Universality of scanning tunneling microscopy in cuprate superconductors

We consider the problem of local tunneling into cuprate superconductors, combining model based calculations for the superconducting order parameter with wavefunction information obtained from first principles electronic structure. For some time it has been proposed that scanning tunneling microscopy (STM) spectra do not reflect the properties of the superconducting layer in the CuO$_2$ plane directly beneath the STM tip, but rather a weighted sum of spatially proximate states determined by the details of the tunneling process. These "filter" ideas have been countered with the argument that similar conductance patterns have been seen around impurities and charge ordered states in systems with atomically quite different barrier layers. Here we use a recently developed Wannier function based method to calculate topographies, spectra, conductance maps and normalized conductance maps close to impurities. We find that it is the local planar Cu $d_{x^2-y^2}$ Wannier function, qualitatively similar for many systems, that controls the form of the tunneling spectrum and the spatial patterns near perturbations. We explain how, despite the fact that STM observables depend on the materials-specific details of the tunneling process and setup parameters, there is an overall universality in the qualitative features of conductance spectra. In particular, we discuss why STM results on Bi$_2$Sr$_2$CaCu$_2$O$_8$ and Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$ are essentially identical

Interpretation of scanning tunneling quasiparticle interference and impurity states in cuprates

We apply a recently developed method combining first principles based Wannier functions with solutions to the Bogoliubov-de Gennes equations to the problem of interpreting STM data in cuprate superconductors. We show that the observed images of Zn on the surface of Bi$_2$Sr$_2$CaCu$_2$O$_8$ can only be understood by accounting for the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. This calculation thus puts earlier crude "filter" theories on a microscopic foundation and solves a long standing puzzle. We then study quasiparticle interference phenomena induced by out-of-plane weak potential scatterers, and show how patterns long observed in cuprates can be understood in terms of the interference of Wannier functions above the surface. Our results show excellent agreement with experiment and enable a better understanding of novel phenomena in the cuprates via STM imaging.Comment: 5 pages, 5 figures, published version (Supplemental Material: 5 pages, 11 figures) for associated video file, see http://itp.uni-frankfurt.de/~kreisel/QPI_BSCCO_BdG_p_W.mp

Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: a numerical RPA study

We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from p-wave at very low electron fillings to d_{x^2-y^2}-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise sub-dominant triplet solution over the singlet d-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasi-particle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet d_{x^2-y^2} gap as well as the chiral triplet gap solution.Comment: 11 pages 11 figure

Random local strain effects in homovalent-substituted relaxor ferroelectrics: a first-principles study of BaTi0.74Zr0.26O3

We present first-principles supercell calculations on BaTi0.74Zr0.26O3, a prototype material for relaxors with a homovalent substitution. From a statistical analysis of relaxed structures, we give evidence for four types of Ti-atom polar displacements: along the , , or directions of the cubic unit cell, or almost cancelled. The type of a Ti displacement is entirely determined by the Ti/Zr distribution in the adjacent unit cells. The underlying mechanism involves local strain effects that ensue from the difference in size between the Ti4+ and Zr4+ cations. These results shed light on the structural mechanisms that lead to disordered Ti displacements in BaTi(1-x)Zr(x)O3 relaxors, and probably in other BaTiO3-based relaxors with homovalent substitution.Comment: 5 pages, 4 figure

Orbital-dependent self-energy effects and consequences for the superconducting gap structure in multi-orbital correlated electron systems

We perform a theoretical study of the effects of electronic correlations on the superconducting gap structure of multi-band superconductors. In particular, by comparing standard RPA-based spin-fluctuation mediated gap structures to those obtained within the FLEX formalism for an iron-based superconductor, we obtain directly the feedback effects from electron-electron interactions on the momentum-space gap structure. We show how self-energy effects can lead to an orbital inversion of the orbital-resolved spin susceptibility, and thereby invert the hierarchy of the most important orbitals channels for superconducting pairing. This effect has important consequences for the detailed gap variations on the Fermi surface. We expect such self-energy feedback on the pairing gap to be generally relevant for superconductivity in strongly correlated multi-orbital systems.Comment: 8 pages, 5 figure

Magentically-Induced Lattice Distortions and Ferroelectricity in Magnetoelectric GdMnO3

In this work we investigate the magnetic field dependence of Ag octahedra rotation (tilt) and B2g symmetric stretching modes frequency at different temperatures. Our field-dependent Raman investigation at 10K is interpreted by an ionic displacive nature of the magnetically induced ferroelectric phase transition. The frequency change of the Ag tilt is in agreement with the stabilization of the Mn-Gd spin arrangement, yielding the necessary conditions for the onset of ferroelectricity on the basis of the inverse Dzyaloshinskii-Moriya interaction. The role of the Jahn-Teller cooperative interaction is also evidenced by the change of the B2g mode frequency at the ferroelectric phase transition. This frequency change allows estimating the shift of the oxygen position at the ferroelectric phase transition and the corresponding spontaneous polarization of 480 {\mu}C/m2, which agrees with earlier reported values in single crystals. Our study also confirms the existence of a large magnetic hysteresis at the lowest temperatures, which is a manifestation of magnetrostiction.Comment: 5 pages, 3 figure