubbard model describes a partly filled spin‐polarized e_{g} band on a cubic lattice, as occurs in ferromagnetic manganites. We demonstrate that the absence of SU(2) invariance in orbital space has important implications — superexchange contributes in all orbital ordered states, the Nagaoka theorem does not apply, and the kinetic energy is enhanced as compared with the spin case. As a result orbital‐ordered states are destabilized by doping, and instead a strongly correlated orbital liquid with disordered orbitals is realized.

Local moment systems: magnetism and electronic correlations
View Description Hide DescriptionWe describe local‐moment systems by the (multiband) s‐f model (ferromagnetic Kondo‐lattice model) which traces back the characteristic properties of such materials to an interband exchange coupling between itinerant conduction electrons and localized magnetic moments. We first present a many‐body approach to the electronic and magnetic properties of the single‐band model. The exchange coupling leads, on the one hand, to a distinct temperature‐dependence of the electronic quasiparticle spectrum and, on the other hand, to magnetic properties, as e. g. the Curie temperature T _{C} or the magnon dispersion, which are strongly influenced by the band electron selfenergy and therewith in particular by the carrier density. Results for the electronic part are given in terms of quasiparticle densities of states and quasiparticle band structures and for the magnetic part in terms of the selfconsistently derived Curie temperature and spin wave spectra. The transition from weak‐coupling (RKKY) to strong‐coupling (double exchange) behaviour is worked out. The multiband model is combined with an ab‐initio bandstructure calculation to describe real magnetic materials. The proposed method avoids the double counting of relevant interactions and takes into account the correct symmetry of atomic orbitals. For the ferromagnetic metal Gd we get a selfconsistently derived Curie temperature of 301.5 K and a T = 0‐moment of 7.81 μ_{B}, very close to the experimental values. Furthermore a striking induced temperature‐dependence of the 5d conduction bands explains respective photoemission data. For the ferromagnetic semiconductors EuO and EuS we present results for electronic and magnetic bulk properties as well as for thin films.