J. Schmalian

Theory for superconducting properties of the cuprates: doping dependence of the electronic excitations and shadow states

The superconducting phase of the 2D one-band Hubbard model is studied within the FLEX approximation and by using an Eliashberg theory. We investigate the doping dependence of Tc, of the gap function Δ(k,ω) and of the effective pairing interaction. Thus we find that Tc becomes maximal for 13% doping. In overdoped systems Tc decreases due to the weakening of the antiferromagnetic correlations, while in the underdoped systems due to the decreasing quasi-particle lifetimes. Furthermore, we find shadow states below Tc which affect the electronic excitation spectrum and lead to fine structure in photoemission experiments.

Self-consistent summation of many-particle diagrams on the real frequency axis and its application to the FLEX approximation

Abstract A new numerical method for the summation of Greens function diagrams on the real frequency axis is presented. We apply our approach to the fluctuation exchange approximation for the two-dimensional Hubbard model, thereby taking full account of the momentum and frequency dependence of the Greens functions and the resulting interactions. Using the contour deformation technique in the complex frequency plane, the self-energy integrals are evaluated by a combination of Fourier and Laplace transformation and a subsequent application of the Fast Fourier Transformation. In contrast to the imaginary frequency approach, this method gives direct access to dynamical properties with high energy resolution and good numerical stability. Results for the electronic spectral density are shown which exhibit new fine structure within the elementary excitations and in particular the shadows of the Fermi surface, recently observed in high- T c superconductors.

Theory for the interdependence of high-Tc superconductivity and dynamical spin fluctuations

We analyze the doping and temperature dependence of the quasi particle excitation spectrum of the 2D one band Hubbard model in the normal and superconducting state using the fluctuation exchange approximation. It is shown that above T c shadow states resulting from short range antiferromagnetic correlations occur with small but finite excitation energies which decrease for decreasing doping, reflecting a dynamically broken symmetry with increasing lifetime. Simultaneously, the intensity of these new states increases, the quasiparticle dispersion is strongly flattened, and a pseudogap in the density of states occurs. Within the superconducting state, we find that the gap function Δk has \({d_{{x^2} - {y^2}}}\) symmetry. We explain the doping dependence of the superconducting state as consequence of the increasing stiffness of the antiferromagnetic correlations near half filling and a decrease of the spin fluctuations for large doping, yielding an optimal T c . Furthermore, our results for the spectral density below T c explain the dip structures found in photoemission and tunneling experiments. Finally the elementary excitations in double layers are discussed, yielding a blocking of the quasi particle inter-plane transfer and below T c a large additional contribution of inter-layer pairing such that Cooper pairs are formed by electrons from the same layer as from different layers with almost equal probability.

Electronic theory for the transition from Fermi-liquid to non-Fermi-liquid behavior in high-Tc superconductors

Abstract We analyze the breakdown of Fermi-liquid behavior within the 2D Hubbard model as a function of doping using our recently developed numerical method for the self consistent summation of bubble and ladder diagrams. For larger doping concentrations the system behaves like a conventional Fermi-liquid and for intermediate doping it behaves similar to a marginal Fermi-liquid. However, for smaller doping, pronounced deviations from both pictures occur which are due to the increasing importance of the short range antiferromagnetic spin fluctuations. This is closely related to the experimentally observed shadow states in the normal state of high T c superconductors. Furthermore, we discuss the implications of our results for transport experiments.

INTERPLANE MAGNETIC COUPLING EFFECTS IN THE MULTILATTICE COMPOUND Y2BA4CU7O15

We investigate the interplane magnetic coupling of the multilattice compound Y_2Ba_4Cu_7O_{15} by means of a bilayer Hubbard model with inequivalent planes. We evaluate the spin response, effective interaction and the intra- and interplane spin-spin relaxation times within the fluctuation exchange approximation. We show that strong in-plane antiferromagnetic fluctuations are responsible for a magnetic coupling between the planes, which in turns leads to a tendency of the fluctuation in the two planes to equalize. This equalization effect grows whit increasing in-plane antiferromagnetic fluctuations, i. e., with decreasing temperature and decreasing doping, while it is completely absent when the in-layer correlation length becomes of the order of one lattice spacing. Our results provide a good qualitative description of NMR and NQR experiments in Y_2Ba_4Cu_7O_{15}.

High-Tc-superconductivity and shadow state formation in YBa2Cu3O6+δ and Bi2Sr2CaCu2O8+δ

Abstract The normal and superconducting state of YBa 2 Cu 3 O 6+δ and Bi 2 Sr 2 CaCu 2 O 8+δ are investigated by using the mono- and bilayer Hubbard model within the fluctuation exchange approximation and a proper description of the Fermi surface topology. The inter- and intralayer interactions, the renormalization of the bilayer splitting and the formation of shadow bands are investigated in detail. Although the shadow states are not visible in the monolayer, we find that the additional correlations in bilayers boost the shadow state intensity and will lead to their observability. In the superconducting state we find a d x 2 − y 2 symmetry of the order parameter and demonstrate the importance of inter-plane Copper pairing.

Electronic theory for bilayer effects in high-Tc superconductors

Abstract The normal and the superconducting state of two coupled CuO2 layers in the high-Tc superconductors are investigated by using the bilayer Hubbard model, the fluctuation exchange approximation and the Eliashberg theory. We find that the planes are antiferromagnetically correlated. The inter-layer hopping is renormalized which causes a blocking of the quasi-particle inter-plane transfer. This is related to the fact that each inter-layer hopping process is accompanied by spin-flips due to the opposite antiferromagnetic environment in the other plane. Thus, due to the corresponding large inter-plane scattering rates, an incoherent coupling of the layers occur. Finally, the superconducting order parameter is found to have a dx2-y2 symmetry, where the d-wave state is characterized by a large contribution of inter-layer pairing such that Cooper pairs are formed by electrons from the same layer as from different layers with almost equal probability.

Superconductivity and dynamical short-range order in high-Tc systems

Abstract We analyze the doping and temperature dependence of the quasi-particle excitation spectrum of the 2D one hand Hubbard model in the normal and superconducting state using the fluctuation exchange approximation. It is shown that above T c shadow states resulting form short-range antiferromagnetic correlations occur with small but finite excitation energies which decrease for decreasing doping, reflecting as dynamically broken symmetry with increasing lifetime. Simultaneously, the intensity of these new states increases, the quasi-particle dispersion is strongly flattened, and a pseudogap in the density of states occurs. Within the superconducting state, we find that the gap function Δ k has d x 2 - y 2 is symmetry. Furthermore, our results for the spectral density explain the dip structures found in photoemission and tunneling experiments. These fine structures result from an enhancement of the scattering rate at shadow states slightly above the superconducting gap.

Theory for the doping dependence of spin fluctuation induced shadow states in high-Tc superconductors

Abstract We analyze the doping dependence of the intensity and energetical position of shadow states in high-Tc superconductors within the 2D Hubbard model, using our recently developed numerical method for the self-consistent summation of bubble and ladder diagrams. It is shown that shadow states resulting from short range antiferromagnetic correlations occur for small but finite excitation energies which decrease for decreasing doping, reflecting a dynamically broken symmetry with increasing lifetime. Simultaneously, the intensity of these new states increases, the quasi particle dispersion is strongly flattened, and a pseudogap in the density of states occurs. Finally, we discuss the importance of flat bands at the Fermi level and nesting of the Fermi surface as general prerequisites for the observability of shadow states.