Electronic excitations in Bi2_2Sr2_2CaCu2_2O8_8 : Fermi surface, dispersion, and absence of bilayer splitting

From a detailed study, including polarization dependence, of the normal state angle-resolved photoemission spectra for Bi$_2$Sr$_2$CaCu$_2$O$_8$, we find only one CuO$_2$ band related feature. All other spectral features can be ascribed either to umklapps from the superlattice or to ``shadow bands''. Even though the dispersion of the peaks looks like band theory, the lineshape is anomalously broad and no evidence is found for bilayer splitting. We argue that the ``dip feature'' in the spectrum below $T_c$ arises not from bilayer splitting, but rather from many body effects.Comment: 4 pages, revtex, 3 uuencoded postscript figure

Surprises in the doping dependence of the Fermi surface in Bi(Pb)-2212

A detailed and systematic ARPES investigation of the doping-dependence of the normal state Fermi surface (FS) of modulation-free (Pb,Bi)-2212 is presented. The FS does not change in topology away from hole-like at any stage. The data reveal, in addition, a number of surprises. Firstly the FS area does not follow the usual curve describing Tc vs x for the hole doped cuprates, but is down-shifted in doping by ca. 0.05 holes per Cu site, indicating either the break-down of Luttinger's theorem or the consequences of a significant bi-layer splitting of the FS. Secondly, the strong k-dependence of the FS width is shown to be doping independent. Finally, the relative strength of the shadow FS has a doping dependence mirroring that of Tc.Comment: 5 pages, 4 figures (revtex

Bridge trisections of knotted surfaces in 4--manifolds

We prove that every smoothly embedded surface in a 4--manifold can be isotoped to be in bridge position with respect to a given trisection of the ambient 4--manifold; that is, after isotopy, the surface meets components of the trisection in trivial disks or arcs. Such a decomposition, which we call a \emph{generalized bridge trisection}, extends the authors' definition of bridge trisections for surfaces in $S^4$. Using this new construction, we give diagrammatic representations called \emph{shadow diagrams} for knotted surfaces in 4--manifolds. We also provide a low-complexity classification for these structures and describe several examples, including the important case of complex curves inside $\mathbb{CP}^2$. Using these examples, we prove that there exist exotic 4--manifolds with $(g,0)$--trisections for certain values of $g$. We conclude by sketching a conjectural uniqueness result that would provide a complete diagrammatic calculus for studying knotted surfaces through their shadow diagrams.Comment: 17 pages, 5 figures. Comments welcom

Theory for the Interdependence of High-Tc_c Superconductivity and Dynamical Spin Fluctuations

The doping dependence of the superconducting state for the 2D one-band Hubbard Hamiltonian is determined. By using an Eliashberg-type theory, we find that the gap function $\Delta_{\bf k}$ has a $d_{x^2-y^2}$ symmetry in momentum space and T$_c$ becomes maximal for $13 \; \%$ doping. Since we determine the dynamical excitations directly from real frequency axis calculations, we obtain new structures in the angular resolved density of states related to the occurrence of {\it shadow states} below T$_c$. Explaining the anomalous behavior of photoemission and tunneling experiments in the cuprates, we find a strong interplay between $d$-wave superconductivity and dynamical spin fluctuations.Comment: 4 pages (REVTeX) with 4 figures (Postscript

Shadow on the wall cast by an Abrikosov vortex

At the surface of a d-wave superconductor, a zero-energy peak in the quasiparticle spectrum can be observed. This peak appears due to Andreev bound states and is maximal if the nodal direction of the d-wave pairing potential is perpendicular to the boundary. We examine the effect of a single Abrikosov vortex in front of a reflecting boundary on the zero-energy density of states. We can clearly see a splitting of the low-energy peak and therefore a suppression of the zero-energy density of states in a shadow-like region extending from the vortex to the boundary. This effect is stable for different models of the single Abrikosov vortex, for different mean free paths and also for different distances between the vortex center and the boundary. This observation promises to have also a substantial influence on the differential conductance and the tunneling characteristics for low excitation energies.Comment: 5 pages, 5 figure