The electronic Hamiltonian for cuprates

A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations

Gap Nodes and Time Reversal Symmetry Breaking in Strontium Ruthenate

We study the superconducting state of Sr$_2$RuO$_4$ on the bases of a phenomenological but orbital specific description of the electron-electron attraction and a realistic quantitative account of the electronic structure in the normal state. We found that a simple model which features both `in plane' and `out of plane' coupling with strengths $U_{\parallel}=40$meV and $U_{\perp}=48$meV respectively reproduced the experimentally observed power law behaviour of the low temperature specific heat $C_v(T)$, superfluid density $n_s(T)$ and thermal conductivity in quantitative detail. Moreover, it predicts that the quasi-particle spectrum on the $\gamma$ -sheet is fully gaped and the corresponding order parameter breaks the time reversal symmetry. We have also investigated the stability of this model to inclusion of further interaction constants in particular %those which describe `proximity coupling' between orbitals contributing to the $\gamma$ sheet of the Fermi surface and the $\alpha$ and $\beta$ sheets. We found that the predictions of the model are robust under such changes. Finally, we have incorporated a description of weak disorder into the model and explored some of its consequences. For example we demonstrated that the disorder has a more significant effect on the $f$-wave component of the order parameter than on the p-wave one.Comment: EPJ B submitte

The Effects of d_{x^2-y^2}-d_{xy} Mixing on Vortex Structures and Magnetization

The structure of an isolated single vortex and the vortex lattice, and the magnetization in a $d$-wave superconductor are investigated within a phenomenological Ginzburg-Landau (GL) model including the mixture of the $d_{x^2-y^2}$-wave and $d_{xy}$-wave symmetry. The isolated single vortex structure in a week magnetic field is studied both numerically and asymptotically. Near the upper critical field $H_{c2}$, the vortex lattice structure and the magnetization are calculated analytically.Comment: 14 pages, REVTeX, 2 EPS figures, Journal of Physics: Condensed Matter (in press

Magnetic field induced rotation of the d-vector in the spin triplet superconductor Sr2_2RuO4_4

In zero magnetic field the superconductor Sr$_2$RuO$_4$ is believed to have a chiral spin triplet pairing state in which the gap function d-vector is aligned along the crystal c-axis. Using a phenomenological but orbital specific description of the spin dependent electron-electron attraction and a realistic quantitative account of the electronic structure in the normal state we analyze the orientation of the spin triplet Cooper pair d-vector in response to an external c-axis magnetic field. We show that for suitable values of the model parameters a c-axis field of only 20 mT is able to cause a reorientation phase transition of the d-vector from along $c$ to the $a-b$ plane, in agreement with recent experiments.Comment: 6 pages, 7 figures. Submitted Phys Rev

Spin-Orbit Coupling and Symmetry of the Order Parameter in Strontium Ruthenate

Determination of the orbital symmetry of a state in spin triplet Sr$_2$RuO$_4$ superconductor is a challenge of considerable importance. Most of the experiments show that the chiral state of the $\hat{z} (k_x \pm ik_y)$ type is realized and remains stable on lowering the temperature. Here we have studied the stability of various superconducting states of Sr$_2$RuO$_4$ in the presence of spin-orbit coupling. Numerically we found that the chiral state is never the minimum energy. Alone among the five states studied it has $=0$ and is therefore not affected to linear order in the coupling parameter $\lambda$. We found that stability of the chiral state requires spin dependent pairing interactions. This imposes strong constraint on the pairing mechanism.Comment: 4 pages, 4 figure

Variational QMC study of a Hydrogen atom in jellium with comparison to LSDA and LSDA-SIC solutions

A Hydrogen atom immersed in a finite jellium sphere is solved using variational quantum Monte Carlo (VQMC). The same system is also solved using density functional theory (DFT), in both the local spin density (LSDA) and self-interaction correction (SIC) approximations. The immersion energies calculated using these methods, as functions of the background density of the jellium, are found to lie within 1eV of each other with minima in approximately the same positions. The DFT results show overbinding relative to the VQMC result. The immersion energies also suggest an improved performance of the SIC over the LSDA relative to the VQMC results. The atom-induced density is also calculated and shows a difference between the methods, with a more extended Friedel oscillation in the case of the VQMC result.Comment: 16 pages, 9 Postscript figure

Factors influencing the stable carbon isotopic composition of suspended and sinking organic matter in the coastal Antarctic sea ice environment

A high resolution time-series analysis of stable carbon isotopic signatures in particulate organic carbon (δ<sup>13</sup>C<sub>POC</sub>) and associated biogeochemical parameters in sea ice and surface waters provides an insight into the factors affecting δ<sup>13</sup>C<sub>POC</sub> in the coastal western Antarctic Peninsula sea ice environment. The study covers two austral summer seasons in Ryder Bay, northern Marguerite Bay between 2004 and 2006. A shift in diatom species composition during the 2005/06 summer bloom to near-complete biomass dominance of <i>Proboscia inermis</i> is strongly correlated with a large ~10 ‰ negative isotopic shift in δ<sup>13</sup>C<sub>POC</sub> that cannot be explained by a concurrent change in concentration or isotopic signature of CO<sub>2</sub>. We hypothesise that the δ<sup>13</sup>C<sub>POC</sub> shift may be driven by the contrasting biochemical mechanisms and utilisation of carbon-concentrating mechanisms (CCMs) in different diatom species. Specifically, very low δ<sup>13</sup>C<sub>POC</sub> in <i>P. inermis</i> may be caused by the lack of a CCM, whilst some diatom species abundant at times of higher δ<sup>13</sup>C<sub>POC</sub> may employ CCMs. These short-lived yet pronounced negative δ<sup>13</sup>C<sub>POC</sub> excursions drive a 4 ‰ decrease in the seasonal average δ<sup>13</sup>C<sub>POC</sub> signal, which is transferred to sediment traps and core-top sediments and consequently has the potential for preservation in the sedimentary record. This 4 ‰ difference between seasons of contrasting sea ice conditions and upper water column stratification matches the full amplitude of glacial-interglacial Southern Ocean δ<sup>13</sup>C<sub>POC</sub> variability and, as such, we invoke phytoplankton species changes as a potentially important factor influencing sedimentary δ<sup>13</sup>C<sub>POC</sub>. We also find significantly higher δ<sup>13</sup>C<sub>POC</sub> in sea ice than surface waters, consistent with autotrophic carbon fixation in a semi-closed environment and possible contributions from post-production degradation, biological utilisation of HCO<sub>3</sub><sup>−</sup> and production of exopolymeric substances. This study demonstrates the importance of surface water diatom speciation effects and isotopically heavy sea ice-derived material for δ<sup>13</sup>C<sub>POC</sub> in Antarctic coastal environments and underlying sediments, with consequences for the utility of diatom-based δ<sup>13</sup>C<sub>POC</sub> in the sedimentary record

Interlayer Coupling and p-wave Pairing in Strontium Ruthenate

On the basis of a three orbital model and an effective attractive interaction between electrons we investigate the possible superconducting states, with $p$ and $f$-wave internal symmetry, of Sr$_2$RuO$_4$. For an orbital dependent interaction which acts between in plane and out of plane nearest neighbour Ruthenium atoms we find a state for which the gap in the quasi-particle spectra has a line node on the $\alpha$ and $\beta$ sheets of the Fermi Surface, but it is complex with no nodes on the $\gamma$-sheet. We show that this state is consistent with all the available experimental data. In particular, we present the results of our calculations of the specific heat and penetration depth as functions of the temperature.Comment: 4 pages, 5 figure